The Empire of Chance: How Probability Changed Science and Everyday Life [1 ed.] 9780521331159
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Table of contents :
The Empire of Chance
Title Page
Contents
Acknowledgements
Introduction
1
2
3
4
5
6
7
8
References
Name Index
Subject Index
Review
Citation preview
The Empire of Chance
The Empire of Chance
I n t r o d u c t i o n
F o r t u n a ,
t h e
favorite
o f
learning, w a r n s s h e
fickle,
p h i l o s o p h y
B o e t h i u s '
that
o n l y
truthful,"
c e i v e d
w h e e l - t o t i n g
as
s e q u e n c e
o f
u p h e a v a l s
a n d
F o r t u n a
e v e n t
s c i e n c e
s c i e n c e
p h y s i o l o g y , sciences.
Paris
B e r n a r d
F o r t u n a
T h e
l a w s
o f
" t a m i n g
c h a n c e , "
in
statistics
h a d
b e g i n n i n g s t h e
t o
physics,
tical
( a n d
m a r c h
w a s
t o
p r o b a b i l i t y identity
w i t h
Scientia
a n d
t o
m a t t e r s
t h e o r y .
t h e o r y
n o t
P e r h a p s
has
h a d
its applications.
m a t h e m a t i c a l
t h e
e v o c a t i v e
phrase,
p r o b a b i l i t y
a
arch-rival
in
p r o b l e m s
s i m p l e
t h e
a n d
a n y
until
there
1 9 3 3
X l l l
(see
t h e
t h e
A t h e n s
at
o f
least
a n d
o n e
in
t h e
t h e o r y
t h e r e
B u t o f
part
i n t i m a c y
w a s
arguably
B y
p r o b a b i l i t y
a n d
F r o m
its
s p r e a d
j u r i s p r u d e n c e ,
o f
a n d
f r o m
statistics.
t o
i n n u m e r a b l e
o t h e r
3.6),
e m p i r e
n i n e t e e n t h ,
t w e n t i e t h .
r e l a t i o n s h i p
I n d e e d ,
f r o m
t h e
a n d
t o
a c c u m u l a t i o n
t h a n
D e s p i t e
F o r t u n a .
p r o b a b i l i t y
baseball,
m o r e
g r o w i n g t h e o r y
in
a n y
i n d e t e r m i n i s m
p r o b a b i l i t y
p s y c h o l o g y
practical)
allies.
is
c o n -
w i t h o u t
s h a r e d
a n d
a n d
c e n t u r y ,
P h i l o s o p h y
c h a n c e .
c h a n c e
h e r
a
m e d i e v a l
c h a n c e ,
a n d
t h e y
insurance,
testing,
m o t i o n
b e e n
c h a n g e a b l e ,
o f
B e r n a r d ,
t o
m e d i c a l
e x i s t e n c e
s e p a r a t i n g
g a m b l i n g a n d
a n d
illustrious
large
o f
D a m e
u n s t a b l e
n o t
n e v e r
t o u c h s t o n e
m i l l e n n i a
a
H a c k i n g ' s
f r o m
h a d
b a n i s h
w e r e
has
s o b e r
v e r y
causes,
r u l e d
i n f e r e n c e ,
e m p h a t i c a l l y
m a t h e m a t i c a l
t o
r e a l m
Ian
b i o l o g y ,
s o
a b o u t
already
c e n t u r y
p o l l i n g , n o t
C l a u d e
s o u g h t
t h e
t w o
m i d - s e v e n t e e n t h
i n d u c t i v e
a g r o n o m y ,
o f
t h e
e i g h t e e n t h
analysis,
w a s
r e c o n c i l e d
in
o f
that
r a n d o m
o v e r
faith: as
b y
in
article
e v e n
t h e
P h i l o s o p h y
t h e
I n
c h a n c e ,
h e r s e l f
D a m e
f r o m
Y e t
against
the
o f
Philosophy,
" s h o w s
p r o d u c e d
A r i s t o t l e o f
sciences. of
p r e a c h e s
causes."
in
t h e
Consolations
w h e n
"an
a n d
g o d d e s s
data
s o c i o l o g y , a n d
o n
o t h e r
this
t r i u m p h a l
until
b y
a
m a t h e m a t i c s ,
b o r d e r i n g n o
t o
p r a c -
applications o f
in
"pure" t h e
early
u p o n t h e o r y n i n e -
Introduction
XIV
t e e n t h (see
century,
1.5).
T h i s
F o r
as
b e c a m e deaths,
t o o l
v e r y
tainty
in
t h e
m i n d
W h e n
t h e
British
analysis
o f
e d u c a t i o n a l a n d
s o
It
in
t o
a
p e a s
in
fact
t h e
n o r m a l
bility o f
o r
moyen
in
e r r o r
s o c i o l o g y ,
c u r v e
r e p r e s e n t
c a m e
t o
intelligence p r e t a t i o n s c e n t u r y
q u o t i e n t s d e r i v e d
s u c h
b o o k
science
a n d
tistics
in
stock,
e u g e n i c s
a n d
o f cer-
2.2).
m e a s u r i n g
h e
h a s
o f
(see
o f
analysis
w e l l
t h e s e
l a u n c h e d
its
r o o t s
in
a g r o n o m y ,
agricultural
in B.
t h e
t h e
is
b e e n p r o f o u n d as o f
sciences. has
p r o b a b i l i t y
p i e c e m e a l .
e x p a n d e d alliance.
a n d
b y I n
A l s o ,
as
b o o k ,
m i n d ,
b e e n
d o m a i n
o f
c o n q u e s t w e
this
by,
v i e w
has
these
b e e n
O u r
t h e
sense: T h e
L.
A .
p r i m a r y a n d
statrans-
s t r u c t u r e
b u r e a u c r a c y significance
p e r h a p s until a n d
t o
a d m i r -
T h e s e
a n d
r e v o l u t i o n
a
a n d
objects.
m o d e r n
probability
a n d
its
has
inter-
it
T o d h u n t e r ,
r a n g e
f r o m
special
c h a n g i n g
sciences
n o r m a l
statistics
society.
s h a p e d
e x -
a l m o s t
p r o b a b i l i t y
a n d
f r o m
a n o t h e r .
a n d
appreciated,
v a r i o u s
for
S c h n e i d e r .
h o w
e x t r a o r d i n a r y
t h e
t h e
I v o
analyze
h a v e
in
Isaac
t h e
w h i c h
t o
statistics
w i d e - r a n g i n g ,
rarely
decisive this
scholars
T h e y
T h e
o n
a n d
p r o b a -
particular
o v e r
s h a p e d
t h e
v i v i d
m o l e c u l e s
B u t
p r o b a b i l i t y
also
nature,
k n o w l e d g e .
m o d e r n
o f
o f
t h e
discipline
o f
e v e r y t h i n g ,
8.1).
u n d e r s t o o d
w a s
W e
s h e d
o n e o f
g a s
a l m o s t
(see
Stigler, a n d
theirs.
ideas
is
s u c h
S t e p h e n
o f
origi-
"errors"
5.6). E v e n t u a l l y
b r i d g e s
p r o b a b i l i t y
o f
n o t
o u r
b u t
o f
w o r k
t r a n s f o r m a t i o n s
a n d
f r o m
nature's
t h e
a p p l i c a t i o n s
s h a p e d ,
S h e y n i n ,
2.5;
t o
s t r e n g t h
r e p r e s e n t e d
o f
yields, a n d
w e r e
t h e
i n d i v i d u a l
applications
p a s s e d
d e v e l o p m e n t
as w e l l
o f t e n
early
t e c h n i q u e s
o n
first
t h e n
d i s t r i b u t i o n
"application"
h a v e
o n l y
(see
w h e r e
i n f l u e n c e
s t u d i e d
t h e
at
anarchic
life,
t r a n s f o r m e d
as
o f
a n d
a d v a n c e
in a s t r o n o m y ,
a n a l o g i e s
t o o l
ideas
c u r v e
p r o p e r t i e s
n o t i o n s
h o w e v e r ,
o f p o w e r
t o
t h e
O .
f o r m a t i o n s
a n d
a b o u t
treated
c o n c e r n ,
probabilistic
is
m a t h e m a t i c a l
tration
variance
births, k i n d s
w o r l d
a w a y
c o n -
probability
a d e g r e e
t h e
p a r e n t
its
o t h e r
f r o m
in
F a c t o r
b y
a b o u t
a n d
i n v e n t e d
their
4.4).
o f
t h e n
its
c o n c r e t e
m a t h e m a t i c a l
M a i s t r o v ,
t o
f r o m
probabilistic
T h i s
less
f r o m
2.5;
letters,
itself
applications.
e x a m p l e ,
c h a n g e d ,
G a l t o n
b e l l - s h a p e d
collective
t h e
(see
for
h i b i t i n g o r d e r l y
o f
Francis
its
n u m b e r s
c o u n t e d
t h e o r y
m o d i f i e d
for o f
t h e
was
m u c h
d e a d
e v e n t s
c o n t e x t s ,
o b s e r v a t i o n a l
I'homme
as
o f
analysis
rule
analogies. T h e
ably
as
W h e n ,
p r o b a b i l i t y
d e v i a t e d
c o r r e l a t i o n s
t h e o r y
c o m p i l a t i o n s
o f
p o l y m a t h
specific
t h e
i n v a d e d .
ratio
p s y c h o l o g y ,
w a s
fluctuations,
m e a n i n g
h i g h l y
o t h e r
t h r e a t e n e d
o n .
w a s
n a t e
it
t h e o r y
e v a l u a t i n g
o f f s p r i n g
a p p l i c a t i o n
its history, p r o b a b i l i t y
b a r o m e t r i c
the
t h e
a n
p r o b a b i l i t y
for
crimes,
m u c h
o f
disciplines
statistics,
h o w
o f
that
t h e
a
failure
m u c h
m e a n s
q u e s t s
t h e
b e c a u s e
n o w
b e e n
statistics t h a n
t r a n s f o r m a t i o n s
b y
w a s infil-
s y n o p -
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x v
Introduction
tically,
as
t h o u g h t
a single a n d
T h e s e case
historical
life
is
s e c o n d
e n c o u n t e r s
b e e n
neutral
l a n g u a g e
o f
-
o f
t h e
t h e
m i n d
p r o p e r
trade,
(see
u s e
o f
t h e
results
statistics
b u t
o f
N o t e v e n
also
e x t e n t
T h e s e
h a v e
w h i c h
strands
B e l g i a n
are
s t a t e m e n t s p l a y e d
h o w
w i t h
W h e n
t h e r a p y
(see
T h i s
b o o k
is a
s t u d y
o v e r
a o f
t h e b y t h e
r e l e v a n c e
o f
W h a t e v e r
are in
as
o p p o s e d
t h e
a n d
trans-
i m p l i e d
2.3; 4.2; 7.3).
t r a n s f o r m ,
at
as m o d e l s
M e n d e l i a n s
o n l y
t h e
statistics
physicians
n o t
n o
i n t o
has
biological i n h e r i t a n c e
d o u b t e d
be,
s o c i o l o g y ,
c h a n c e , t h e
causality,
d e t e r m i n i s m
t h e
t h e m s e l v e s
t h e
o f a n d
(see
a n d
interactive
b o n d s o n
e x a m p l e , b u t
in
l i n k i n g t h e
a n d
b i o l o g y
p h i l o s o p h i c a l
t w e n t i e t h - c e n t u r y
t h e
issues
this
b o o k .
physicist
J a m e s
o u r as
(see
m o s t
lapi-
4.3). T h i s
o f
b o o k
probabilistic
in
n i n e t e e n t h -
m o s t
p h y s i c s
2.6;
" a b s e n c e
a n d
statistics
t h e
inference.
in
u s
(see
-
p r o b -
raising
their w o r k
c h a n c e
w i t h
o f
e x a m p l e ,
t h e m e s
g a v e
8.3);
p a i r e d
for
British
Laplace
n u m b e r s
i n f l u e n c e s
will in
c o n t e x t :
w a s
t o
e v i d e n c e ,
t h e
free
1.5;
set
p h i l o s o p h y ,
scientific
in e v o l u t i o n a r y
d e p e n d i n g
d e t e r m i n i s m ,
w i t h
issue
b e
C o n s i d e r ,
p e r m e a t e
B e r n o u l l i
role
ideas.
Q u e t e l e t
t h e
c a n
i m p o r t a n t
e x p l a n a t i o n ,
t o g e t h e r
w i t h
for
h o w e v e r ,
m o s t
c h a n c e
A d o l p h e
s u p p l e
c e n t u r y
it
i n e x o r a b l e i m p l i e s
t h e
i n d e t e r m i n i s m . e m p i r e
c o m p a s s
o f
h a u s t i v e
t o u r
d e s c r i b e
t h e
a
o f
c h a n c e
single o f
o r i g i n s
c h a n g i n g t o w a r d s
all, a g a i n , i n
is
t o o
v o l u m e .
a n d t o
for at
b e g i n
d e v e l o p m e n t
t h e
e n d
d e t e r m i n i s m , c o n t e x t
a i m
W e
i n t e r p r e t a t i o n s
t h e
vast
W e
its d o m a i n s .
t h e m i d - s e v e n t e e n t h
-
will,
a s e m i n a l
c o u l d
t u d e s
i m p a c t
t e c h n i q u e s
w a r r e d
qualitative o f
b r a i d e d
o f
n o t i o n s
d u c e
o f
probabilists J a k o b
d o c u m e n t s
T h e
S o m e
g r a p p l e d
dary
strictest
o f
statistician
t h e
o f
u l t i m a t e
in
has e n t e r e d
t h e
statistics
n o t i o n s
i n v o l v e d
free
5.6);
b r a n d
the
process.
discussions
M a x w e l l
d e s i g n "
o f
probability
s a m e
m o d e r n
h a v e
m e t h o d s
i n f e r e n c e
A A ) .
t h e y
science
ideas a n d
t h e
o n
e n d e a v o r .
a d o p t e d
o f
(see
trials,
a n d
t h e
sciences.
ideas t o
t o v i e w
w i t h
w h e n
o f theories,
issue
scientific
e x t a n t
E v e n
influence
quantification.
d e t e r m i n i s m ,
C l e r k
in
o f
t h e v i e w
ethics
p r o b a b i l i t y
t h e
abilistic
T h e
t h e
all i m p o r t a n t
in
at
clinical
t r a n s f o r m e d
effects
w a s
o f
statistics
b i o m e t r i c i a n s
t o g e n e t i c s ,
w h o s e
area
p s y c h o l o g i s t s
6.4). W h e n
t o u c h ,
o f t e n
o f
W h e n
r a n d o m i z e d
t h e y
t h a n
o n e
a n d
probability.
rather
-
o t h e r
t h e y also c a m e
a p p r o a c h
P e a r s o n i a n
n o
translations
mathematical
t e c h n i q u e .
t o o l o f
t o
probability
m e r e
the level o f m e t h o d s c e n d e d
m o v e m e n t
o f
o f t h e o f
t h e
c h a n g i n g c h a n g i n g
u s a
m a p
in
its
c o m p r e h e n s i v e ,
w i t h o f
t o
t w o
in
t h e
b u t
a n
e x -
historical
p r o b a b i l i t y
a n d
n i n e t e e n t h
century.
p r o b a b i l i t y
calculus,
c o n c e p t i o n s
entirety
o f
applications.
c h a p t e r s statistics
H e r e
e a c h
o f
that f r o m
w e
i n t r o -
c h a n g i n g
a v e r a g e s
I n
n o t
atti-
a n d
errors
t h e
s u b s e -
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Introduction
XVI
q u e n t
f o u r
m e n t a l
chapters,
m e t h o d o l o g y ,
n o t
s i m p l y
b u t
t o
t o
list
e x a m i n e t o
assess
i m p a c t
t h e
r e p o r t s
t o
s u c h
k e y
p o i n t s
o f
h a v e
applications d i v e r s e
as
h a v e
legal
s o m e t h i n g
fairness
like
t h e
a n d
o u r
o r
lay
v a l u e s
h u m a n
v i c t o r i o u s
has
a n d
w e
daily
c l a i m
t o
a l o n e
a n d
leave
w o u l d
h o w
intelligence.
t h e
sciences
f r o m
Finally, t h e
s t u d y
v o l u m e s .
if quietly,
a b o u t w e
t o
w e a t h e r
r e q u i r e
d e e p l y ,
hilltop,
fields,
e x h a u s t i v e
a s s u m p t i o n s
general's
t h e s e
is
c o n s e q u e n c e s
life,
a n
e x p e r i -
o b j e c t i v e
e n t e r e d
o n
s h o w
O u r
c o n c e p t u a l
7,
n o
t h e m
that
application:
p s y c h o l o g y .
statistics
w e
instances
altered
a n d
b r o a d
c h a p t e r
c a t a l o g u e
s e l e c t e d
o f
p r o b a b i l i t y
W i t h
A g a i n ,
t o
area
c i r c u m s t a n c e s
p r o b a b i l i t y
-
o n e
physics,
applications.
m a m m o g r a p h y .
w e
o n
at w h i c h
historical
applications
R a t h e r ,
f o c u s
b i o l o g y ,
t h e
t h e
a t t e n d a n t
o f
w e
t h e s e
m a t t e r s
survey,
territory
as
f r o m
w e
h a v e
c o v e r e d . W e
e n v i s i o n
fields t o
a n d
as
b r o a d
i n t e r e s t e d
a m i n i m u m .
d u t y
a
T h e
a u d i e n c e
l a y m e n ,
h a n d f u l
is a b o o k
b y
several
h a n d s ,
story, w i t h
that
o v e r l a p
intersect,
T h e
p l o t
a n d
line
h o n o r
t h e s e
Fisher
in
z i g z a g s
b o u n d a r i e s
t h e
c h a p t e r
statistics
f r e e d o m
for
c o l l a b o r a t i o n o f
t h e
t o p i c
o f
a n y
single
o r in
r e q u i r e d a u t h o r . three.
light
its
c h a p t e r s
o f
( a n d
s t r e t c h e s c h a n c e , A s special p r o j e c t
that d o
a p p e a r
f r o m
technical d o
w e
n o t
all
t h e
a n d
rather
it:
b e g i n n i n g l o t t e r y
scholars
k n o w ,
c o n d i t i o n s .
disciplinary
entire
" T h e
A l l
six
a
m a n y
material
d o
d o u b l e
u s
a
i n
o u r
Bielefeld,
b y
all
R.
o f
o n
o f
t h e
us,
b o o k
o f
b e
t h e
R e p u b l i c
i d e n t i f i e d c o n -
narrative
that
e m p i r e
o f
p a g e .
y e a r - l o n g C e n t e r
o f
g r o u p . c o u n t e d
c o l l a b o r a t i o n t h e
re-
as w e
t h e
title
b y
t h e n
t h e
n o t
a
A
n a t u r e
o t h e r s
a n d o f
h a v e
o f
c o m p e t e n c e
h o p e ,
w i t h
A .
s o c i o l o g y .
t h e
t h e
n o t
i m p l i c a t i o n s
p l a n n e d
W e
at
d i d
e x p e r i m e n t a l
in
o n e
subjects
m e m b e r s
F e d e r a l
as
will, w e
w o r k ,
R e v o l u t i o n "
t h e
m e m b e r s
w h o l e h e a r t e d
w e r e
refrain.
m e e t
o n
e x c e e d s
w a s
n a m e s
a
interdisciplinary
rather p r e s e n t
D u t i f u l
like
e x a m p l e ,
W e
e p i s o d e s
F o r t u n a
t h o s e
d r a f t e d
b y
a n t h o l o g y .
reappear,
-
w e l l
w e a k n e s s e s .
b u t
o r d e r
Probabilistic
S t u d i e s
that
o f interests
e n d .
s u c h o f
a n d
c o l l a b o r a t i v e
t o t o
s c o p e
w e r e
its
in
as
d i s c u s s i o n
t h a n
for
as
m a n u s c r i p t
a diversity
a
o n
c h a p t e r s
a n o t h e r
p h y s i c s
t h e
a n
r e p e a t
d e b a t e s o v e r
k n o w l e d g e
original a u t h o r s ,
u s e d
in
b e c a u s e
S o m e
c o n c e i v e )
f r o m
will
that
will,
w e l l
t h e
o f
t o
r e a d e r as
m e a n s
a p p e a r a n d
discipline t h e
n o
t h e m e s
e n c o u n t e r
criticism
their
it is b y
a n d
a r a n g e
reflect
b u t
p s y c h o l o g y
o f
B u t
s t r e n g t h s
b y
o n e
essential
its c o n t e n t s
c e i v e d
k e p t
c o m m o n
a n d
b i o l o g y ,
w a s
e v e n
a n d
-
o n
a n d
a m o n g
scholars
t h e r e f o r e
characters w h o
f r o m
m e t h o d o l o g y
T h a t
h a v e
o f e q u a t i o n s
tell a c o n t i n u o u s
v i s e d
a n d
b o t h
e x p l a n a t i o n s .
T h i s
t w o
c o m p r i s i n g
r e q u i r e s research
for
Inter-
G e r m a n y .
Essays
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Introduction
w r i t t e n
b y
D a s t o n , eds.,
a n d
1 9 8 7 )
r a n g e
o f
d e n s e
that
n a t i o n s ,
c o n n e c t
narrative,
p r e l i m i n a r y
a b o v e ,
W e
as f r o m
( 1 9 8 8 ) .
W e n o t
also
a d d r e s s e d
in
w h e e l
t a t i o n
turns:
flip-flop
w i t h
a n d o f w e
that
as
see
n o
is
t h e
that
o n l y
p h y s i c s
says,
c h a n g e , o f
" b u r y
F o r t u n a ' s
t h e
this
study.
e m p i r e s
e m p i r e
o f
will
c o n -
i n t o
t h e
a n d
a
i n t e n s e
u p o n
still
o u r
g r e a t e r
w i t h
o u r
m e n t i o n e d
f o r t h c o m i n g ) ,
T h e o d o r e
P o r t e r
L o r r a i n e
research
b u t
twists,
O u r
s t o r y
D a s t o n
o n
crucial
s u b t l e Y e t
also h e r
o w n .
t u r n a b o u t s ,
a n d
c o n f o u n d s
f r o m
strange
a n d
t o
statistical
b u i l d
( 1 9 7 5 ;
m e n ,
c h a n c e .
b o t h
w i d e
literature.
b o r r o w i n g
w i t h
a n d
collections
original
a
essays
d i s c u s s i o n s
t h e
ironic itself.
M o r g a n ,
h o p e d
d e m a n d
( 1 9 8 6 ) ,
fates
a n d
t o p e r p e t u a t e
( 1 9 8 7 ) ,
m u c h
(Kriiger,
across
probabilistic
H a c k i n g
o p p o s i t e s ;
m e c h a n i s m a n d
o n
scholarly
m a n y
their
l e i t m o t i f
as G i b b o n s i g n
as
find
i n t o
o r
o f
six
that w o u l d
Stigler
p r o b a b i l i t y
w e
" c h a n g e a b l e , "
e n d u r i n g ,
f o r t u n e ,
o f
m e a n i n g s
d e t e r m i n i s m ,
F o r t u n a
n o t
Ian
t o p i c
t h e s e
m a n y
M u r r a y
e x i s t i n g
c o n t a i n
as
m a n y
results
g o v e r n e d
o u r
b y
S t e p h e n
t h e t h e
t o
v o l u m e s
o f
w o u l d
b o o k s
D a v i d
o f
a p r o j e c t that
t h e
i n
also h o p e d
heavily
a n d
o f
s u b s e t
g r o w t h
d r a w n
( 1 9 8 1 ) ,
i m p r o b a b i l i t i e s
that
r e c e n t
G i g e r e n z e r
b i o g r a p h i e s
at
a d d i t i o n
h a v e
i n c l u d e
F o r t u n a ' s
o n e
O u r
thick
G i g e r e n z e r ,
c o n t a i n e d
year w i t h
I n
M a c K e n z i e G e r d
F e w
p e r s p e c t i v e .
c o l l e a g u e s , w e
( 1 9 8 6 ) ,
t o p i c s
the
a n d
t w o
K r i i g e r ,
centuries.
v i e w e d
B i e l e f e l d
fill
i m p o r t a n c e
e l e m e n t s
that
efforts.
n o w
1 9 8 7 ;
t h e
a n d
c o n s e n s u s ,
as w e l l
D o n a l d
o n e
t h e
c o l l a b o r a t i v e
project
eds.,
t h e
a u n i f i e d
collegiality o f
B i e l e f e l d
this
d e m o n s t r a t e
fields,
f r o m
in
H e i d e l b e r g e r ,
a n d
single ideas
participants
xvtt
s o c i o l o g y ;
pairings
o f
d r a m a t i c ,
w h e r e a s
t h e
a
t u r n
o f
s c o r n e d e p i s o d i c
vicissitudes
cities in a c o m m o n
suffer
w o r d s
probability
P h i l o s o p h y a n d
e x p e c -
t h e
g r a v e , " w h e e l .
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" S 3 F o r t u n a T h e
s l o w
P e t r a r c h , t h e
(left)
a n d
S a p i e n t i a
b r e a k d o w n Remede
B i b l i o t h e q u e
de
I'un
o f et
( r i g h t )
this Vautre
N a t i o n a l e ,
a r e
d e p i c t e d
o p p o s i t i o n fortune
prospere
is
t h e et
h e r e
i n
t o p i c
adverse
t r a d i t i o n a l o f
(Paris,
t h i s
o p p o s i t i o n .
b o o k .
1 5 2 4 ) ;
S o u r c e :
c o u r t e s y
Paris.
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o f
G o d
. . .
that
state
here.
has afforded o f
us only
mediocrity
a n d
the
twilight
o f probability;
probationership
h e
has
suitable, I p r e s u m e ,
b e e n
pleased
t o
place
to
us
in
. . J o h n
Locke
(1690)
1
Classical
probabilities,
1 . 1
I n
J u l y
o f
p r o b l e m
1 6 5 4
w h i c h
c a m e
a r e i n t e r r u p t e d t h a t
p o i n t .
d e n c e
a t t e m p t
H o w
in
t o
1, p p .
i n c l u d e d
a m o n g
t h e
d a m n e d .
d i c t a t e s t h e
t h e
3 3 - 7 ;
p a y - o f f
t w o
u n c e r t a i n
o f
s t a k e
h o w
e v e n
c.
1 5 2 5 ]
bliss
m a k e
f o r
t h e
b u t
p r o s p e c t
it
t h e
a n d t h a t
m e r e l y
o f salvation
o f
f o u n d i n g first 1 9 7 0 ,
later,
Pascal
c o n v e r t
s p o r t -
G o d ' s
rational
e x i s t e n c e , m i s e r y
for
self-interest
w o r l d l y
(Pascal,
t h e
[ 1 6 5 4 ]
infinite
finite
at
c o r r e s p o n -
n o t
y e a r s t o
p l a y e r s
u n e v e n
t h e
(Pascal,
o d d s
s a v e d
T w o
w a s
S o m e
g a m b l i n g
s c o r e
as
d e s i g n e d
Pascal a r g u e d
c e r t a i n
t h e
c o u n t s
1 9 6 6 ) .
a
e n s u i n g
t h o u g h
w a g e r
a b o u t
P o i n t s :
T h e
m a t h e m a t i c a l l y
c o n d i t i o n s ,
infinite
o f
c h a n c e , w i t h
d i v i d e d ?
s m a l l w e
o u r
P r o b l e m
o f
i m a g i n a r y
infinite
F e r m a t
m a t h e m a t i c i a n s
[ c o m p .
m a t t e r
sacrifice
t h e
b e
c h a n c e
a n
b u t
as
P i e r r e
p r o b a b i l i t y ,
h i s Pensees
s u c h
t o
a g a m e
F r e n c h
C a r d a n o ,
U n d e r w e
o f
t h e
g a m e s
n o
w r o t e
k n o w n
m i d s t
is i n f i n i t e ;
t h a t
b e
s h o u l d
t r e a t
t h e
Pascal
t o
t h e
I N T R O D U C T I O N
m a t h e m a t i c a l
i n g l i b e r t i n e s :
t o
i n
b e t w e e n
d o c u m e n t
vol.
Blaise
1 6 6 0 - 1 8 4 0
p l e a s u r e s
[ 1 6 6 9 ]
1 9 6 2 ,
p p .
1 8 7 - 9 0 ) . T h e s e o t h e r
t w o
f a m o u s
p h i l o s o p h i c a l ,
p r o b a b i l i t y . m e n t s
o f
d o n e d
t h e
It
Pascal
r e v e a l
e m e r g e d
at
s e v e n t e e n t h
t r a d i t i o n a l
ideals
fruitful
a t t e m p t
t o
N e i t h e r
w o u l d
h a v e
m a n u s c r i p t s ,
t h e
d o u b l e
t h e
c r u x
c e n t u r y : o f
a p p l y b e e n
r o o t
o f a
t w o
n e w
c e r t a i n t y ;
m a t h e m a t i c s sufficient
t h e o f
o n e t h e
m a t h e m a t i c a l m a t h e m a t i c a l
i m p o r t a n t
p r a g m a t i c
a n d t o
a
w i t h o u t
r a t i o n a l i t y
t h a t
t h e o f
m o v e a b a n -
a n d
r e m a r k a b l y
o f
e x p e r i e n c e .
d o m a i n s t h e
t h e o r y
intellectual
s u s t a i n e d
n e w
a n d
o t h e r .
P h i l o s o p h i c a l
1
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2
Classical
n o t i o n s
a b o u t
d e g r e e s
o f
antiquity, t o
w h a t
certainty as d o
q u a n t i f y
T h i s
o f
w a s
an
t h e s e
particularly
h a v e
true
scholarly o u r
lations
o f
p r o b a b i l i t y
m e d i e v a l
a n d
h a p p e n s
called
m a n u s c r i p t , dice
a
m a t h e m a t i c s
a b o u t
w h e n
p a n d e d b o o m
it
d i d
rapidly o f
t h e
p r i c i n g
o n
i n f l u e n c e d 1 9 8 7 ) .
t h e
N o r
ticians; o n
Italy
t h e
1 9 5 6 ;
H a c k i n g ,
t h e o r y ,
b u t
probability reverse
a n y
w e r e
tive a n d m e d i e v a l
o f
rhetorical
a b o u t
B.C.,
t h e
spirit
o f
m a t h e m a t i c a l
formalism.
o f
probabilities,
has s o
w h i c h
o f its
a
until
applications.
attracted
l o n g o f
C i c e r o
p p .
o v e r d u e . t h e
in
in
f r a g m e n t s
t h e
I n
classical
a
for
that
n o n e
t h e
o f
o f a n d
w h i c h
w r i t i n g s
t e n t h - c e n t u r y toss
probabilistically
Y e t
is
f o r m u -
his rhetorical
possibilities
r e a s o n e d
C h a n c e
earliest
c o n n e c t e d
8 5 - 9 0 ) .
1 9 7 3 ) .
c o n s i d e r a b l e
S u g g e s t i v e
b e l i e v e d
3 6
o f
t w o
a b o u t
t h e s e
in-
flowered
less
versa
m i g h t
o f
subjects
appear
stimulating T h e
t o
that o f w o r d s
that
t h e
f o l l o w e d
o f
later
Pierre
( K e n d a l l ,
m a t h e m a t i c s
in
o f
o f
p r o b a b i l i t y
t a n d e m , rather
w i t h
t h a n
the
s i g n a t u r e s
l i n k e d
that parallels t h e
o b j e c -
probabilities, b u t C i c e r o a n d h i m
-
D a s t o n ,
t h r o u g h
v e r s i o n s
d o c t r i n e
for
m a t h e m a -
p e r s u a s i o n
d e v e l o p e d
in a w a y
s e n s e s o f m a t h e m a t i c a l tradition
that
col-
basis
m u c h
t h e
Pascal
in c o m b i n a t o r i c s
R e n a i s s a n c e
n o t
1 9 7 4 ;
inspire
f r o m
earliest
h a v e
w o r k
[ 1 9 6 4 ]
strictest
t h e
d i d
-
e x -
c o m m e r c i a l
m a t h e m a t i c a l
c h a n c e
t h e
t h e
later
c a m e
i n s u r a n c e
insurers
w h o
s p e c u l a t e
for
a
( M a i s t r o v ,
early probabilists o f
d u r i n g b u t
d e v e l o p
r e c o g n i t i o n
O n e
1 8 6 5 ) .
centuries,
p r o b a b i l i t y
M a r i t i m e
C o u n t r i e s
m a t h e m a t i c i a n s vice
t h e
m a t h e m a t i c a l
i n s p e c t i o n .
L o w
m u c h
t h e
w h y
u p o n
t h e
n o t
t h i n g s w i t h
subjective
all
d e t e r m i n i s t s
o f t e n
( T o d h u n t e r ,
a t t e m p t e d
the
e v e r y w h e r e
I 9 6 0 ,
a p r e c o n d i t i o n
t w o
t h e o r y
85
s i x t e e n t h
n e w
1 9 7 5 ) .
w a s
t h e
e v i d e n c e
w a s
contrary,
Laplace
c o m b i n a t o r i c s
a n d
s h i p w r e c k s ,
d i d
w o u l d
i n d e p e n d e n t
a l m o s t
T a l m u d i s t s
a n d
It
o n e
f r o m
r e q u i r e s
e l e m e n t a r y .
u p
d i s s o l v e
insurers,
S i m o n
t h e
also
p r e m i u m s .
N o r
n o
d a t e
probability.
fifteenth
statistics
1 6 5 0 ,
m a t h e m a t i c s
w a s
h y p o t h e s e s
in
e x p e r i e n c e
v a r y i n g
q u a n t i f i c a t i o n
s e e m s
( R a b i n o v i t c h ,
o f
plausible
t h e
e n u m e r a t e d
p a t e r n i t y
it
is o r d i n a r i l y
a n d
t h e
for
p r o b a b i l i t y
( C i c e r o ,
1 9 5 6 ) ,
a n d
Several
lect
m o n k
( K e n d a l l ,
heritances i n t o
a
probabile
o u t
a b o u t
B E G I N N I N G S
A r o u n d
w h a t
circa
calculus
b e c a u s e
t u r n
c o r p u s :
w i t h
b o t h
d o
b e f o r e
e x i s t e n c e
a n d
a n d
unreliable
flesh
t h e
t h e o r y
t h i n k i n g
l e a r n e d
t o
m a t h e m a t i c a l p e r h a p s
t i m e ,
sufficed,
T H E
c o m p a n i o n ,
probabilistic
usually
o f
t h e
probability.
a l o n e
m a t h e m a t i c a l
a t t e n t i o n ,
c o n s t a n t
o f
for
o f
this
B u t
s e n s e s
1.2
p r e h i s t o r y
w i t h
interpretation
this c e n t u r y h a d n o
T h e
m o s t
o f c h a n c e .
e n t e r p r i s e
matter,
o n l y
c o n n e c t e d
g a m e s
a n y
m a t h e m a t i c a l subject
h a p p e n s
probabilities
h a d
d o n e
s o
l o n g
the
b e f o r e
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Classical
( H a c k i n g ,
1 9 7 5 ; G a r b e r
b l i n g
h a r d l y
n o t
w a s
h a v e
b e e n
q u a n t i t a t i v e bility
d i d
T h e clues,
o f
catalyst
o n e s .
It is, i n
c o m e
t h e
1 9 7 9 ) .
t h e
s e v e n t e e n t h
t r a n s f o r m e d
short,
o n
r e t u r n
t h e y
c o n c e p t
easier
s a n d
w a s o f
e x a m p l e ,
tickets
d e f i n i t i o n for
t o
t h e
t o
t h e
are
n o t
i n s t e a d
a n
cast
p a s s i o n
c e n t u r y ,
say w h e r e
t w o
for
g a m -
s o
c o u l d
a n d
probabilities
m a t h e m a t i c a l
in
e v e n t
e
a n d
t h e
e x p e c t a t i o n
implies,
w e
n o w
t o
b e
d o
i n t o
p r o b a -
s u p p l y
w e
called
d e f i n e d
o u t c o m e
as
v a l u e
s o m e
d i s c o v e r t h e
probabilities.
calculus
T h e
t h e
that
f u n d a -
p r o d u c t
o f
V:
E
s o m e o n e
h o l d i n g
a prize o f $ 1 0 , 0 0 0
d e r i v e
probabilists
o f
later
=
o f
m u s i n g s ,
c a m e
t e r m s
its
p r o b a b i l i t y
Pascal
e x p e c t a t i o n ,
f o r a fair l o t t e r y w i t h
early
t h e
qualitative
m a t h e m a t i c a l
P(e)V
for
Similarly,
t h e y are r e c o g n i z a b l y part o f w h a t
p r o b a b i l i t y
S o ,
3
f r o m .
I f w e
probabilities,
m e n t a l
o f
that
earliest w r i t i n g s
h o w e v e r .
a l t h o u g h
Zabell,
i n v e n t i o n
t h e
not
v e r y
a n
a n d
probabilities
e x p e c t a t i o n
e x p e c t a t i o n
t h e
o u t
w o u l d
f r o m
w a s
o n e
t h e
o f
a
t h o u -
b e $ 1 0 . A s
t h e
probability,
p r i o r
a n d
b u t
irreducible
n o t i o n . E x p e c t a t i o n tract. t o
Pascal
e a c h
his
o n
in
definition
o f
r e a d e r
as
e q u i t y
w e r e
fair
justice"
a n d
a n d
equal
physicist
that
in w h i c h
B u t
first
intuitively
clear
t o
ratiociniis
that
ludo
equity:
as
aleae m a d e
n o
a
e q u a l
fair g a m e
s e r v e
c o n -
p u b l i s h e d ( 1 6 5 7 ) ,
e q u a l
t o
o r
r e n d e r i n g
first
t h e
e x p e c t a t i o n e x p e c t a t i o n s
o n e ' s
later probabilists
g e n e r a t i o n t o
t h e
H u y g e n s
" w o r k e d
o f
P o i n t s
I n
in
o f
S i n c e
t e r m s
e n o u g h
o f
h i m .
players p o s s e s s e d in
t h e
P r o b l e m
t e r m s
6 0 ) .
expectations for
De
it in
p.
t h e
t h e
Christiaan
is, o n e
1 9 2 0 ,
in t e r m s o f a fair e x c h a n g e
b e l o n g e d
d e f i n e d
[ 1 6 5 7 ]
as o n e
t o
probability,
g a m e ;
circular.
d i s a d v a n -
w o u l d
define
e x p e c t a t i o n s ,
strikes
t h e
this
m o d e r n
o f
probabilists,
n o t i o n s
as
t h e
d e f i n i t i o n s
s t u f f
o f
o f
p o s t u l a t e s .
T h e s e c o m e
i n t u i t i o n s
increasingly
m e r c i a l
law,
e x c h a n g e
t h e
d r e w
u p o n
i m p o r t a n t
aleatory
p u r c h a s i n g
n e x t
year's
Pascal's
w a g e r
p r e s e n t
vices
a c q u i r e d o n e r a t i n g
a n
w h e a t
for
p r o m i n e n c e m e r c h a n t s
annuity,
u p o n
the
o f
s i x t e e n t h -
certain value
c r o p ,
h i n g e d
in
a c a t e g o r y
contract. Jurists
o f a p r e s e n t a n d
a g a m b l e , o n
a
( H u y g e n s ,
fair g a m e
a n d
"in
p o i n t
u n d e r s t o o d
his s o l u t i o n
m a t h e m a t i c a l
d e p a r t u r e
t a g e "
w h a t
m a t h e m a t i c i a n
o b t a i n e d
a
d e s c r i b e d
player
treatise D u t c h
in t u r n w a s
a n d w h o
a
a n d
o u t
b u y i n g
t h e
a
similar
trade
certain
m a d e
that
o f
n e x t o f
s u c h
a g r e e m e n t s
i n s u r a n c e cast t h e
o f
as
t h e
interest
a
c o m -
b i d d i n g net.
e n j o y m e n t
p r e f e r r e d
t h e
staking
fisherman's
A l e a t o r y
f r o m
b e -
as
-
policy,
certain
salvation.
n o t o r i e t y
loans w i t h
a n
h a d
s e v e n t e e n t h - c e n t u r y
d e f i n e d
o r
joy
a g r e e m e n t
for a future, uncertain o n e
t a k i n g
u n c e r t a i n
legal
o f
c o n t r a c t s w a y
c h a r g e s
o f
o f
e x -
u s u r y
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4
Classical
( C o u m e t , m o r a l
1 9 7 0 ) .
e q u i v a l e n t
as h o n e s t l y
as
p e t i t i o n e d
o n
loans, o n
o f
t h e
for
It w a s m e n t
o f
t o
prices,
f u t u r e
l a w
b e c o m e
o f
fold
t h e
s i x t e e n t h
a n d
C a t h o l i c s
S e x t u s
t h e
ideal
l o o k
H i s
-
bear
o f
h o w
w i t h
a
libertine w a g e r s
the
R e f o r m a t i o n
in
k n o w l e d g e
place
it w a s
p r e c i s i o n
o f
a d m i t s :
f r o m
m a t h e m a t i c i a n
r e a s o n i n g
b y
less
class
it is e v i d e n t l y a n d
revival
o f
b e t w e e n
t h e
ele-
p r o b a b i l i t y
stakes, d i d
a n n u i t y
s o
-
s e m i n a l
u s i n g
i n f l u e n c e
h a d
o f
t h e
t h i n g s
just
s o
a n as
t o a c c e p t
f r o m
a
i n q u i r y
since
d o c t r i n e b u t
that
m a i n t a i n e d m a n
in
p r e Ethics
e d u c a t e d t h e
m a n
n a t u r e
p r o b a b l e
rhetorician
I n
u n d e r m i n e
Nicomachean
o f far
t h e
p h i l o s o p h y
r e a s o n a b l e
m a r k
foolish
d e m a n d
m o d e s t
the
i n t o
P r o t e s t a n t s
t o
intellectual
f r o m
m i d -
certainties.
c o m b i n e d
t h e
h a d
t h e
b a c k
sceptical
k n o w l e d g e ,
t o g u i d e
is
led
b y
b e t w e e n
the
m o r e
certain
"it
o f
b e
t h e o l o g i c a l
g u i d e d a
e x p e c t a t i o n s
rationality
m u s t
other,
d i c t u m
equally
t o
o f
t h a n
the
t h a n
q u o t e d :
e a c h
b r a n d
e m e r g e d
Aristotle's
m u c h in
t h e
c o n t r o v e r s i e s
still s u f f i c i e n t
practice. w a s
that
gradually
inevitability that
probability
m a t h e m a t i c i a n s
t h e y
t o
rather
o n
its
t h e
w h i c h
i n t e r l o c u t o r
his s c h o o l
In
interest
is r e c e i v e d , "
that
w i t n e s s
3 0 %
special
2 8 9 ) .
g a m b l i n g
in
a
p r o p o r t i o n
w h a t
-
interest
for
a n d
early applications
n e w
a n d
certain
a
p.
a n d
t e r m s
E m p i r i c u s
subject a
t h e
t h e
o f
k e p t
a d d r e s s e d
e x a m p l e
century,
2 4 - 2 5 )
for
t h e
h a n d , a n d
a n d
( 1 0 9 4 b
all o f
equality
t h e
successfully
1 6 4 5
c h a r g i n g
t h e
contracts,
o n e
n o n e t h e l e s s c e p t
all
t h e
Aristotle. a c c e p t e d
t o
a n d
u n c e r t a i n
o n
w e r e
1 9 5 7 ,
d a n g e r
t h e y
s y n o n y m o u s
b y
is
his
T h u s Jesuits in
w a s
contracts.
a n
century.
t h e r e
b e t w e e n
-
w h o
lawyers,
m e r c h a n t
P r o p a g a n d a
( N o o n a n ,
e x p e c t a t i o n s
is
for
c a n o n
t h e
h a v e .
is c o n s i d e r e d
in a l m o s t
aleatory
a l m o s t
Christian
o f
e q u a l
w o u l d
that
r e c e i v e d "
t h e
e a r n e d
c o n v e r t s ,
"there
p r o b l e m s
w a g e r
s e v e n t e e n t h
b r o w
C h i n e s e
inheritances
o f
Pascal's
his
f u n d a m e n t a l
t h e
a r g u e d
t h e r e f o r e
p r o v i d e d
is
risk,
C o n g r e g a t i o n
q u a n t i f y
B o t h
c o n c e p t
o f
" p r o p o r t i o n
theory.
t h e
a n d
o f
a n d
c o n d i t i o n
e q u i t y
a t t e m p t e d
o f
s w e a t
w h a t
this
labor,
their
the
a n d
e l e m e n t
S a c r e d
d a n g e r ,
d a n g e r
o f
t h e
t h e
d i s p e n s a t i o n
t h e
T h e
probabilities
o f
t o t h e
r e a s o n i n g
d e m o n s t r a t i v e
p r o o f s . " T h e clashes a n d
o f
u l t i m a t e
result
o v e r
f u n d a m e n t a l
t h e
t h e
radical
t e e n t h - c e n t u r y
i m p a c t
w a s
m o r e
l e d g e
w h a t s o e v e r .
side's
claims
t o
t h e
w a s
o f
M i c h e l t o
d e
e r o d e
c h a l l e n g i n g
a p o l o g i s t s
o n
t h e
basis
C o u n t e r - R e f o r m a t i o n a n d
their
M o n t a i g n e t h e
reasoning.
s o u g h t either
t o t o
justification,
a n d
d o m a i n
all c l a i m s
w h o o f
a n d faith
that o f p r o b a b l e
d e v a s t a t i n g ,
l e g i t i m a c y
o f
vastly
t o e x p a n d
R e l i g i o u s
R e f o r m a t i o n principles
s c e p t i c i s m
t h i n k e r s
strative p r o o f a n d
o f
o f
o t h e r t h e
T h e i r
a n y
k i n d
u n d e r c u t
( a m b i g u o u s )
six-
d e m o n -
i m m e d i a t e o f t h e
k n o w o t h e r
r e v e l a t i o n
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Classical
o r
( d u b i o u s )
w e r e
a
a u t h o r i t y
d o u b l e - e d g e d
e r u d i t s "
d e n i e d
t h e
d e m o n s t r a t i o n s ; this
e x t r e m e
religious f r o n t e d m o s t
w i t h
p h i l o s o p h i c a l ,
O r
e d g e
( P o p k i n ,
t h e
t o
" m i t i g a t e d
c o n d u c t
l o n g e r
o f
t o
p r o s p e c t bare
i m p e l
t w o ,
o r
t w e e n t h e
certain
n e w
Pierre
in
e n o u g h
t h e
l i k e l i h o o d
p p .
3 5 2 - 3 ) .
p e c t a t i o n
p r e f e r r e d
W i l k i n s ,
L o n d o n ,
R u l e s
a n d
a r g u e d
in
a n d
o f
profit,
Principles
their A c t i o n s ,
m u s t
religion
( W i l k i n s ,
basis
belief,
o f
scepticism,
for
as
" h e all
[ 1 6 7 5 ]
t h e s e
t h e
R a t h e r ,
C o n -
a n d
o f
t h e
s e v e n p o s i t i o n
a n d
p e r h a p s
p r o b a b l e
w a s
k n o w l -
i n d e e d
k n o w l -
b a d
a n
Principles
w o u l d
m a n k i n d
w r i t e r s
t o p.
d o
d o 16).
w e r e
o b s e r v e
the
of
w a s
w o n t
e m p h a s i s k e y acidly
t o t o
that
1 9 6 5 , o f
the
R o y a l
e x -
s a m e . Society Religion
a l o n g
v o y a g e t o
g o v e r n m e n t o f science a c t i o n
d e f e n s e
o b s e r v e ,
is
also
Natural
u p o n t h e
it
b u t
a c c o r d i n g
t h e
a n d
[ 1 6 6 2 ]
w a s
o f
rational
itself,
like" in m a t t e r s
T h e
o f
rationality
o f
that
A r n a u l d
readers
idea
in
the
e x a m p l e
non
n e w
rationally,
n e i t h e r
b e -
is i n
Duties
a n d
relationship
N i c o l e ,
t h e
hazard
t h e
risk the perils o f
act
t h e
reverse,
t h e
m e n
o f
qua
a n d
c o n v i c t i o n
p r o d u c t
A n t o i n e
their
n o
m i s e r y
a sterling
m e m b e r and
t o
the
sine
b u t
f o u n d i n g
that
t h e
for
o r
the
o u t c o m e
( A r n a u l d
willing
bliss
a n d
the
o f
t o
w a s
r e a s o n a b l e
is a b o u t
infinite
t h u s
d i s c o u r s e
o f
r e c k o n i n g
c o l l e a g u e s
analogies,
w e r e
F o r
probable,
belief
d e g r e e
action.
a n d
m e r e l y
rational
c a u t i o n i n g
a n d
the
that
o f a g a m b l e ,
pass
the
o f
it is a b o u t
s p o k e s m e n
1 6 9 9 ,
t h a n
h a n d
n u m b e r
attain
Pascal's w a g e r
n o r
o r
t o
b e p e r s u a d e d
rather as
s o
t o
r e a s o n i n g
g o o d
Of
attack.
o n e
o f
certainty,
i n t e r m e d i a t e
for
c o m b i n e d
Logique,
D u t c h
his
u n d e r t h e
reverie
o f
p h i l o s o p h i c a l
rather
R o y a l
m i x e d
that just as m e r c h a n t s n a m e
P o r t
b i s h o p
sceptical
k n o w l e d g e
pay-off,
c o m m e r c i a l
A n g l i c a n
a
in t e r m s
it will c o m e
E n g l i s h
c o u l d
"libertins
m a t h e m a t i c a l
m a t h e m a t i c s
rarified
b u t
e x i s t e n c e ,
h o w
t h e
s o u r c e s
a n
in
criterion
u p o n
influential
that
o u t
o f affairs
u n c e r t a i n
c o n s i d e r
a
o n
respectability
e x p e c t a t i o n .
s u c h
w i t h
increasing
m e n
f r o m
m a n
Pascal's
m a d e
t o
the
respectively.
a n d
their
n o t
t h e
stake
an
e x c e p t
n e w
r e s t e d
c o n c e i v e d
a n d
a r g u m e n t s
1983).
T h e
G o d ' s
sinner,
N i c o l e
( 1 6 7 5 )
t u r n
rationality.
j u d g m e n t
J o h n
life.
i m p r e s s i o n s
carve
that
d e m o n s t r a t i o n ,
o f
significantly
t o
t u r n e d
o f g a i n , i.e. u p o n
saint
o t h e r ,
for
a p r u d e n t
in
p r o b a b i l i t y
awaits
in
sceptics"
o f
traditional
that p r o b a b l e
case
p y r r h o n i s m
d o g m a t i s m
certainty
S h a p i r o ,
daily
c o n v i c t i o n
o f
their
a w a t e r t i g h t
sufficient that
m a k e
t h e
d e s t r u c t i v e
s i m u l t a n e o u s l y
fideist
o n
insisted
1 9 6 4 ;
t h e
c a m e
still i n s i s t e d
t h e y
s e n s e
their
b e g a n
a t t e m p t e d
h o p e
y e t
rather,
order
t h e s e
all
a n d
e d g e .
o f
w r i t e r s
a b a n d o n e d
r e v i v e d
o f
b e t w e e n
s c e p t i c i s m
t e e n t h - c e n t u r y
In
all
5
that
Meditations
T h u s
a c h o i c e
m e t a p h y s i c s ,
T h e
reliability o f e v e n
variety.
a n d
d i s c o v e r e d
s w o r d .
D e s c a r t e s '
c o r r o s i v e
that
s o o n
probabilities
as
s u c h o f a n d t h e
against
e v e n
t h e
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6
Classical
m o s t
c o n f i r m e d
s c e p t i c
probabilities
t o o k
his
m e a l s
just
as
if
t h e
e x t e r n a l
w o r l d
e x i s t e d . E x p e c t a t i o n ness,"
as
e s t e d
it
in
w a s
w a s
o f
practice
a n d
t h a n
it m o n e y
t o
o f
o u r
a n d
s e n s e
o f
t h e o r y a t i o n
as a
tuitive T h e s o
S o
that
o f
w h e n
h a r m o n y ,
1 . 3
T h u s
t h e
calculus
trine
rationality
little
conjectandi
o f
b a c k g r o u n d . M o n t m o r t , N i c h o l a s
J a k o b
e n d
this
c o n c e p t ,
v o l v e
q u e s t i o n s
J u s t a n d
w h a t
r e m a i n s
"probability" 1 9 6 8 ) ; h e n c e
1 6 5 7
o f
m a t t e r h a d
o f
m e a n t
t h e J e s u i t
o f
t o p i c s
( J o h n t h e
n e w
p r o b a b i l i t y i n t e r p r e t o f
t h e
in-
m e n . w a s
it
w a s
p o s t u l a t e s
t o
t h e
c o h e r e
p r o b l e m s
o f
for
t o
s o m e
w a s
subject,
w a r r a n t e d
o f p r o b a b i l i s m ,
f r o m
definitive
Ars this
( H u y g e n s ,
Pierre
d e
D e
like
W i t t ,
t h e
e m e r g e d
w h i c h
o f
N i c h o l a s
for as
t h e a
n e w
distinct
c o n t i n u e d
t o
re-
thereafter. f r o m
O r i g i n a l l y b y
Halley,
e v a l u a t i o n
H o o p e r ,
t i m e
day.
d o c -
against
a m b i g u o u s
this
m o d e s t
applications
h a d
e x p e c -
o n l y
t h e applications
m e a s u r e d
o p i n i o n
m o r e
o f
s e v e n t e e n t h - c e n t u r y
Craig, G e o r g e
o f
calculus
( J o h a n n
p r o b a b i l i t y
c o n t r o v e r s y
in o n
that
d o m a i n
m o s t
a
n e w ,
g a m b l i n g
e x p e c t a t i o n
d o c t r i n e
t h e
o t h e r ,
a n d
Bernoulli's
annuities
p e r i o d ,
a n
t h e
w o r k s
evidentiary
a l t h o u g h
i n s t a n c e
J a k o b
like
a n d
t h e s e probabilities a
t o
a r a n g e
c o n s t i t u t e d
o f
t h e
a
legal
r e a s o n a b l e n e s s
w i t h
e v e r y w h e r e
p u b l i s h e d
later
t h e
r e a s o n a b l e
d e f i n i t i o n s
first
a l m o s t
t e s t i m o n y
a n d p r i m i t i v e a r o u n d
q u a n t i f y
a n d
m o n e y ,
c o d i f i c a t i o n
w i t h
-
I N T E R P R E T A T I O N
t o
B e r n o u l l i )
m o r e
classical
o f
g o o d
b e l o w .
a t t e m p t
o f
a c c e p t e d
q u a n t i f y i n g
t h e
clashed
a m e n d e d
c o n t r a c t s
c o u r t r o o m
t h e
o n e
t h e
first
in
-
t h e
i n d u l g e n c e
m a t h e m a t i c a l
t h e o r y
in
c o v e r e d
B e r n o u l l i )
B y
t h e
it w a s
o r
inter-
u p o n
q u a n t i f y
practice
w a s
T h e
Bernoulli),
a n d J a k o b
see
surfaces
A l e a t o r y
historical o r
t h e o r y .
that
t o
s t a m p e d
C L A S S I C A L
treatise
1 7 1 3 ,
o f
a n x i o u s l y
a n
discourse.
H u y g e n s '
results
shall
b e t w e e n
p r o b a b i l i t y
that
o n e
s e e k i n g
a n d
h e a v i l y
t h e
i n v o l v e d
belief
less
t h e o r y ,
u n c e r t a i n
that
w e r e
certain
as a m a t h e m a t i c a l
t h e
classical
c h a n c e
t h e r e b y
alliance
rationality
w e
o f
a n d
l e a r n e d
a n
" r e a s o n a b l e -
a p r e s e n t ,
scientific
future,
d r e w
s h o w
e x c h a n g e
b e c a m e
calculus";
T H E
tations, o f
o f
w h o
as
a
t o
o r
sceptics
t h e y
e x a m p l e s t o
rationality
b u t
M a t h e m a t i c i a n s
b e g a n
t h e
m a t h e m a t i c i a n s
for
for
u n d e r l y i n g
identification
belief,
inevitably
s t a n d a r d s
principles
r e s t o r e
-
salvation.
" r e a s o n a b l e
s t r o n g
t h e
p a s s i o n s
as well.
a n d
rational
n e w
m i t i g a t e d
a l o n g - a c c e p t e d
e x p e c t a t i o n s
rationality
t h e
T h e
r e a s o n a b l e
invest,
t h e o r y ,
t o
called.
c o n t r a c t s
t h e r e f o r e
b e
b e t t e r
in
aleatory
lusts
central
s o m e t i m e s
e q u i t y
d o c t r i n e
t h u s
t h e t h e
a u t h o r i t y
o u t s e t , w o r d ( B y r n e ,
casuists w i e l d e d
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t o
Classical
a b s o l v e
a l m o s t
a n o t h e r t h e
h a d
e v e r y
t a k e n
m i t i g a t e d
this
o f
n o t
o f
o n
levels
v a r i e d
o r d e r e d tainty,
scale, a n d
r e m a i n e d
standing
( 1 6 9 0 ) that
a
I n
t h e
b o t h
o f
o f
f r o m
a n d
practice
s e i z e d
d e g r e e s i n t o
a
o f
l i n g
(J.
o f
r e a s o n i n g
that
t h e
t o
j u d g e p p .
( f o r Ys
as
s e e m
in
m u c h
t h e
as
1 7 1 3 ,
fact
o f
that
o f
m e t h o d s : frequencies
in
e q u a l o f
s o m e
a n
s e v e n t e e n t h - c e n t u r y
w a s
a n cerveritate
b y
Under-
c l a i m e d t h e n
IV.i). as
a
t h e
in
repeat-
t o
disbelief
u n i m p e a c h a b l e
e x -
B e r n o u l l i t h e s e
o r d e r e d t o
o n
g r e a t e s t
m i g h t h a v e
fledg-
t h e
t h e
[ c o m p . w e r e
p o i n t s
t h e
o f
" a r i t h m e t i c
m a y
t h e
J a k o b
d e s c r i b e d
(Leibniz,
w i t n e s s )
t o
H o w e v e r ,
d o u b t
t h e a c c u s e d
T h e s e
2).
assurance
o f
h a n d ,
q u a n t i f y i n g
probabilities
a k i n d
at
c o u r t r o o m
translation
o f
s u b m i t t e d
o f a relative o f
o r
w a r r a n t e d
m u c h
t h r e e
L e i b n i z
d e g r e e s
legal
o f
t h e
m a t h e m a t i c a l
create
a n d
w o r d
x v - x v i ) .
c h a p t e r
as a m e a n s
I n d e e d ,
IV.
n u m e r o u s
1988,
t h e
e v i d e n c e
o w e d
L e i b n i z
total
t h e s e
t h e
a n d
o f
o p i n i o n
1 9 5 9 ,
c o n v e r t i n g
f r o m
that
legal
part c,
o f
1 7 0 5 ]
s o m e t i m e s o f
p r o o f
"
c o u n t
o n l y
m a d e
t h e m
tractable. w h o
set
a b o u t
n o n - a r b i t r a r y
possibilities
events;
d o i n g ,
fractions
m a t h e m a t i c i a n s
probabilities
as
( D a s t o n ,
e v i d e n c e
t e s t i m o n y
s u c h
De
B u t l e r
a n y
t o
[ 1 6 9 0 ]
c o n c e i v e d ,
p r o p o r t i o n e d
T h e
m a t h e m a t i c a l l y
T h e
( L o c k e ,
clear
r a n g i n g
o f
t h e s e
o f m o r a l
m e a n i n g
o f
p r o p o r t i o n e d
e v i d e n c e ,
in s o
k i n d s
t e r m s
e x a m p l e ,
legal
v e r y
s e n s e
hazards"
carefully
4 6 0 - 5 ) .
e x p r e s s e d
assent
probabilities
t h e
m e d i e v a l
"analysis o f
Bernoulli,
o f
Human
J o s e p h
o f life," h e
t h e
W i l h e l m
a n d
certainty
o f
G r o t i u s '
Concerning
B i s h o p
G o t t f r i e d
c o n t i n u u m ,
calculus
1 9 6 2 ,
n e w
certainty,
full
certainty
like
t h e
its
m a k e
o n l y
t h e
iii).
qualitatively o f
n o t i o n
H u g o
g r a d e
t h r o u g h
d e s c r i p t i o n s
a d m i t
Essay
v e r y g u i d e
t e s t i m o n y
analogies
u p o n
o f
h i g h e s t
" m o r a l "
t h e
e v e n
r e a s o n a b l e n e s s
t h e
t h e
b u t
f r o m
discussions,
f r o m
o f
l a n g u a g e
m a t h e m a t i c i a n s
p.
t h e s e
w e r e
a n d
t h e
t o
t h i n g s
L o c k e ' s
W h e n
f r o m
precise
a u t h o r ,
m o s t
o f
o r
H o w e v e r ,
m o d i f i e d
d e m o n s t r a t i o n , d o w n
literature
t o J o h n
are
a d e g r e e
t h i n g s
t h e
1 7 3 6 ,
probabilities
a m p l e s
o f
b y
t h e o l o g i a n
1 9 3 5 ) .
c e n t u r y
r a n g i n g
T h e
t o
that
( D e m a i n ,
p r o p o n e n t s
e v i d e n c e ,
thereafter.
o f
T h e
a t t a i n e d
a u t h o r
that o n e
s e v e n t e e n t h
certainties,
e m p h a s i s
a staple
g r o u n d s
m a t t e r
conjecture.
( 1 6 2 4 )
t o
a n d
o f
7
t h e
probability.
a n d
a n d
early
s e n s o r y
c h a n g e d
a u t h o r i t y
t h e
b u t
the
c o n t e x t
o f
certainty
( B u t l e r ,
"probability" b y
o f
"probabilities
cliche
v i e w
o f
slightly
christianae
i n g
t h e
t e s t i m o n y
religionis
1 7 3 6
m i l d
certainty
certainty
b a s e d
o n
s e n s e
" m a t h e m a t i c a l "
"physical"
t r a n s g r e s s i o n
s c e p t i c i s m
qualitative
s p o k e
a
probabilities
a n d
b a s e d
d e g r e e s
m e a n i n g s
o f
o f
f a s h i o n o n
trying c a m e
u p
physical
subjective
"probability,"
t o
w i t h
at
s y m m e t r y ;
certainty s u c h
m e a s u r e
o r
as t h e
least
t h e s e t h r e e
o b s e r v e d
belief.
( O t h e r
a p p e a r a n c e
o f
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8
Classical
t r u t h first
o r
t h e
w a s
t h e
s t r e n g t h
w e l l
s e c o n d
l o n g - t e r m i n g
a p p l i e d
o f
I n
t h e
six
f o r m e d
f e w
that
m o r e
detailed
a g e
at
w h a t
regular.)
d e m o g r a p h i c
data
p o r t i o n e d
t o e v i d e n c e
arose
w h a t
o f e v i d e n c e
w a s
t e s t i m o n y ,
o f
b o t h
Latter-day " W h a t b e e n I n
d o
probabilists
a
their
b o l d
line
o f probability,
"subjective"
sense,
o f
else; o f
p r o p o r t i o n -
a n d
legal
relative
d r a w n
w h i c h
"probability"
t o
w i t h
a n
a n d
c o r r e s p o n d s t o
i n s o u c i a n c e
m e a n that
m o r t a l i t y
s i x t e e n t h u s e d b y
w h o m
w a s
a n d
d e g r e e t h e
distinct,
t h e
in
o r d e r
t o
a r g u e p r o -
m u c h
o f
a n d
c o n v i c t i o n
probabilities
t o
t h e
a n d
o f
t h e
first
q u e s t i o n ,
m u c h
c o m p a t i b i l i t y
i n k
( N a g e l , t w o
o f
t h e w o r l d ,
t o
o f
m i n d .
states
Y e t
senses, shifting their
m o r e
has
1 9 5 5 ) .
" o b j e c t i v e "
t o states
b e w i l d e r s
a n d
j u d g m e n t .
a n s w e r s
all t h r e e
in-
belief
just h o w
t o
o f
a n d o f
o n
c o l l e c t e d
t h e o r y
s e n s e
t h e
m o r t a l i t y
age,
insurance,
that
after
a u t h o r s
p r o b a b i l i t y
w h a t
L o n d o n
b a s e d
at w h a t
a b o u t
a n d
a s s u m i n g
bills o f
in
c e n t u r y
t h e
t h e
table
w e r e
c o n d i t i o n s
( S i n c e
b e t w e e n
c o r r e s p o n d
a n d
d e c a d e
e p i s t e m i c
q u i t e
e q u i p r o b a b l e
e a c h
applications
as
s u g g e s t e d
d i e d
t o p r o d u c e
m e r i t s
is n o w
t h e
table
life
t h r e e
o f
f r o m
G r a u n t
t h e o r i e s
these
m e a s u r e ? "
u s e d
later
historical,
v i e w
w h i c h
killed
a n d
t h e s e
c a m e
G r a u n t ' s
enlisted
inspired
probabilists a n o t h e r
little
g a m b l i n g
satisfy
f r o m
2 9 - 3 0 ) .
a n d
r e q u i r e d a n d
f r o m
m o r t a l i t y
affairs.The
f r o m
c o u r t r o o m
a r g u i n g
particular,
third
j u d g e ,
probabilities
spilt
m e a n i n g s
t h e
a
a n d
h u m a n
m i n d
b u t
T h e
a s s u m p t i o n s
S e t s
E i g h t e e n t h - c e n t u r y
in
t h e
cities
diseases
p r o v i d e n c e
in
a n d
t h e o r y .
originally
d e a t h ,
annuities,
k i n d
dice
c o n t e x t s ,
situations
p p .
o f
d i v i n e
quantified.)
legal practice
p o p u l a t i o n
price
for
t h e
d e r i v e d
a n d
t h e
1 9 7 5 ,
n o t
w a s
o r
statistics
t r a d e s m a n J o h n
o f
[ 1 6 6 2 ]
m o r t a l i t y
t h e
o t h e r
parishes
a b o u t
c o i n s
d i f f e r e n t
f r e q u e n c i e s
fraction
g u e s s w o r k
f r o m
a p p r o x i m a t e
cause,
o f
s y m m e t r y
E n g l i s h
o n l y
like
m a t h e m a t i c a l
1 6 6 2
s a m e
c o m p u t e
t h e
b y
faith
t o
e m e r g e d
g a t h e r e d
t o
d e v i c e s
successfully
e v i d e n c e .
v e r y
t h e
n o t
third e c h o e d
t o
Statistical
( G r a u n t ,
r e g i s t e r e d
t h e
for
-
w e r e
c o l l e c t i o n
physical
m o r t a l i t y
r o u g h l y o f
o n
w a y .
data
o n w a r d s .
a g e
s e n s e s
b a s e d
a n o b v i o u s
t h e
certainty
t o g a m b l i n g
natality
o n
applications
o u t c o m e s
bills
o f
analogy,
g a m b l i n g
stability; a n d
v a r i o u s
d i f f e r e n t
t o
d e p e n d e d
d e g r e e s
T h e
s u i t e d
o f
probabilities
a n d
t h e
classical
f r o m
o n e
n i c e - m i n d e d
successors. W h y
w e r e
classical probabilists
o f p r o b a b i l i t y jective
a n d
s o
subjective
y a w n s
b e t w e e n
t e e n t h
a n d
v i c t i o n
easily, a n d
t h e m
s e n s e s in
s e v e n t e e n t h
f o r m e d
in
t h e
o f t e n
able
t o
v e r y
fruitfully?
w e r e
c u r r e n t
n o t
o f
t h e n
t h e
f o u n d j u d g e
it in
t h e s e
d i f f e r e n t
I n part,
s e p a r a t e d
p h i l o s o p h y .
c e n t u r i e s
m i n d
c o n f l a t e
Legal
plausible
b e c a u s e
b y
t h e
theorists t o
p r o p o r t i o n
t h e
t h e
o b -
c h a s m
that
o f
six-
a s s u m e t o
n o t i o n s
t h e that
c o n -
w e i g h t
o f
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Classical
t h e
e v i d e n c e
p r e s e n t e d ,
g e n e r a l
c o n t e x t ,
rational
m i n d
t h e
g r e a t e r
[ 1 6 9 0 ] t o
c o n n e c t
b e
t o
g r o u n d s vol.
t h e
First, p r e c e p t m i n d
i n v o k i n g
assents
1 9 5 9 ,
should
II, p.
t o
that
t h e
3 6 6 ) . a n d
qualitative
o n
least
actually
a s s u m p t i o n
probabilities
o n e
t w o
subjective
b e g u a r a n t e e d
it
t h e
" p r o p o r t i o n a b l y
A t
assent
9
r e p e a t e d
p r o b a b i l i t y
o b j e c t i v e h a d
L o c k e
a c l a i m
o f
a p p o r t i o n
s h o w n
a n d
probabilities
t o
side
t h e
o r
f u r t h e r
strict
d i d
so.
relation S e c o n d ,
o t h e r "
n o t
t h e
the
t h e o f
( L o c k e ,
w e r e
qualitative
t o
m o r e
e v i d e n c e :
e l e m e n t s
s e n s e s o f
a
p r e p o n d e r a n c y
t h e
in practice. It w a s
in
o f
in
r e q u i r e d
probabilities.
e n o u g h
e v i d e n c e ;
e v i d e n c e
that it
t h e
h a d
t o
t o
b e
h a d
q u a n t i f i e d . T h e
e m p i r i c i s t
p h i l o s o p h y - « 0 w - p s y c h o l o g y
e i g h t e e n t h
centuries
a n d
D a v i d
H u m e
that
m a d e
t h e
f r e q u e n c i e s
for
this
t o
a n
that
e v e r
past
t h e
vivacity o f
in
a n
rejected
t h e m o f
[ 1 7 3 9 ]
o f
w o u l d
o c c u r
belief t o
t h e
1 9 7 5 ,
p.
t h e
in
vivacity
past
e l e v a t e d
a k i n d
e v e r
c o n c u r r e d
o r
o f
w a s
prejudice,
t h e
T h e y d e n c e h a d
also
w h a t s o e v e r
originally
e v i d e n c e .
F o r
t h e
t o
b e e n t h e
a n
judge,
t h e
f u t u r e
b a s e d
the
c o n j o i n b e i n g
that
[ 1 7 5 8 ] w h e n
subjective
1 9 5 5 ,
a
n e w
c o l o u r s / '
t h e
belief
c o n j u n c that
t h e y
m a t c h i n g
explicitly
past
"as
the
this
t o
o f
t h e
cal-
1 7 4 9 , v o l . I,
a l t h o u g h
u n e x c e p t i o n e d
h e i g h t e n
c o n f e r r e d
Hartley,
habitual,
t o
c o n v i c t i o n
a p p e a l i n g I V . x v ;
p s y c h o l o g y
his
"Essay
e x p e r i e n c e
c h a p t e r
u n c o r r u p t e d probabilities
10). A l l b y o f
p p . o n
t o
at
h o w -
u p b r i n g i n g b e l i e f
w i t h
f r e q u e n c i e s .
i n c r e a s i n g
p r o t o t y p e t h e
1 9 5 9 ,
m i n d ,
f r e q u e n c i e s , t h e
c o n t e n d e d
cerebral
H u m e
f r e q u e n t
the
a
b e e n .
irresistibly
firmer
m e c h a n i s m
c o r r e s p o n d i n g
retained
m o r e
tallied
h a d
t o
r e p e t i t i o n
t h e
t h e
m e r e l y
t h e
h e
e x p e r i e n c e s
m i n d
idea,
( H u m e ,
l i n k e d
b u t
( H a r t l e y
o n
t h e y
ideas
r e c u r r e n c e
u p
brain,
i n f e r e n c e s
e a c h
t h e
[ 1 6 9 0 ]
n o r m a l
o f
past
H a r t l e y
b a s e d
probabilities s h o w e d
a n
it w a s
r e a s o n a b l e n e s s
irresistibly
o b j e c t i v e
o f
rational
that
as
set
a n a d d i t i o n a l vivacity o n
Since
a n d
belief
that
o f
e x p e r i e n c e ,
L o c k e
b e
Hartley,
b e s t o w s
1 3 5 ) .
w o u l d
o f
a u t o m a t i c a l l y their
a n d
Hartley,
association
s e n s a t i o n t h e
s u c h
D a v i d
a p h y s i o l o g i c a l
in
o f
s e v e n t e e n t h
belief in
g r o o v e
t h i n g s
a n d
t h e
that
o f
r e p e a t e d
i m p r e s s i o n ,
m e n t a l
replied
least
e a c h
rationality L o c k e
m a c h i n e
late
Locke,
o f
p r o v i d e
a
f r e q u e n c i e s
M i r a c l e s "
t o
I m a g e s
again.
H u m e
as
d e e p e r
that
c u l u s o f probabilities; L o c k e , 3 3 6 - 9 ) .
far
t h e o r y
d e g r e e s
inevitable.
t o
e v e n t s
scaled
e v e r
belief
a
c o u n t i n g
r e c o r d - k e e p i n g : e t c h e d
p r o p o r t i o n
t i o n
s o
t h e pencil, w h i c h
( H u m e ,
o f
t h e
desiderata. J o h n
r e f i n e d
a n d
w e n t
e x p e r i e n c e , pace
m a d e
s t r o k e
e v e n t s
s t r o n g e r
that
b o t h
a n d
a k i n d
H a r t l e y
n o t o r i o u s l y o n
m i n d
m e n t a l
v i b r a t i o n
c r e a t e d
o f p a s t
a c c o r d i n g l y .
satisfied
o f
t e n d e n c y in o f
t o
c o n t r a s t d e g r e e s
p r o b a t i v e
w e i g h t
r e d u c e
t o o f o f
t h e
all
legal
belief
f o r m s
o f
evi-
d o c t r i n e s
that
p r o p o r t i o n e d
e y e - w i t n e s s
t o
t e s t i m o n y
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10
Classical
that
t h e
a c c u s e d
u n s h e a t h e d
b l o o d y
its quantity. h a d
led
t o
It m a t t e r e d
in
his
probabilities: t e s t i m o n y ,
tales
o f
e r r e d its
internal
b r e a d t h
a n d
a n d
c o n s t a n c y
o f
t e s t i m o n i e s
o n
probabilities
ther.
H u m e
has
b e c o m e
t h e
m i n d
e n c e s
in
a m o u n t
ority"
t o
ability
" W h e n
t o
[ 1 7 3 9 ]
a l l o w e d
associationist
a n d
d i d
b e c o m e
e n o u g h
s i o n
o f
distinct
probabilists
arial m o n y
o f
e m b r a c e d
in
the
w o r k
n o its
w a s
h a p p i l y
f r e q u e n c y
the
credibility
in
w r i t i n g s still
w h i c h
A c c o r d i n g t o
t o
H u m e ,
small
differ-
o n
t e n
a n d
t h o u s a n d a c c o u n t
o f
fur-
e v i d e n c e
e x p e r i m e n t s
slide
o n e
side
o n e ,
that
t h e
superi-
o f
as
c o - e x i s t e d Bernoulli
o n e
t o
t h e
illusion
t h e
t w o .
t h e
o f
e n d
b e
m a d e
their
subjective
o r
t h e
t o
distoro f
probabilities It w a s
n o t
w h i c h
i n t e r p r e t -
the
t w o
classical o f
statistical
probabilities
s o
v e r -
(at least)
u n d e r s t a n d i n g
e p i s t e m i c
w h e n
a n d
classical
e l e m e n t s :
p r o b -
f r e q u e n t i s t
b e t w e e n
p r o b l e m s
that
w i t h
o f
o f
r e c k o n i n g
o b j e c t i v e
b e t w e e n
t o
physical
O n l y
this m e n t a l
a n d
t o
s e n s e
justification.
a t h o r o u g h g o i n g
m u s t
s h o w s
p r o p o r t i o n e d
a u t h o r s ,
f r o m
i n t o
subjective
range
w e l l
s o m e
explicit
m a r k e d
t h e o r y
o f J a k o b
t o
a c h o i c e
T h e
as
as
K i n g
e v a l u a t i n g
c o u n t a b l e
willy-nilly
t o
i n t r o d u c e d
that a c h o i c e
their
his e x -
T h e
" t h e
sensitive
u p o n
e m p h a s i s
t r i u m p h
that
o b j e c t i v e
probabilities
o r
d e m a n d a n d
t o
a c c o r d i n g
b e t w e e n
probability.
a p p l i e d
latter,
belief
shifted
t h e o r y
realization
senses
also,
p a s s i o n
t o
e v e n t s .
t h e
b e c a u s e
p h i l o s o p h i c a l t h e
o f
1 4 1 ) .
little
g a p
d e v e l o p m e n t
ation, as t h e
ability
t h e
p r o b a b i l i t y
t h e
classical probabilists
probabilities
t h e
a n d
p s y c h o l o g y
clear
o t h e r
for
e v o l u t i o n ,
o r
tale
fluid.
as w e l l
t o
e x q u i s i t e l y
t h e
t o
p.
this
create
c o n t r a d i c t o r y
w i t h o u t
place
legal
a c c u m u l a t e d
a l w a y s
Later
this
that
a liar
t h e
n o t
e v i d e n c e
t o
c a u t i o n a r y
t o
w a s
e v i d e n c e
similar
close
as
w i t h
e v i d e n c e ,
integrity,
t h e
a
m u r d e r
e v i d e n c e
n u m b e r ,
c h a n c e s
o n
v e r y
o f
m a d e
o f
past
e x p e r i e n c e ,
I V . x v ) .
w a s
subjective
w i t h
that p r e j u d i c e
m u c h
1 9 7 5 ,
that
a n o t h e r
a n d
his
o f
t h e
c o u n t e r
identical
t h e
p r e f e r e n c e
f r e q u e n c i e s
s y m m e t r i e s
it
in
a m b a s s a d o r
the
e n d p o i n t
c o u n t e d ;
t h e
s e n s e
r e p e a t e d ,
t h o u s a n d ,
g i v e s
for
t h e
w a t e r
also
1 9 5 9 ,
t h e
t h e
o f
totals:
g u a r a n t e e
o b j e c t i v e
t i o n s
s u m
a n d
o f
t o l d
ran
o f
L o c k e
[ 1 6 9 0 ]
n a r r o w e d
o n l y
t e n
Y e t
H e
that
q u a n t i t y
e x p e r i e n c e "
t h e
( H u m e ,
T h e
variety.
r e p r e s e n t s
t h e
j u d g m e n t
m e r e
quality
skill a n d
D u t c h
S i a m e s e
t h e
k i n d s
etc.
canals
o f
r e m a i n e d
their
o n
s c e n e
t i m e s
t h e
t h e
o f
t h e
L o c k e
o f
f r o z e n
t h e
m a n y
o f w i t n e s s e s ,
( L o c k e ,
n o t
h o w
d i s m i s s e d
t h e
o f
f r o m
consistency,
w h o
t r u s t i n g
d e r i v e d
n o t
o f g e n e r a t i o n s
in
fleeing
d i s c u s s i o n
i c e - s k a t i n g
p e r i e n c e
s e e n
c o n v i c t i o n s .
n u m b e r
S i a m ,
o f
b e e n
s w o r d
successful
tradition
K i n g
h a d
probabilities
o f
p r o b a c t u testi-
Laplace.
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C l a s s i c a l
1 . 4
B u t
t h e
w r i t i n g s
m a t i c a l l e d
t o
p r o b a b i l i t y t h e
g e n u i n e n o
e r n e d t h a n
n e e d all
t h a t
o n
m e c h a n i c s T h e
w a s
v e r y
n a t u r a l
M o i v r e ' s
f r o m
w o r d s ,
1 7 5 6 , p .
e n o u g h plify
t o
in
a n d
(J.
sciences " c a n
a n d
a d j u s t
t h e
t h e y
t h a t
c o u l d e q u a l l y
w h o
h a d
i n s i s t e d b e
d i d
b e l i e v e d ,
c a r v e d
t o
a
c o n c e d e p l a c e
t o
d a t a
o f
n o r
w o u l d
p r o v e
r a t h e r
f e e b l e
t o
w a s
w e r e
i n
a n
p r i n -
t o
o u r
g a m b l e d
s o m e
d a y
t h e
for
o n
g a m -
s c i e n c e
c h a n c e ,
c h a n c e
o f
in
in
t h e
A b r a h a m
D e
u n d e r s t o o d "
place,
( D e
statistical
b u t
p h e n o m e n a
just
t o o
w h e n
g o v -
m i n d
still
a p l a c e
c e r t a i n
a c c o r d i n g l y
n o t
IV.i).
t h a t
t h a t
o f
relative
p r e d i c t ;
o u t
m a n
d e f i n e d
r e g u l a r i t y
u n r u l y
1 7 1 3 ,
s u b -
h i d d e n ,
all e v e n t s
p r i m i t i v e
w r o n g l y ,
T h e i r s
p e o p l e s
n o w
o r
i g n o r a n c e ,
states
t h e r e f o r e
b a c k w a r d
m a t h e -
s u p e r - i n t e l l i g e n c e )
t h i n g s .
t h a t
o f
as i n c o r r i g i b l y
intellects
o f
w e r e
B e r n o u l l i ,
f r o m
u n d e r l y i n g
rightly
h u m a n
b e
o f
m a i n t a i n e d
s e e m
n e i t h e r
2 5 3 ) . T h e y y e a r
t h e
Variability, ly
p e r f e c t e d
m o r a l
y e a r
w o u l d
t o
n a t u r e
a s t r o n o m e r s
d i c e
that,
causes, h o w e v e r
t o o l s
p r o b a b i l i t i e s
m a t h e m a t i c i a n s
a n d
[1718]
a n d
t h a t
r e m a r k e d
E u r o p e a n
c o i n s
real
h i s t o r y
s e c u l a r i z e d
h a d
m a k e s h i f t
t h e
t h a t
t h e
m e a s u r e
n e c e s s a r y
p r o b a b i l i t i e s
d e t e r m i n i s m
B e r n o u l l i
m a n i f e s t o e s
L a p l a c e ' s
t h a t
t h e
i n
classical i n t e r p r e t a t i o n
( o r
t o
a n d
t h e
figures
p r o b a b i l i t i e s
G o d
i m m e d i a t e l y
k n o w l e d g e .
t o w e r i n g
t h e
t h a t
w o r l d ,
p r e d i c t a b l e ,
b l i n g
o f
T h e r e f o r e
t h e
e p i s t e m o l o g i c a l
eclipses
v i e w
o f p r o b a b i l i t i e s ;
o f
p e n e t r a t e
t w o
c o n t a i n e d
t h a t
e v e n t s .
states
ciple
also
m a i n t a i n e d
c h a n c e ;
D E T E R M I N I S M
t h e s e
s t a n d a r d
jective. B o t h
h a d
o f
11
p r o b a b i l i t i e s
t h e y like
( P e a r s o n ,
M o i v r e ,
r a t e s
w e r e
c o n f i d e n t
m o r t a l i t y
1 9 7 8 ,
v a r i e d
p p .
t o
s i m -
3 1 9 - 2 9 ) .
as illusory as c h a n c e
w h e n
ful-
i n v e s t i g a t e d . I n
t h e
o r d e r
t o
classical
u n k n o t
p r o b a b i l i s t s ,
p a n m a t h e m a t i c a l ability t i n g
a r o s e
s p o k e
t h e
effects
c l u s i o n s
first
d a t e s
for
in
s o m e t h i n g
least
m u s t a
p r e c o n d i t i o n A t
o f
m u s t
t h e
flourished t o
l a n g u a g e at
a p p a r e n t w e
w h o l e
o f
g l a n c e ,
t h e
p e r i o d
n e w
a
as
G o d ' s s t r o n g
c h a n c e
p a r a d o x i c a l
o f
like
w h i c h
t r e a t m e n t ; a
t h e o r y
it e m e r g e d . s p e c t a c u l a r
g l u e
s u c c e s s e s
f r o m
n a t u r e
t h a t
t h a t w a s
D e t e r m i n i s m
t h u s
s e e m e d
P a s c a l
" g e o m e t r i e
d u
p r o b in
if
fitt o
n a t u r e
fully
c o n n e c t e d p r e m i s e s
o f t h e
r a i n b o w s
c o n n e c t e d
o f
t o
Classical
a s s u m e d
b e c a u s e
d e s c r i p t i o n
e v e n
d e t e r m i n i s m
p r o b a b i l i t y
G a l i l e o
t h e
t h e r e f o r e
a r d e n t
e x p e r i e n c e ,
w a s
a r g u m e n t .
e v e n t s
a b o u t
o f
v i e w p o i n t :
m a t h e m a t i c a l
m a t h e m a t i c a l
t i m e
this
t h a t
t h e
w h i c h
d o m a i n s
as
o f
b e y o n d
in
p h i l o s o p h e r s
m a t h e m a t i c a l f o r
l o o k
m a t h e m a t i c s ,
f r o m b e
p a r a d o x
d u r i n g
strings. N a t u r a l
t e r m i n e d , a n d
spirit
a n d
m a t h e m a t i c s
v i b r a t i n g
t h e
d e -
c a u s e s
a n d
c o n -
b e c a m e
a
n a t u r e . t h e
least
a d m i t t e d h a s a r d "
likely
t h a t
c a n d i -
t h e r e
(Pascal,
w a s
[ 1 6 5 4 ]
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12
Classical
1 9 7 0 ,
vol.
I, p a r t
2, p.
analyze g a m b l i n g script
o n
tician,
t h e
a n d
o b l i g e d
H e
subject
assert
this
r e s o l v e d
w a s
a
t i o n
p r o b l e m s
g r e a t
t h e
t h e
t h e
in
relinquished
his
o f
claim
o f
D e t e r m i n i s m
m e t
as
m a d e
w e r e
T h o s e
real,
t o
o r
" C h a n c e "
Aristotle,
o w e s
y o u
o r
a n
w i t h
a m p l e
beauty,
a n d
o r d i n a r y
m e a n i n g o n
e n d o w m e n t c h i l d r e n
u s a g e ,
ability theory.
b u t
T h i s
o f
o n l y w a s
M o i v r e
ability
m a d e
that,
p r o p o r t i o n
t h e
neatly
o f
D a n i e l
B e r n o u l l i
p l a n e
o f
t h e
t h e
B e r n o u l l i , a b o u t t h e
b y
sions
o f
o f t h e
a n
c o n t e m p o r a r i e s
A l m o s t c h a n c e "
o f c h a n c e
a n y -
rate
a n d
t h e
for
intricate
b e c a m e a n d
f r o m
N i c h o l a s
a n
d e s i g n
like
B e r n o u l l i
c h a n c e w o r l d .
v o c a b u l a r y w h o ( o f t e n a t o m s ) , w e a l t h ,
s u r v i v e d
classical
u p o n
a r g u e d )
d i u s e
t h e
f e m a l e
p r o b -
o f o f
a r g u m e n t deity.
tiny
births t o
t h e t h e
o f
" f r o m T h e
A r b u t h n o t ' s
like
p r o b -
i n
a
dis-
g u a r a n t e e
t h e
1 7 1 0 ) ;
p l a n e t s
solar t o
t h e
in
t h e
s y s t e m
( D .
h a v e
c o m e
h u m a n
d e s i g n "
for
m a t h e m a t i c a l w e r e
d ' A l e m b e r t ,
in
particularly
( A r b u t h n o t ,
c o n s t r u c t i o n
a n d
o f
health,
stability u n l i k e l y
b e n e f i c e n t
e x p e r i -
their probabilist allies
a l i g n m e n t
o r
t o
t h e
m e a n i n g s
m a r r i a g e
a single
s y m m e t r y
t h e -
close
e v e n t s
p u r p o s e
in
as
run.
s o m e o n e
g o o d
a
a n c h o r i n g
a n d p u r p o s e ,
e x c e e d
A r b u t h n o t
e v e n t s
E p i c u r e a n
role
t h u s
b y
in
o f
o f
r e m a r k e d
s h o u l d
s o
a b s e n c e
t h e s e
H e
l o n g
n o t i o n s
( m e e t i n g
o f
f a v o r
t h e
p h i l o s o p h i c a l
i m p o r t a n t
m o n o g a m o u s
t o
intelligent
like
( o r
as e v i d e n c e
a r g u m e n t
a n
o f
A r b u t h n o t
m a l e
o f
p o i n t e d
m o r t a l i t y
A l l
o p p o s i t i o n
a r r a n g e d
ecliptic
" m e r e
p l a y e d
year,
o l d e r
g o o d s
in
it r e q u i r e d
m a t h e m a t i c s
necessity"
natural theologians
institution
1 7 5 2 ) .
regular
e x i s t e n c e
after
t h e
c o n n e c -
f o r t u i t o u s
r a n d o m n e s s
m a r k e t ) ,
1 9 8 0 ) .
m u c h . J o h n
year
future
o n e
e v e n
c o i n c i d e n c e
"blind
in
( h e
probability.
variable
c o n c e i v a b l e
w i t h
o f
o f
tables.
l u c k
2 6 4 - 5 ) .
least
that
o f
e v e n t s
theory
at
a p p l y i n g
" e x t e r n a l "
(Sorabji,
divine p u r p o s e , o f w h i c h D e
t h e
t h e
s o
part
t h e
actual
e v e n
rolls,
g a m i n g
b a n i s h e d ;
e m b r a c e
g e n u i n e
b e e n
t o
as in
w a s
c h a n c e "
for
call
h a d
w a y
necessity,
l u c k
six
necessary
1 9 6 6 , p p .
probabilities,
variously
t h e
1 5 2 5 ]
c o m p a t i b l e
m i g h t
" f o r t u n e "
m o n e y
i d e n t i f i e d
w e
t h e
m a n u -
m a t h e m a -
e v e r y
t h e
t h e
t o
m a t h e m a t i c a l l y
in
at
m a t h e m a t i c a l
o f
I n his
i n t e r v e n t i o n
a n d
as t o
s t a n d a r d s n o t
t h e
felt
o n c e
d i s r u p t e d
c.
a t t e m p t s
Italian physician,
C a r d a n o
t o
probabilities,
w e r e
w h a t
since
t h o r o u g h
t h e
t h e
this p r o b l e m .
e x p e r i e n c e
w h e n
" g e o m e t r y
s t a n d a r d s
a n d
arrived
c o n s t a n t
t h e n
w i t h
the
u n d e r l y i n g a
just
probabilities [ c o m p .
m a t h e m a t i c a l
o c c u r r e d
w h i c h
f o u n d i n g
s o
die
a p p e a l
o w n ) ,
t h e o r y
stable
e v e n t s
w h a t
e n c e .
t o
d e t e r m i n i s m
e x p r e s s i o n s
variable
his
a
his o w n
a n
( C a r d a n o ,
Classical p r o b a b i l i t y c l i m a t e
w i t h
o v e r
1 5 2 5 ) ,
o f
o f
u n d e r l y i n g
o f particular players
c.
earliest
G i r o l a m o
face
face
conflict
b e l i e v e r
b e t w e e n
e a c h
in
v e r y
s t u m b l e d
g a m b l e r
that
flew
T h e
( c o m p o s e d
i n v e t e r a t e
t o
a l t h o u g h
1 0 3 4 ) .
probabilities
criticized
w h o
n o t e d
eye; t h e v e r b y that
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C l a s s i c a l probabilities
all o t h e r
i r r e g u l a r
p r o b a b l e . i n g
H o w e v e r ,
c h a n c e
c h a p t e r
in
I n d e e d ,
s u c h
inspired
r a t e s
o f
O n l y
t h e
i n
r e g u l a r i t i e s
B u t
f o r
side
t h e
causal
visional,
a n d
It
p e n e t r a t i n g
a
p r e c e p t
t h e
p a r t
o f
a t i o n
b y
h o w
t h e
m a t t e r
t h e
m o r e
fluid
w a s
s o u n d
b e
t o
o f
v a r i o u s
p r o b a b i l i t y (Laplace,
m e n .
w a s
in
[1814]
w i t h
failed W h e n
A s
t o
i n t u i t i o n s t h e
p r e d i c t
t h e
results o f
d r a w i n g
p .
it
w a s
l u n a r o f
a n d
p u t
" o n l y Its
p a r t
h e l d
u p
Classical
it
in
o f
a
t o
w a s
a
a
w a s
t h e o f
s o
t h e
test.
m u c h
t h e
t h e o r y
p s y c h o l o g y .
If
I n
a
m o d e l t h a t
c o n t r a s t d i d
a n d
m a t h e m a t i c i a n s
h a d
t o n o
c o n d u c t
m a t h e m a t i c a l a
c a l c u l u s "
m a t h e m a t i c a l o f
t h e
s q u a r e w h o
t o n o t
t h e o r y
a
a s t r o n o m i c a l
n o t
a
w i t h
c e r t a i n
d e s c r i b e d
for
as
e x p l a n -
t h e o r y
t o
o f
t h e
w a s
m a t h e m a t i c s
w o r s e
d i d
o f
c e n t u r y ,
p a s s a g e ,
m a t h e m a t i c a l
e m p i r i c a l
slant,
c o n j e c t u r e , "
beliefs
t h a t
c h a r -
i n t e r p r e t a t i o n
r e d u c e d
less
p r o -
s u b j e c t i v e
m a t h e m a t i c s
f a m o u s
it
t h i n g s ,
s u b j e c t i v e
A r i s t o t l e ' s
t h e
as
t h u s
m a t h e m a t i c a l
viz.
o n o u t -
m e r e l y
w a s
p r o b a b i l i t y
s e n s e
o f
c o n f l a t e d
o f
celestial m e c h a n i c s
p r o b a b i l i t y it
f o r m s
m i x e d
m a t t e r ,
p e r t u r b a t i o n s ,
m e n ,
b y
f r o m
a i m s
s u b j e c t i v e .
" a r t
i n d e p e n d e n t
s t a t u s
o f
w o r l d
1 9 3 b 2 2 - 1 9 4 a l 5 ) .
g o o d
t h a t
t h e
e i g h t e e n t h
d e r i v i n g t h e
s t o o d
" i n t e r p r e t a t i o n "
o r
4 9 ) .
lease
t h a t
associationist
a n
t h e
m i x e d
s u b j e c t
t h a n
classical
r e a s o n a b l e
t e r m
m a t t e r s .
6 ) .
like t h e
this
m a t h e m a t i c s ,
L a p l a c e
a p p l i c a t i o n s
s u c h ,
its
e s s e n c e
1 9 5 1 ,
set o f p h e n o m e n a , m o t i o n .
A s
o f
o f
p .
statistical
n e w
w e r e
p r o b a b i l i s t s
in
a
p r o b a b i l i t y
c h a n c e s , "
{Physics,
p r i o r
s u b j e c t
i n d e p e n d e n t
r e a s o n a b l e
t h e o r y
a
h e l p
call
called
a
l i g h t
t o
o f
o p t i c s
a p p l i e d
p r e s u p p o s e
e x i s t e n c e
o r
a n d
necessarily
t h e
(see
d i f f e r e n t
see
t h a t
s e e -
g e n e r a l , 1,
p r i n c i p l e s "
t h e r e f o r e
classical
v a r i o u s l y
m a t h e m a t i c s , "
m o d e r n
a p p l i e d
t h e
" d o c t r i n e
h a r m o n i c s
o f
t o
a n d
w i t h
" l u c k "
t h e r e f o r e
p r o b a b i l i t y
m i s l e a d i n g
for
T h e
o f
v e r y
P r o b a b i l i t i e s a n d
vol.
c h a n c e
a n d
in
Siissmilch,
a l l e g e d
c o u l d
m a t h e m a t i c a l
s e n s e
f r e q u e n c i e s
t h e o r y
" m i x e d
o f
a
t h e o r y ,
t h e o r y .
p r o b a b i l i t y
i g n o r a n c e o f
w e
i m -
h a n d i w o r k
1 7 7 5 ,
o f
a n d
s p r i n g s
causes.
D a r w i n
c o n s t a n t ,
t h e
a n d
as
e i g h t e e n t h - c e n t u r y
"a
[ 1 7 4 1 ]
its d u e
If
just
p a s t o r J o h a n n
" c h a n c e "
d e t e r m i n i s m
s o m e w h a t
m a t h e m a t i c a l was
h u m a n
b y
o b j e c t i v e
is h o w e v e r
g i v e n
n e c e s s a r y
t h e
b a c k g r o u n d
" h i d d e n
i n t e r p r e t a t i o n
p r a c t i c e a n d
o f
t h e
o f
w h e n
s u p e r s t i t i o n s .
t o
o n l y
figment
i n
c e n t u r y ,
u n t i l
d i v i n e
m o r t a l i t y ,
(Siissmilch,
variability
o f
G e r m a n
t h e
r a t i o s w e r e
p e r s i s t e d
m a n y
a n d
a g a i n s t
w e r e
b i r t h
t r a c e s
t h e
classical p r o b a b i l i s t s o r d e r
classical
in
belief
t h e
w a s
d i s c o v e r
a c t e r i z e d
o r d e r . "
e x a m i n e d
life.
w o u l d
like
m i d - n i n e t e e n t h
c o n t r o v e r s i e s ,
t h e
m a r r i a g e ,
b e a u t i f u l
w e r e
w a s ,
w h o ,
natality,
a n d
T h e
beliefs
d e m o g r a p h e r s ,
o r
t h e o l o g i a n s b y
a n d
w e
n a t u r a l
e v e r y w h e r e
c o m p l e t e ,
really
t h e
o f p l a n e t s
r e f u t e d
4 ) .
statistical s a w
a r r a n g e m e n t s
13
l u n a r t h e o r y
t h e o r y . w i t h
r e t u r n e d
t h e t o
b o a r d .
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Classical
14
1 . 5
T h e
p r o t r a c t e d
s u c h
a clash
a n d
illustrates
" g o o d letter
t o
latter's c o i n
h o w
sense."
Essai
toss
d'analyse
sur
w i t h
a
P a u l
r e c e i v e s
a c c o r d i n g fair
E
price
=
t h e
o f
(Vi
S i n c e a n
t o
t h e
+
t h e r e
is a
small
H o w e v e r ,
the
t o
as
t h e r e
is
in
c l u d e s
a n
infinite
results
o f
t h e
m i g h t for
o f
this
o f
m a t h e m a t i c i a n s m a t h e m a t i c a l
T h i s celebre
o n l y
Paul's
X
R a t h e r , t h e o r y
A p p l i e d
e i g h t e e n t h
u p
. .
. +
m o d e l i n g
o n
( a n d
t h e
t h e
o n .
a
play
until the s o
in
o f
P a u l
h e a d s
a first
s e c o n d
R e c k o n e d
t h e r e f o r e
event,
all
[(1/2)" X
e v e n
p a y - o f f s
a
fair
the
w o u l d
p a y
l a b e l e d
t h e
s t r u c k
is
b e
s o
suitability
that
r o u t e
c e n t u r y .
o f
a
in
s u m
p a r a d o x ,
w e r e
t o
play
it
c o n -
a s s u m p t i o n s
o f
w i t h t h e
p r e -
that
t h e
the
t o
t h e
m a n i f e s t
m o d e r n
o p e n
e y e s
a n d
that
m a t h e m a t i c a l
n o t
t o
infinite.
p a r a d o x i c a l
o d d s
their
t h r e a t e n e d
is
e x p e c t a t i o n
t h e
w a s I n
a small
as
at
p r o d u c e
s t r a i g h t f o r w a r d ,
o f
.
in p r o p o r t i o n
f r o m
t h e m
. .
c o m m e n t a t o r s
this
d e r i v e d
+
will
e x p e c t a t i o n
e v e n
d e f i n i t i o n
$2"-')]
c o i n
increase
s u b s e q u e n t
c o u l d
s e n s e
theory,
e d i t i o n
a n d
t u r n u p
m a t h e m a t i c i a n s
t h e
b u t
n o t
e x p e c t a t i o n
it
Pierre
o f
just
B e r n o u l l i
s e c o n d
c o m e s
+
results
o f
task
toss, $ 4 , a n d
that
an
m a n
probability
N i c h o l a s
t h e
w a s
be:
t h e
a n d
o f
e x p e c t a t i o n
$ 4 )
s u c h
p r o b l e m
their
b y
in
c o i n
third
m a t h e m a t i c a l
results a n d g o o d
s e n s e t h e o r y
the
clash
m i x e d b e t w e e n
t h e v e r y validity o f
m a t h -
probability. is w h y
a m o n g
St.
t h e
b e t w e e n
p r o b l e m s ,
t h e
St.
P e t e r s b u r g ,
n a m e d
issues o f
t h e
the
a
probabilists.
t h e
first
p r o b l e m
that
n e w
p r o b l e m , I n
trivial 1 7 3 8
in
itself,
N i c h o l a s '
b e c a m e c o u s i n
a resolution o f the p a r a d o x in the annals o f the
d e f i n i t i o n
r e a s o n a b l e n e s s p r o p o s e d
P e t e r s b u r g
classical
Bernoulli published o f
the
since
o f
q u e s t i o n e d
t h e
t o o k
( 1 7 1 3 ) .
m a t h e m a t i c i a n s
sense.
o f
If
c h a n c e
calculation t h e
h a v e
class
e m a t i c a l
the
m a t h e m a t i c a l
s i m p l y
hasard
(i/s
B e r n o u l l i
a n s w e r .
g o o d
+
r e a s o n a b l e
T h e
de
w o u l d
finite
c o n t r a d i c t i o n
n o t h i n g
dictates
$ 2 )
probabilities
validity.
dictates
p u b l i s h e d
until
tails, a n d
n o
a n d
g a m e )
X
N i c h o l a s
the
p r o p o s e d
m e t h o d ,
b u t
A l t h o u g h
n o
e q u a l
o f
o b s e r v e ,
g a m e .
tained
(V4
r u n
decreasing
q u i c k
t h e
$ 1 )
P e t e r s b u r g
Paul $ 1 ; if h e a d s d o e s
s t a n d a r d
X
a n d
first
coin.
$ 2 ; if n o t
p l a y i n g
u n b r o k e n
w a s
lesjeux
fair
St.
m a t h e m a t i c i a n s
M o n t m o r t ,
toss, Pierre agrees t o p a y toss,
t h e
reasonableness
p r o b l e m
d e
g a m e
o v e r
seriously
T h e
Pierre
R E A S O N A B L E N E S S
c o n t r o v e r s y
b e t w e e n
probabilities
o f
after
o f
the
s u c h
o f
the
a t t e m p t s .
A c a d e m y ;
probabilistic
a n i m a t e d
n o t i o n
m a n y
it also
e x p e c t a t i o n
s u b s e q u e n t
r e a s o n a b l e n e s s ,
D a n i e l ' s raised a n d
the
a
cause
D a n i e l A c a d e m y
m e m o i r
n o t
f u n d a m e n t a l
its relationship
c o n t r o v e r s y .
a n d
a
I n
r e d e f i n i t i o n
essence, o f
t o h e
e x p e c -
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Classical
t a t i o n w a s
t o
m a t c h .
like
t h e
an
o f
p r u d e n c e
e q u i t y
t h a n
t h a n
t h e
p r o d u c t
k n o w n v i d u a l
p r e f e r e n c e
richer
y o u
assuringly
small
m o n i z e d
m e n
o f
their c a r g o t a t i o n
g a v e
it
o f
H e
o f
w a s
affairs
k n e w
several that
o u t c o m e
w i t h y o u
a c c e p t e d t o
o n
that
c o n f i r m e d
their
b e
e x p e c t a t i o n
o f
d e f i n e d
w h a t
b e c a m e
later
relative
t o
m o r a l
utility
d e r i v e for
beliefs:
for
a n d
( D .
a
re-
t h e
St. har-
e x a m p l e ,
t o
distribute
m a t h e m a t i c a l )
w i s d o m
t h e
e x p e c t a t i o n
tables n o t
t o
indi-
that
m a k i n g
f o r t u n e ,
a n d
( b u t
h a d
o u t
t o
able
o n e ' s
g a m i n g
m o r a l
m o r e
p r u d e n c e ,
B y
w a s
o f
P e t e r s b u r g
u n d e r s t a n d i n g
h e
s h o w
t h e
ships, a n d
St. a c t e d
v a l u e s
h a p p y .
practices
a v o i d
o f
a n d
t h e
w e a l t h ,
t o
t h e
e x p e c t a t i o n
s u b s t i t u t e d
m a k e
able
o f
e x p e c t a t i o n
characteristics
players
e x p e c t a t i o n
d e p e n d i n g
also
o f
" m a t h e m a t i c a l "
t h e
m o n e t a r y
w i d e l y
results
t h e
like
t h e
d e f i n i t i o n
t o
t o
i n d i v i d u a l
H e r e
values,
t a k e s
o t h e r
a m o n g
the
is, B e r n o u l l i
m o r e
d e f i n i t i o n
in situations
" m o r a l "
e x p e c t a t i o n s ,
g a m e .
w i t h
a n d
m o n e t a r y
t h e
stake.
c o n t r a s t
T h a t
for
t h e
at
t h e
s t a n d a r d
that
p r o b a b i l i t y
f u n c t i o n
P e t e r s b u r g
s o b e r
t h e
as its utility.
l o g a r i t h m i c
I n
p r o p o s e d
o f
are,
w a s
15
i g n o r e s
a r g u e d
fairness,
accordingly.
t h e
w h o
e q u i t y
o f
B e r n o u l l i
that
j u d g e
B e r n o u l l i
m o r e
m o d i f i e d
as
impartial
risk-takers,
p r o b l e m
O b s e r v i n g
probabilities
e x p e c -
B e r n o u l l i ,
[ 1 7 3 8 ]
1 9 5 4 ) . Significantly, o f
trade
n a t e d
a n d
t h e
p r o f e s s o r as a n " t o
D a n i e l
c o m m e r c e ,
earlier o f
b o t h
justice."
H i s
t h e
Bernoulli
N i c h o l a s
s i d e d
tracts;
D a n i e l
d e n c e ,
d e r i v e d
l o n g e r
a n
matical
D a n i e l m e a n s
w i t h w i t h f r o m
o f
t h e
l a w
w h e t h e r
that
w h e r e i n s e n s e
t h e
increasingly
c o m m e r c e . b u t
p r o b a b i l i t y
probabilities u p
P o i s s o n , p o i n t e d
-
b y
w a s tails? o u t
t h e
o t h e r
p r o b l e m it
that
a c c o r d
w a s
Swijtink,
t h e l e n g t h
o f
o f
at issue
d e r i v e d
w h o
Basel
w i t h
e x p e c t a t i o n
o f
as
w e l l failed
e q u i t y
a n d
e x p e c t a t i o n
s h o u l d
t h e
m o d e l
consisted.
aleatory
c o n -
e c o n o m i c
r e a s o n a b l e
m e r c h a n t ,
w a s
b e t w e e n
f r o m
s e n s e
m a n
a n d
p r u -
w a s
t h e
n o
m a t h e -
shift.
P e t e r s b u r g
n o t
d o m i -
e x p e c t a t i o n
p r o b l e m
classical probabilists.
lay
h a d
r e a s o n a b l e n e s s
c a n n y
St.
that
d e f i n i t i o n
W h a t
w i t h
really physically
(see
in
n e w
that
w o r l d
B e r n o u l l i ,
m o r a l
p r o t o t y p i c a l
reflected t o
that
e q u i t y
a
t h e
e x a m p l e s
i m p o r t a n t
T h e
f r o m
U n i v e r s i t y
s u c h
o f
rather
s o l u t i o n
t h e
probabilistic
o l d e r
t h e
his
d r a w n
N i c h o l a s
participant
t h e
a c c e p t e d
at
e x p e r i e n c e . "
rather
t h o u g h t
t u r n
replied
j u d g e
legal
o b j e c t e d
e v e r y
w i t h
t h e
w e r e
e x p e c t a t i o n .
c a n o n
o f
n o t
b u t
universally
c o n t i n u o u s l y D e n i s
w a s
Bernoulli's
d ' A l e m b e r t ,
a n d
D a n i e l
impartial
t h e o r y
o f
t o
m a t h e m a t i c i a n ,
p e r f e c t l y
cousins
e x a m p l e s
c o n t r a s t
p r o s p e c t s
r e a s o n a b l e n e s s ,
w i t h
R o m a n
c o u s i n
" h a r m o n i z e [ d ]
in
d i s c u s s i o n s
a c c o m p l i s h e d
e v a l u a t e
B e r n o u l l i ' s
t h e
1 9 8 6 ) . o f
S o m e ,
m o n e t a r y
p o s s i b l e
for
O t h e r s ,
t h e g a m e
w a s
w a s
a
b y
like
n o J e a n
v a l u e s fair
like
c o i n
b u t t o
S i m e o n -
l i m i t e d
b y
t h e
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16
C l a s s i c a l
w e a l t h t h a t as
o f
t h e
t w o
players.
m a t h e m a t i c a l
a n
a v e r a g e
1 9 8 7 ) . t h e
m a n y
H o w e v e r ,
v e r y
w e r e
o f
as e x p e c t a t i o n
a t t e s t s
t h e i r
i n g
t h e
this
fluity.
If
h a d
k n o w n
w a s
t h e
t h e i r
i n
o f
b y o f
e x t e n d
at
a
w o r d s ,
ideal
o f
a
i n t o
a p p l i e d
1 9 8 0 ;
J o r l a n d ,
a n d
fact
s t r u c k
t h a t
as
f u n -
g o o d
g o a l
at
classical
p o s t u l a t e s
calculus w i t h
o f
s e n s e
q u a n t i f y -
a n d
w h a t
e n v i s i o n e d
o f
strife.
e v e r
a h o s t
q u i p p e d n e e d s a
a
k i n d
n u m b e r s
t o
a n d
d o e s
o f
t h e i r
t h a t
f u n d a m e n t a l
o n e
t h a t
s u g g e s t e d
o f
f o r
t o
a p p l y i n g
w a s
h o p e
o f
t o
t h e
h e l p
hommes
w h e n
i n d e p e n d e n t
t u r n i n g
t h e
relied
u s e
t r u l y
t h e
f a m o u s
t h e
e v e r y o n e ' s
a n d
" a r t
s o m e
o f
also
o n l y
situ-
m e t h o d , b e s t
c a p -
d i s c r e t i o n , m a t h e m a -
satisfaction, w o u l d
o f
e x t e n t
p e r p l e x i n g rules
o f
fascin-
m e t h o d s
p e r s o n a l
l e a r n e d
i n v e n t
t o
L e i b n i z
t h a t
t h e
s e v e n t e e n t h -
e n d ,
o u g h t .
o u t
e v e n
r u l e s
a l w a y s in
t o
f o r m a l -
s e v e n t e e n t h - c e n t u r y I n
t h e
p o s s i b l e
f e w t h a t
m a n y
c h a r a c t e r i s t i c " a n d
i n t u i t i o n s
sophistry.
f o r m a l
e l i m i n a t e d
a m o n g
i d e a s
B y
f o r t u n a t e
D e s c a r t e s '
p r o b l e m s
" u n i v e r s a l
t h e
l i m i t e d
calculus
O b s e r v i n g
set
u n a i d e d
m a t h e m a t i c a l
b y
a
w h a t
T h i s
it
a
c a l c u l a t i o n s )
o r
lights
o f
t h e s e
r e a s o n i n g
e x t r e m e .
o f
b y
m e c h a n i z e d
e c h o e s
w e r e
e n o u g h
O n l y
p r o b a b i l i t i e s
o b s c u r e d
calcur e p l i e d
c o m m o n .
c o d i f y
o f
a n d
p r o b a b i l i s t s
e y e s i g h t
t h e
a t t r a c t i o n
lesser
e m p h a s i z e d
spectacles.
p r o b a b i l i s t s '
a n o f
t o
t o
p r e f a c e
n a t u r e .
calculus
f r o m
a p r o p r o s
f o r m a l
r e s o l v e d
t h e
fatal
t o
b y
s u p e r -
e n l i g h t e n e d
s u b c o n s c i o u s
n o r m a l
r e a s o n i n g ,
calculus
t h e r e f o r e
o n e
allure it,
a n d
for
c o m p l i c a t e d
o f
t a k e n
actually
p r o b a b i l i s t s
b e n e f i t
t h i n k e r s . T h e
m e t h o d
b e
o f
t h e
t h a t
t o
risk
e q u a t i o n s
a c c u r a t e l y
c o m p a r e d
s e v e r a l
n o t
s o u g h t
n a t u r a l l y
c e r t a i n
a
T h e
r e a s o n
similarly,
A n d
a
o b v i o u s . w a s
t h e
w h a t
o f
s e n s e
r e s p o n s i b l e
c a m e
e c h o e d
e n d o w e d
b e
r a n
m a c h i n e r y
t h e
t o
w e l l
c o u l d
s u c h
o n e
w i t h
s o
calculus
Leibniz
assign
a r g u e d
w h e n
real o n e ,
m a t h e m a t i c a l
p r o b a b i l i t i e s
b e l i e v e d
t h a t
e x e r t e d
o f
c o u l d
e x t r e m e l y
D e s c a r t e s ,
t h e
o f
n o t
m a n y .
w a s
e l a b o r a t e
eclaires
s e n s e
j u d g m e n t ,
ticians
a
a l w a y s
t h a t
after
c o m m o n
s o m e t i m e s
h a n d
t a k e s
t h e
b e l a b o r i n g
s e n s e
ations. A s
a n d
w a s
m a t h e m a t i c a l
all
p r e f a c e
artificially;
g o o d
w i t h
t u r e d
m i x e d
t h e n
p r i n c i p l e s
c o n j e c t u r e "
o n
( D a s t o n ,
t h e i r
as
e i g h t e e n t h - c e n t u r y
B a c o n ,
o n l y
a n d
r e a l i g n
t h e
b u t
d e f i n i t i o n s
-
g o o d
c o n t e n t ,
a t i o n
t o
t o
C o n d o r c e t ,
T h e
a l o n g
polloi
c o u l d
T h e o f
hoi
b e f u d d l e d
issue
o r d e r
w i t h
N .
t h e o r y .
r e s u l t s
calculus
v i s i o n
t h e
eclaires
p a r a d o x
y i e l d e d
p r o b a b i l i s t s
o p t i c a l
i z e d
g a m e
calculus
hommes
t h e
t h e
u s e
s a m e
t h e
t h e
p r o b a b i l i s t s
s e e m
elite
m o d e l
o f
A .
c o r r e c t ,
classical
-
t h e
V o l t a i r e ' s
( w h i c h
t h e
all
d i d
i n t u i t i o n ;
f o r
i n d e e d
t i n k e r
i n
M . J .
m a t h e m a t i c a l
c o m m i t m e n t
g o a l ,
case
l a t i o n s
s m a l l
t o
like
r e a s o n a b l e .
G i v e n
that,
t h a t
t h e
w i l l i n g
d a m e n t a l t o
w a s
r e p e t i t i o n s
all a g r e e d
f o u n d a t i o n s
p r o b a b i l i s t s
Still o t h e r s ,
e x p e c t a t i o n
t o
probabilities
h e
s o m e h o w
a r i t h m e t i c - l i k e
o p e r -
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Classical
a t i o n s t o
t o
p e n
t h u s
c o m b i n e
a n d
b y
p a p e r
t a k i n g
(Leibniz,
a b l e n e s s
c o e r c i v e
Classical s c r i p t i o n t h e
o f
it
for
w a s
t h e
o f
o f
t h e
t h e
a w i t n e s s .
t o m e
solar
o f
as
t h e
w h e n
w h o
T h e
w a s
h o w
t o
t h e
as a n
t h e
a
call
Sir;
a n d
q u e s t i o n "
f r o m J a k o b
m a k e
o n c e
m e n ,
B e r n o u l l i
i n s t r u m e n t
n e w - s t y l e
a n
w a s
o f
r e a s o n -
a c c e p t
annuity,
a
t h e
t h e
far
II
t w o as
p r e -
against d i d
in
n o t case
descriptive.
B u t
in rational
decision
a b o u t
b e l i e v e
a n d
a n d
t h e
t h e o r y
o r
F r e d e r i c k
i m p r o v e
s o
o f
results
t h e o r y ,
majority
prescriptive,
s e n t
their
w h e n
their
great t o
d e s c r i p t i o n
a n d
t h e o r y
the
a
c h e c k e d
a m e n d e d
p u r c h a s e
t h e o r y
o n
at
w h e t h e r
C o n d o r c e t
calculations
t h u s
instruct
it a b o u t
calculate,
settle
calculus
t o
arose
d e m o n s t r a t i o n .
r e a s o n a b l e
t o
s y s t e m ,
their
M a t h e m a t i c i a n s
" p a r a d o x . "
b e
H e r e
so,
o f
elite
u s
s o o n
probabilists
a t t e m p t i n g
w a s
"Let
s h o u l d
old-style
t h e o r y
also a i m e d
uncertainty,
t u o u s l y
t h e
w e
a c o n t r o v e r s y
a r m s :
w i e l d e d
m a t t e r s ,
as
t o
Classical
P o i s s o n
P e t e r s b u r g
o f
15).
m a t h e m a t i c i a n s
the probabilists
m a t i o n
p.
17
w h e n e v e r
a call
ink,
r e a s o n a b l e n e s s .
t h e
St.
u n d e r
a n d
p r o b a b i l i t y
i n t u i t i o n s
jibe,
1 9 5 1 ,
in u n c e r t a i n
as
replace
p e n
S i m e o n - D e n i s
c o n s e n s u s
H e n c e f o r t h ,
w o u l d t o
[ 1 6 7 7 ]
t h r o u g h
t h e m .
probabilities
t h e
for-
the
t e s t i m o n y
s o m e t i m e s
p r e s u m p -
o f
judicial
Prussia s y s t e m
a
w e i g h t y
( C o n d o r c e t ,
1 7 8 5 ) . T w o m a t e l y
a m b i g u i t i e s , u n d e r m i n e d
matical.
T h e
s p a r k e d o f
b y
s a m e
o n
first
t h e
t h e
p r o p e r
i n g h o w
t o
f e w .
s e n s u s
t o
It
c o n t r i b u t e d w a s
s e c o n d
d ' A l e m b e r t
o v e r
carrying
o f f
L o n d o n .
T h e
F r a n c e
o n
their
as
m u c h
r e p o r t s t h e
t h e r e led
t h e
o f
t h e
d r e a m
o f
a calculus in
T h e
just
e i g h t e e n t h o n e - s e v e n t h
t e c h n i q u e
o f
that w o u l d face
w h e r e
d e b a t e
i n o c u l a t i o n
L a d y
t h e
n o t
a g r e e
t o
t h e
select
o f
in
d e b a t e o f
c o n s e n s u s
o f
believ-
o v e r
t h e t h e
w i d e n
clear
o f
d i d
p e r s i s t e d
m a g n i t u d e
natural
s o l u t i o n s
b e l o n g e d
e n d l e s s
b r a n d s
just
F r e n c h e n l i g h t -
that
c o n -
e v i d e n c e
that
sorts.
c o n c e r n e d
t h e
b o t h
m a t h e -
distinct
m e r c h a n t
ulti-
e x p e c t a t i o n
d i f f e r e n t
probabilists
t h e
tenacity
o v e r
several
v e r y
d e s p i t e
a n d
r e a s o n a b l e n e s s
w e r e
t o
b u t
c o n f u s e d
d e b a t e
s h r e w d
t h e
u p h e a v a l
several
o f
t h e
in
their
as
r e n d e r
faith
s m a l l p o x o f
t o
in
m o n o l i t h i c ,
p r e s c r i p t i o n .
d e c a d e s
r e c o g n i z e d ,
e x p e c t a t i o n ,
a n
their
o f
a n d
H o w e v e r ,
a m b i g u i t y
a n d
m i d d l e
o f
w a s
t o
o n
p r o b l e m :
fair j u d g e
t o o k
d o u b t
d e s c r i p t i o n
t h e
T h e
shatter
N o
early
s o m e t i m e s
eclaires.
it.
r e a s o n a b l e n e s s T h e
t h e y
r e a s o n a b l e n e s s
R e v o l u t i o n e n e d
a n d
d e f i n i t i o n
d e f i n e
clearly
classical p r o g r a m
St. P e t e r s b u r g
o f hommes
that
e v e r
s u r f a c e d
p r o b l e m .
c o m p a n y
in
t h e
r e a s o n a b l e n e s s ,
t h e
n e i t h e r
W o r t l e y
t o
b e t w e e n
d r a m a t i z e d c e n t u r y o f
t h e
t h e
D a n i e l t h e
against
E n g l a n d t h e
b e t w e e n
B e r n o u l l i
r a v a g e d
p o p u l a t i o n s i n
line
difficulty.
s m a l l p o x
M o n t a g u
i n o c u l a t i o n
d r a w
o f
disease,
D u r i n g E u r o p e ,
Paris
a n d
a n d
a n d
V o l t a i r e
l o n g
prac-
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18
Classical
ticed
in
m i g h t a n d
T u r k e y ,
b e
c u r b e d .
t h e r e
w a s
d i e
D a n i e l
B e r n o u l l i
u s e d
t h e o r y for
f r o m
t o
a n y
s u b m i t t e d c o u l d
calculate
g i v e n
o n e
t r e a t m e n t
d a t a
t h e
age.
a
d u b i o u s ,
d ' A l e m b e r t ,
h i m s e l f
R a t h e r ,
v e n t i o n a l
probabilistic
t r e a t m e n t
risk
( i n o c u l a t i o n )
p e o p l e
p r e f e r
t o g e t h e r
i n g
t h e
w h e r e a s t h e
O v e r
in
half b a d . "
B e r n o u l l i
s a w
s l o w l y
prescriptive, a b l e n e s s
a
o f
probabilities.
B y
prohabilites
in o f
T h e s e ,
senses
p r o b a b i l i t y
in
failed
b o t h
t h e
real
a a
o n
a t t e m p t e d
t h e o r y
for
direction,
g a p
small
p u b l i s h e d h a d
m a n y
t o
lay
f r o m
r e a s o n a b l e d i d
b e
w i t h
Essai
b e c o m e
t o
.
1 9 7 9 ) .
probability
ideal
t o
o f
a n d
t o o l
.
reveal
t h e
r e a s o n -
subjective
philosophique a
.
reasonable,
d e s c r i p t i v e
t h e
al-
d e s c r i b -
( D a s t o n ,
o b j e c t i v e
his
n o t
l o g i c
o f
classical
t h e
psy-
s h o r t - t e r m
its task
w i t h i n
b e t w e e n
t h e o r y
t o
c o n -
actual
" c o m m o n
self-interest
e m p h a s i s
t h e
m a t h e m a t i c i a n s
d i s i l l u s i o n m e n t
Laplace
o f
m a t h e m a t i c a l
o f
a
piece.
s t r e n g t h
reflected
o f
t h e
sur
rather
a n d
t h o s e
its
T h e y o f
its
is
subjective
h i g h l i g h t e d a
les
t h a n
a
in
b e l i e v e d
that
applications,
their vision o f the
a b o v e
firmly
t o all
b u t
for
their a n d
b o t h
a n
calculus
m i x e d identifit o
b e
distinc-
probabilists
s u c c e e d e d
applications
t h e o r y a n d its p r o p e r
o f
i n n u m e r a b l e
classical
t h e
s e n s e
that c a m e
its
m a t h -
d e n i e d
t h e
t w e n t i e t h - c e n t u r y o f
o f
o b j e c t i v e
s u b j e c t i v e
rationality
i n d e p e n d e n t
applications,
that
t h e
a n d
o f practical s c h o o l e d
a n d
c o m m i t m e n t
p h e n o m e n a ;
f o r m
t h e o r y a n d
that
o f
d e t e r m i n i s m
s t a t e m e n t s ;
that T o
classical i n t e r p r e t a t i o n
c o n f l a t i o n
t h o r o u g h g o i n g
m o d e l i n g
t h e o r y w i t h
t h e
fruitful
p r o g r a m m a t i c g o a l
all
h a l l m a r k s
c h a n c e
i n t e r p r e t a t i o n s
w e r e
o f
p r o b a b i l i t y
as reasonableness.
p o s s i b l e t h e y
t h e
t h e
the
t h e
a c k n o w l e d g e d
o w n
B e r n o u l l i ' s
t i m e
w e r e
o f
m a t h e m a t i c a l
tions,
t h e
probability;
o f
career,
w i d e n i n g
probability:
o f
k n o w n
t h e
its
a
w h y
Bernoulli's
D ' A l e m b e r t
called
p r o b a b i l i t y
r e a s o n s
e n l i g h t e n m e n t .
e x i s t e n c e
c a t i o n
result
1 8 1 4 ,
t h e n ,
e m a t i c a l
in
h e
o p p o r t u n i t y
w h e r e
its l o n g
w h i c h
s i m p l i f y i n g
Bernoulli's
( s m a l l p o x ) ,
l o n g - t e r m .
o t h e r w i s e
this as a n
risk
o f
S c i e n c e s
i n o c u l a t i o n
his
i g n o r e d
c h o i c e
1 7 6 0
p r o b a b i l i t y
f r o m
that
I n
o f
o p p o s e d
c l a i m e d
a
recipients
so.
a n d
a n d
i n o c u l a t i o n ,
w i t h
d a n g e r s ,
A c a d e m y
principal
p r o b l e m
its
o r
m o r t a l i t y
t h e
s c o u r g e
that
m o n t h
scanty
n o t
t h e
t h e
h e l d
p e o p l e
shifted as
o n
a
t h e
w i t h o u t
c h a n c e
Paris
w e r e
l o n g - t e r m
b e t
h e
p u b l i c o f
a n d
m o d e l
B u t
o f
c o u r s e
o f
that
e x p e c t a n c y
d ' A l e m b e r t
this p r e f e r e n c e ,
c o n d u c t
the
t o
t h e
life
o f
c o n f r o n t e d
a large
effect
b e n i g h t e d
t h e o r y
t h e
a n d
c o n d o n e
half g o o d ,
t o
risk-raking:
o f
s m a l l p o x
w e r e
p r o p o n e n t
c o n c l u s i o n s .
o f
s p a c e
in
n o t
h u n d r e d )
statistics
t h e s e
h o p e s
itself w a s
t o
o n
g a i n
f a v o r a b l e
c h o l o g y
t h e
h a d
a v e r a g e
a
m e d i c a l
t w o
m e m o i r
b e
b u t
in
in
B e r n o u l l i ' s
a s s u m p t i o n s
a n d
i n o c u l a t i o n
( a b o u t
t h e
w h a t
p o p u l a r
H o w e v e r ,
a small
w o u l d
that
f a n n e d
probabilities
subject
o r t h e y
matter.
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C l a s s i c a l
1 . 6
G a m b l i n g l e m s
R I S K
w a s
s o l v e d
t h e
b y
I N
a n d
b l i n g p r o b l e m s ,
w h i c h
t h e
t o
this
first
o f
t h e
e d i t i o n
f r o m
i n v o l v e d
m o s t
o f
t e c h n i q u e s early
c h a n c e
a n d f o r
l o n g
o f
analysis
e e n t h - c e n t u r y
f a c t o r s n i t e
like
e d g e
e q u a l
o v e r
t h e
r a p i d
s t o c k - i n - t r a d e
m i g h t
s t r o n g
d o s e
t h e
folly
o f
o f
d i d
t o
Ferdinand c h a n c e s t e a m
w i t h
o f
E n g l a n d
like
ticians
w i t h
a n d
t h e
G e r m a n
( F r e d e r i c k
II
a b o u t
Prussia's
w a r
t h e
f o r
t h e
o f
w e r e
a l g e b r a t h e
I n t e r e s t i n g l y n o
t h o s e
o f
a s s i g n m e n t
o f
a n d
a n d
u n d e r t o o k s e v e r a l
c a l c u l a t i o n s
g a v e
h a d
m a d e
c h a n c e
m e s s a g e
a n d
t h e n
g a m b l i n g
t e n n i s ,
g a m -
c o m p l e x i t y
bit
e x a m p l e ,
a p p e n d e d
o f
s o m e
a
e i g h t -
o f
t h e
b e t t i n g
t e x t
c o c k s
o f
o f
states a
F a t h o m
v e r y
s e v e r a l
little
t h a t
a
defi-
n o t a b l e
I n d e e d ,
t h e
l o t t e r y
t h e r e
w a s
b u t
w e r e
l e a r n e d
l o t t e r i e s
d i c e
t o
b e
B r i t a i n , a n
t o
r e a s o n
f e w b e
cruelly of
o n
fleeced
t h a t t h e
b y
a in
m a t h e m a -
t h e
d e s i g n e r s
F r a n c e ,
Italy,
o p i n i o n . a n x i o u s
m o n e y
e i t h e r
t h e
b e g a n
s e v e r a l
raise
w h o
all
e x p e r t
E u l e r
m o s t
Adventures
c r a z e
f o r
t o
a
p r e a c h e d
T h o s e
N e i t h e r
i n
w i t h
a p p a r e n t l y
p r o v i d e d
w r o t e
p r o p o s e d little
a n d
m a t h e m a -
" c a l c u l a t e
o n l y
l o t t e r y
E u r o p e
h e
t h a t
The
t o
t h e i r
associations.
likely
S m o l l e t t ' s
p r o b a b i l i s t s
e x c e p t i o n :
c a r d s
w i t h
m a t h e m a t i c i a n s
e m p l o y m e n t .
n a t i o n a l
c o n s u l t e d
f o r
c e r t a i n t y , "
s w e p t
ease
edification.
g u i d a n c e
T h o m a s
a n d
G e n o a n - s t y l e
d e b t s . )
o f
at
h o p e d
m o r a l i s t s ,
e i g h t e e n t h - c e n t u r y
b u t
t h e
t h e m ,
T h e
s o r t
a n d
ill
d i s r e p u t a b l e
p a s s i o n
t h e
for
w e r e
t h e i r
1 7 1 9 ) .
e i t h e r
t e x t s
N e t h e r l a n d s
w a s
a
a r b i t r a r y
o f
a m o n g
t h e i r
e x a c t n e s s
T h e
p r o b l e m s
p a t r o n s
g a m e
w i t h
( 1 7 5 3 ) .
u t m o s t
t h e
t h e
f o r
h e r o
Fathom
n o r
l e t t e r s
t h e
o f
a l o n g
a p p e t i t e
s h a r p s t e r s . a n d
r a t h e r
a n d
( D e f o e ,
p r o b a b i l i t y
t h e
p u r e
p r o b a b i l i s t s
D e f o e
r e c k l e s s
p u r s u i t s
Count
o f
t o
m e t h o d s
1 9 6 8 ) .
o f
F e r m a t ' s
( 1 6 5 7 )
t h e
w h a t
p r o b -
p r o b a b i l i t y
aleae
u s i n g
u s i n g
p e r f o r m a n c e
p r o b l e m s
D a n i e l
t h e
little
d i s a p p o i n t e d ,
a
ludo
m a t h e m a t i c a l
B e r n o u l l i ,
p a s t
m o s t
c a l c u l a t i o n
t h e
a
a n d
d e v o t e d
( 1 7 1 8 ) ,
m a t h e m a t i c s
o f
P a s c a l
first
e l e m e n t a r y in
p l a y
c o n t r a d i c t i n g
a n d
o f
v e r y
o t h e r s .
spirits,
s u c h
h a d
size,
p r o g r e s s ,
c u r e
g a m b l e r s t u r n
c h a n c e s ,
sort.
( S c h n e i d e r ,
c o c k - f i g h t i n g
g a m b l i n g
c r u s a d i n g
ticians
o n
o f
t h e
e x c l u s i v e l y
t h e
g a m e s
J a k o b
a n d
e x p e c t a t i o n
w i t h
p r o b a b i l i t i e s
b r e e d i n g ,
D e s p i t e
S o m e
t h e
albeit
I N S U R A N C E
Chances
o f
o f
t h e
this
s t a p l e
of
analysis
o n
latter.
m a n u a l s
a s s u m i n g
o f
D
ratiociniis
Doctrine
b e t w e e n
skill,
t h e
De
d u r a t i o n
w r i t e r s
d i s t i n c t i o n
p r o b a b i l i t i e s
o d d s
o f
o f
t h e
c o m p u t a t i o n s
N
w e r e
s o p h i s t i c a t i o n
c o m p u t a t i o n s
h a r d - a n d - f a s t m i x e d
t h e
b e
H u y g e n s *
M o i v r e ' s
s i m p l e
t h e s e
t o
A
19
c o n t r a c t ,
w e r e
treatise
c o n t i n u e
D e
a n d
a d v a n c e d
e n o u g h ,
H u y g e n s '
B e t w e e n
p r o b l e m s
a d v a n c e d t o
day.
a l e a t o r y
m a t h e m a t i c i a n s
c o r r e s p o n d e n c e
t e x t s
G A M B L I N G
p a r a d i g m a t i c
t h e
p r o b a b i l i t i e s
side
t o t o
p a y d o
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Classical
20
so.
T h e
traditional
sizable profit p i t t e d that
t h e
t h e y
c o r r e c t
p o o r ,
w h o
bitious. A
t h e
t h e
t o
o f J a k o b
the
d e r i v e d
for
trast
g a m e s
t o
T h i s
w a s
n o t
m a t h e m a t i c i a n G e n e r a l b a s e d w i t h t h e
o f
E n g l a n d .
p r i c i n g
o f
s i x - m o n t h creased
in
t h e h e
h e l p d i d
t h e s e
J o h n in
o f
n o t
D e
revise
G r a u n t ' s
table, B r e s l a u
c o m p i l e d
Statistics births,
a n d
W e s t
a
h a v e
u p o n
t h e
c o m b i n a t i o n s
social
t h e r e f o r e t h e
m a y
tax
o r d e r ,
strategy
o f
a n d
t y p e s
for
i t is
t h e
u n l i k e l y
l o t t e r y
despised
o f
n e p h e w
m a r i t i m e
aleatory
at a m -
t o
in-
b u s i n e s s
w e r e
o f
interest
t u r n e d
their
a b o u n d t h e
T h e
w i t h
s u c h
e x p e c t a t i o n
all g r i s t
for
their
mill.
values
w e r e
n o t
easily
probability
e x a m p l e s
their
contracts.
insurance,
u s u f r u c t s that
for
eagerly
N i c h o l a s
aleatory
Friesland
t o
s i m p l y
a s s u m i n g
that
for
o f
3
H a l l e y
a n d
t h e
contracts, in
o n
c o n -
m a t h e m a t i c i a n
o f
e s t i m a t e s
t h e
d a t a
i n s t a n c e
p e r i o d
d e a t h s
b e c a u s e
m o n e y o f
o f
until
in
t h e
first b y
for
a g e
his
t h e
t h e y
d e -
H e
d i d
a s s u m p t i o n s
H u d d e ,
w i t h
a l t h o u g h
s u g g e s t e d
m o r t a l i t y b e y o n d
t o a n y
80.
m a t h e m a t i c i a n s
truly
w a r
in
a n n u i t i e s
d i r e c t i o n
o f
t h e
d y i n g that
A m s t e r d a m J o h a n n e s
E s t a t e s
e x p e c t a t i o n s
a n d
c h e c k
t h e
a n d
m a t h e m a t i c a l l y
c h a n c e s
t h e o r y
g a t h e r e d
t o o k
raise
t o
r e l e v a n c e
p r o b a b i l i t y
(Halley,
first
equal,
g e n e r a l ,
t h e
t h e
intervals
o f
s t a t e s m a n
p r e s e n t e d
t h e
w e r e
p u r c h a s e r s
I n
D u t c h
calculus
o p p o r t u n i t y
p u b l i s h e d
t h e
5 3
s u b s e q u e n t
1 6 7 1 ) .
e x t e n s i o n s
this
w i t h
n e w
a g e s
t h e
1 6 7 1
H u y g e n s '
r e c o g n i z e
f r o m
in
i m p l e m e n t e d )
f e l l o w
t o
w h o
for
a p p l i e d
W i t t ,
a n d
e n d
o b s t a c l e
his original price
d u r i n g
m a r r i a g e s ,
a n d
W i t t ,
( n e v e r
a n d
Leibniz'
selling
his
r e c o g n i z e d
m o r t a l i t y
E d m u n d
at
f u n d s ,
h i m s e l f
q u i c k t o
a n d
f a s h i o n
( D e
w e r e
annuities,
b e t w e e n
m a y o r
t h e
tickets
i m p r o b a b i l i t y
w i n
d e s p e r a t e
t h e o r y
r e s p e c t a b l e
D e
W i t t
o n
o f
as
a
c h a n c e .
annuities,
data
l o t t e r y
classical probabilists
i n s u p e r a b l e
s c h e m e
avail
w e r e
1 6 9 3
p u r e a n
lottery
T a l l e y r a n d
r i s k / b i g
n e g l e c t e d
i n t e r e s t i n g
J o h a n n
r e c o r d s
E u r o p e
m o r e
a regular
t h e
at o n c e
m o r e
d o w r y
p e r i o d
n o n e t h e l e s s against
t h u s
H o l l a n d
a n n u i t y
t h e
b o u g h t
w a y .
rigidity if
g o v e r n m e n t s
3).
futures,
o f
t h e
g a v e
still g r e a t e r
n a t i o n a l
rational
o r
w h o
t h e
h i g h
in p r o b a b i l i t y
Bernoullis
t h e s e
a
t h o s e
in a n y o t h e r
g i v e n
B e r n o u l l i
inheritance,
H o w e v e r ,
B u t
s c h e m e s
against
F r e n c h
o f g a m b l i n g ,
o t h e r ,
o f
r u i n o u s
w a s
c h a p t e r
applications:, w i n e a n
t h e
b u y i n g
t h e m s e l v e s
a t t e n t i o n
o f
this
m a t h e m a t i c s
w r i t i n g s
6 ) .
l e s s o n s
1988,
F e e l i n g in
that
either
( D a s t o n ,
majority
w i n n i n g
t h e
1 7 8 9 , p.
f e w
o f
criticizing
f a v o r e d
a r g u a b l e
the
p a y - o f f
alter their s i t u a t i o n
in
(Talleyrand,
fluence
a n d
i m p r o b a b i l i t y
b e e n
least
n o n p r o b a b i l i s t i c
m a r g i n ,
c o u l d
probabilities
all
b y
o v e r
tables
like
g a m b l i n g ,
a n d
e m p i r i c a l
P r o t e s t a n t
m o r t a l i t y p a s t o r
o f
1 6 9 3 ) . t h e this
f o r m w a s
o f
d e m o g r a p h i c
i n f o r m a t i o n
that
data
o n
g o v e r n -
Downloaded from https://www.cambridge.org/core. Durham University Library, on 03 Oct 2018 at 11:16:36, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.003
Classical
m e n t s
h a d
b e e n
s i x t e e n t h theory.
century,
E n g l i s h
w e d d i n g s , the
k e e p
for
a n d
a n d
law; a n d
t o
r e q u i r i n g
ages
at
t o
d e a t h
table
s u c h
data:
in
n i n e t e e n t h
t h e
t o
law.
B y
e m a t i c a l
literature
empirical life
that
o n
w e r e in
t h e
o f
a n d
t h e
e n t e r e d
t o
significance
c o m p u t e h a d
n o
k n e w i n g
in
"the
1 6 9 9
b e t w e e n
o f
c o n t e s t e d
o f
t h e
H u y g e n s ' o f
o f
b e y o n d
H u y g e n s '
m a t h e m a t i c a l
t h e
t o
statistics m o r t a l i t y
u s i n g
his
" s h o p p e
1 6 5 7
treatise:
p r o b a b i l i t y
t o
for
o n
his that
O t h e r
t e c h -
c o n t e x t
t h e
o f
m a t h -
G e r m a n , t h e
a n d m o s t
m e t h o d s T w o
a d d i t i o n
a n d c o n -
t o
d e f i n i t i o n
direct
w a s
t h e
G r a u n t ' s
a n d
in
t o
the o f
curve.
p o s i n g
fledgling
t h e
o v e r
first o f
o f h o w
t o
( G r a u n t a n d
a century, w a s
t h e
t o
calculus
p r o b l e m
table.
statistics
a n a l o g y
a m o n g
A r i t h m e t i q u e , " for
p u t
a sizable
his
trust:
L o d e w i j k
table
t h e
probabilists.
p r o b a b i l i t y
Christiaan
life"
o t h e r
as
e m p h a s i z e d
p e r h a p s
probabilists,
b r o t h e r
G r a u n t ' s
w r o t e
b y
the
c l a i m i n g
F r e n c h ,
a l t h o u g h
c e n -
i n t o
probabilistic
w a s
dif-
g a m b l i n g
also
e x i s t e d
D u t c h ,
w o r k s ,
w e l l
i m m e d i a t e l y
n e w
t h e r e
in-
f r e q u e n c i e s
M o i v r e
t h e
his
several
f r o m
to
a s s e m b l e d
life e x p e c t a n c i e s .
( 1 7 2 5 )
t h e s e
until
annuities,
D e
b y
h a d
readers,
b u t
statistical
o f
1 6 0 3 ,
t h e y
a n n u i t i e s w i t h i n
Annuities
m a t h e m a t i c a l
e x p e c t a t i o n
m a t h e m a t i c s
n o t h i n g
h e
a n d
c e n t u r y ,
m o r t a l i t y
d e a t h
H a l l e y
until
c o n s t r u c t o f
w h i c h
a d v a n c i n g
in E n g l i s h ,
o f
s h a p e
a n d
d e a t h
G o v e r n m e n t s
b e h i n d ,
d i f f e r e n t
s e r v e d
e x e r c i s e d
w h i c h
close
o f
still v i e w e d
of
particular
Christiaan
a n d
best
subject
Treatise
e x p e c t a t i o n .
c h a n c e ,
t h e y
s o m e t i m e s
d i l e m m a
t h e
w a s
t o
bills
o f
G r a u n t
figures. w i t h
mortality
cause
w h y
his
price
i g n o r e d
is
b e f o r e
T h e s e
c o n t i n u o u s l y
T h i s
t h e s e
B e r n o u l l i
d i s t i n g u i s h e d
e x p e c t a n c y
g r a s p
t h e
bills o f
a n u m b e r
birth
status
a n y
t h e
p r o b a b i l i t y
outbreak.
1 6 2 5
o f
christenings,
a n d
w h y
contracts.
calculating
m a t t e r s
o f
m e a n s
a g e
h y p o t h e s e s
F r a n c e
t h e m i d - e i g h t e e n t h
e x p e c t a n c y ,
Life
aleatory
N i c h o l a s
a n d
read
t h e
i n e q u i t a b l y
M o i v r e ' s
issues
w i t h
t h e m
o f
u s e
like
m a t h e m a t i c a l l y
in
1728.
t h o r o u g h n e s s
u n h e s i t a t i n g l y
k i n d s
c o n t r a c t
c e p t u a l
a n d
1 9 7 1 ) .
s a w
k e p t
w a r y
( M e u v r e t ,
in s u c h
a s s u m p t i o n s
w e r e
register
n i q u e s , a n i n d i c a t i o n
D e
H u d d e ,
bills,
n o t
m a t h e m a t i c i a n s
Latin.
L o n d o n
w i t h
p u b l i s h e d
n o t
half
r e c o r d
o f a m a j o r
regularizing
d i d
table
e q u i t y
a n d
first
d o
t o
o f
after
in
n a t i o n s
traditional m e t h o d s
that
r e c o r d e d
w a y ,
r e p u t a b l e
m o r t a l i t y
first
t h e
a n d
p r o o f
o n l y
bills w e r e
t h e
t o
o r d e r e d
L o n d o n
a n d
led
M a t h e m a t i c i a n s
m o r e
w e r e
city o f
since
n o t h i n g
official
death,
L o n d o n
alacrity
c e n t u r y
probabilities,
o f
t h e
a n d
S w e d e n
tral E u r o p e a n
the
g u e s s w o r k
H u y g e n s
greatly
cause
f r o m
h a v i n g
p r o v i d e
21
register
d e a t h s as a w a r n i n g
w e r e
s h r e w d
m o r t a l i t y c l u d i n g
a n d
t o
parishes
1 5 6 2
track o f p l a g u e
than plague. T h e
f e r e d
t o
as early as
o t h e r
resort
r e a s o n s
burials
o n l y place
a n d
parishes
F r e n c h
listed
probabilities
a p p a r e n t l y
the
a l m o s t
h i m s e l f
b o r r o w all in
o n e
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22
Classical
direction.) definition t h e
L o d e w i j k ' s o f
g i v i n g
find
o f
o f
p e o p l e
years
t h e y
o n
a g r a p h
t h e
years.
a g e
D r a w i n g
matical
a n d
m e t h o d
for
w h e r e p p .
w h i l e
H i s
W h e n e q u a l
the
i n d e e d
t h e
lives.
a n
s o
proclivity
lack
data
blithely
f o r c e d
years
regular
c u r v e
Breslau
table
rather m o r e as
p r o g r e s s i o n .
tician N i c h o l a s
m a j o r i t y
b e l i e v e d
t h e m
t o
W h y n o m e n a
o f
for
in
m o r t a l i t y o f
e q u a l
w i l d
fluctuations
o f for
L o n d o n , study,
o r a
w a r
fact
o n
that
t o
a n d
o t h e r s
d e c i d e
a b o u t
11
m a t h e -
L o d e w i j k ' s for
w a g e r s ,
w h i c h t h e
1898,
m e t h o d
e i g h t e e n t h
L o d e w i j k ' s
w o u l d
m e t h o d ,
s o
G e n e r a l e
o n
h a v e D e
that
o n
regularity.
t h e
statistics
-
n o t
a n d
faith
a
H a l l e y
c o l l e c t e d
t o o k
o f
in
G r a u n t ' s
w h i l e
b e e n
t h e
d i d
g r o u n d s
h i m ,
for
s u c h
a
Halley's
a n
arithmetic
D u t c h
m a t h e m a -
" n a t u r e
a
t h o u g h
a p p r o x i m a t e d
d o e s n ' t
1898,
that
a n d
t w o
initial
p.
89).
m a t h e m a t i c s
I n d e e d ,
t h e s e
itself.
a s s u m p t i o n
s a n g u i n e
-
o f f
m o r t a l i t y
M o i v r e
N e e r l a n d a i s e ,
w r o t e
s u c h
his
w a r n e d
data
m o r t a l i t y
surely
for
that
their
t h e
carried
lives,
calculation
e n c o u r a g e d ,
w e r e
intervals
a l t h o u g h
B r e s l a u
d e a t h
single
a s s u m p t i o n s
o n
e x a m p l e
w h e n
a s s u m e d
w i t h
T h u s
-
o n
t h a n
b e e n
t o
p l a g u e ,
t h e
a s s u m e d
i m p o r t a n c e
m y s t e r i o u s .
d u e
a n n u i t i e s
c u r v e s
h a v e
practical
is s o m e w h a t
-
t o
belief
o f
t o
B u t
t h e
m o r t a l i t y
w a s
fortiori
listen
a l m o s t
for
a
s u b j e c t i n g
analysis.
s h o u l d
w r e c k s
g r a p h
N e e r l a n d a i s e ,
t i m e
o f
it
c o l l e c t i n g
m a t h e m a t i c a l
s h a p e
ease
w h o
its
m e t h o d ,
t h e
o w n
t h r o u g h o u t
in e q u a l
c o n f i r m a t i o n
t h o s e
p e o p l e ,
b e t w e e n
his
G e n e r a l e
w i t h
data
five,
for
a v e r a g e
o f
d i e d
that
p r e f e r r e d
p r o g r e s s i o n ,
h a d
( S o c i e t e
implicitly
p r e c o n d i t i o n
for
d o
closely.
t h e
u s e
has
a n d
difficult
a certain
s w e e p i n g
t h a n
b y
multiply
r e c o m m e n d e d
issue
p o p u l a t i o n
s u c h
aleae:
a different
figures:
c o h o r t
Christiaan's
n u m b e r
p r o p o s e d
prevailed,
t h e
luck
total
paralleled
e x a m p l e
h a d
s i m p l e
S t r u y c k
t h e
o n
Christiaan.
all p r o b a b i l i s t s
s u p p o s i t i o n s "
g r e a t
for
M o i v r e ,
empirical
N o t
b r a c k e t s
( S o c i e t e
o v e r
t o
that
a g e
C h r i s t i a a n
it m o r e
a n s w e r
D e
for
p r o c l a i m e d
t w e n t y
t h e
m o r e
nature's
in
b y
r o u g h l y
f o u n d
a r i t h m e t i c
h a d
ratiociniis
original
c o u n t e d
p a t t e r n e d
G r a u n t ' s
e q u i t y
c u r v e
s a m e
De
d i v i d e
t h e
that
w i t h
o f
Halley,
f o l l o w
o f
that
s i d e d
in
f r o m
o f
w h e r e
m o r t a l i t y
g a v e
d o i n g
h a l f
w r a n g l e d
p r o p o r t i o n
m e t h o d s
a n d
d r a w n
B e r n o u l l i
M o i v r e
closely
Christiaan h o w e v e r
successors a n d
w a s
G r a u n t ' s
e x p e c t a t i o n ,
all
N i c h o l a s
D e
joint
w h i c h
w a s
o f
survive,
a d i s t i n c t i o n
w h e n ,
c e n t u r y .
o u r
e a c h
h a d
m o r a l
p r o f i t
a p p l i e d
for
in
annuities,
5 7 - 6 9 ) .
o n
b y
h e
s o l u t i o n
e x p e c t a t i o n
18 years, 2 m o n t h s .
b a s e d
a n
probabilistic
n u m b e r
n u m b e r
o w n
probabilities
h i g h
greatly
like
It w a s h u g e seas.
a n
regular
t h e
a g e
i n c i d e n c e in w h i c h
c o n f l a g r a t i o n s Y e t
i n f l u e n c e d
o n l y t h e
a n d
n o t o f
o t h e r
fires
all w e r e like
m o r t a l i t y applications
t h e w a s o f
o r
p h e s h i p -
subject
t o
G r e a t
Fire
s i n g l e d
o u t
p r o b a b i l i t y
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Classical
t h e o r y data
d u r i n g
r e v e a l e d
o n c e
s u c h
t h e
D e r h a m d e s i g n
in
t o
rates o f
E n g l a n d
G o d ' s
t h e o l o g y
w e r e
m o r e
d e a t h ,
s o u r c e
for
M o i v r e ' s
t h e
p i o n e e r i n g
d e m o g r a p h i c
t h e o l o g y
" A n A r g u m e n t
w o r k
o n
o f
later,
e x p a n s i v e
e x p r e s s i o n
in
S u s s m i l c h ' s
for
h a n d i w o r k
in
h u m a n
in
t h e
asserting T w o
m o r t a l i t y
s i m p l e
regularity
a n d
its a n c i e n t
at t i m e c o m e s
p r i n c i p l e
o f
in a safe passage?
w a s
a n d
W a s
s e a w o r t h i n e s s
a g e
w a s
t h e
n o t
bility n o r
t h e
b e l i e v i n g
m o r t a l i t y
w i t h o u t
h o w
t h e b u t
t o
a n d
d r a w i n g
T h e
recur-
for
m e m o i r
R e g u l a r i t y
e x t r e m e
d e m o g r a p h i c rates. t h a n
b e e n
natural
1 7 1 0
its m o s t
t h e
v o g u e
C o n s t a n t
o f
t h e
a n d
p r o o f s
S e e i n g
G o d ' s
r e a s o n
o t h e r
p r o b l e m s ,
o r
t h e
n o t
regular.
that
for
t h e o r y . t h e
o f
t h e
o b s e r v e r s
m i n d s
a n
o n e s ,
w a s
t h e
m o r e
t h e
A d a m o t h e r
susceptic r e w ,
state
t h e
h e a v i e s t
o f
t h e
a g e
as
c u t t i n g
inevitafor
r e c o g n i z e d that
s o u g h t
features
m a y
a p p l i e d e d g e
their p r o b a b i l i t y i n t e r e s t e d
O f
h e a l t h
c o n d i t i o n s h a d
in t h e
quantified?
t h e s e
particularly
still l e a r n e d w e r e
in
w a s
for
in
N e i t h e r
sufficient
q u a n t i t a t i v e
p a y m e n t s ,
b e
m o r t a l i t y ;
H o w e v e r ,
mortality,
m o s t a n d
t o
d e a t h
t o w h i c h b y
a g e
for
that w e i g h e d
factors
o f
b u t
c h o i c e
c o m e
captain
w e r e
C e n t u r i e s
a g e
t o
o f
p o p u l a t i o n
m a t t e r e d
f o r
inevitability,
variable
o b v i o u s
s e a s o n
t h e s e
d e a t h
B e g i n n e r s b e s t
t h e
easily n u m b e r e d .
particularly
o f
a n d
c a n d i d a t e
s h i p w r e c k ,
o f
easy
t h e
c h o i c e
c o n c l u s i o n .
r e v e r s i o n a r y
b u t
s o
character
o r
the
that
o f
r o u t e
a n y o f
s o
its
n u m e r i c a l
fire
a g e
n o t
trade
p r o m i s i n g
c a t a s t r o p h e s :
d u l y r e c o r d s
w e r e
p o s s i b l e
m a t h e m a t i c s
search in p r o b a b i l i t y g a m b l i n g
o n e
b e
m a d e
B i b l e
w e r e
o n l y
s u g g e s t i v e .
a n n u i t i e s
t h e
a
trace o f
Halley.
it a m o r e
e s c a p e
e x p e r i e n c e
vessel, o r
a g e - l i n k e d
t h e
t h e
t h e
h a v e
1 7 5 0
is
rather
e n u m e r a t i o n
c u s t o m
material
e v e r y w h e r e ,
B y
it
A r b u t h n o t ' s
c o n t i n u o u s
m i g h t
variables
regularities b e e n
in
A l t h o u g h
a n d
o f
f r o m
h a v e
m o r t a l i t y
o t h e r
t h e
o n e
l o n g
it
A n d
also a candidate,
b o t h
m a d e
a c o m p l e t e
b u i l d i n g
fires?
h a v e o r
w i t h
l u c k
I n d e p e n d e n t it
result
fires
variable: e v e n
W a s
t o
c o u r s e ,
t h a n
c o n n e c t i o n
possible,
s u r v i v e d .
bility
s e e k e r s
all. T h e r e f o r e
i n d e p e n d e n t
t h e
a r g u e d
regularities
is n o
t h e
W i l l i a m
t o
there
o n l y
fit
s e e m
r e c e i v e d
a n d
t o
like
w h o
n o t
c o m p e n d i u m
natality
w a s
d o e s
f r o m
a n d
c o l l e c t e d
adjusted
alleged
available
regularities.
o f d e a t h . W i t h t o
e v e n t s .
c u r v e
T a k e n
t h e
t h e o l o g i a n s
u p o n
w i t h J o h n
that
data w a s
G e r m a n y
G r a u n t
S e x e s , "
aspects o f m o r t a l i t y m a y
for
in
case
o f t e n
N a t u r a l
probability,
w o r k s
B o t h
t h e
regularities.
P r o v i d e n c e
o f
t h e
w a s
t h e o l o g y
s u c h
in
h a n d
B i r t h
it
S u s s m i l c h
O b s e r v e d
G o d ' s
t h e
closely.
in
b e g a n
for D i v i n e
a n d
natural
b e l i e f
n o t
contrary,
eagerly seized
b u t
in D e
in
t h e
a n d J o h a n n
23
It w a s
p o s i t e d ,
p r o v i d e n c e
birth a n d
t h e m e
century.
regularities; o n
regularities
original
ring
e i g h t e n t h
regularities
h y p o t h e t i c a l
t h e
t h e
probabilities
in t h e
o f
t o re-
f r o m latest
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24
Classical
m o r t a l i t y t h e
table
Paris
t h a n
in
w h a t
" a c a d e m i e s
d e
jeu." A n n u i t i e s
s u r a n c e
-
s o
as h e
l o n g
regular his
t h e
a n n u i t a n t (or
a t t e n t i o n
tract
that
m o s t
r e f i n e d
t o
o b s e r v e d
u s e
that
" o f
T h e
for
their
"the
clerks
w o r d s
a p p e n d i n g
a n d
t h o u g h
the
aleatory m a k e ling
t h e m s e l v e s trade
in
a n d
w a s
sellers
p r o b a b i l i t y
glance
o f
m a t i c i a n
o f
L o n d o n
i n s u r a n c e M o s t
regardless
o f
m a n u a l s
i n f l u e n c e
o f
s o
a n d
w e r e
reluctant
in
the
o f
avail
t h e m
o f
vol.
o f
G r e a t
II, p p . as
t o
v i i -
w e l l
t h e
i n t o
calculations.
probabilists
A l -
o t h e r
h o p e d
r e f o r m i n g
as
barely
m a t h e m a t i z i n g
b y
t h e
e q u a t i o n s
o n e r o u s
t h e
a n d
D o d s o n
affairs
t h e
c o n -
rationalizing
estates"
m a n u a l s
f r o m
t u r n e d
1 7 5 3
1 7 7 5 ,
their
t h a n
b y
w i t h
a n d
T h e i r
t h e
t o
bust-
a n d
a n
that
t h e
o f
t h e m s e l v e s
d i d
t a k e
a
a n d
o f
size o f
risk
o n
e i g h t e e n t h insurance, t e c h n o l o g y
b y
for
24ff).
f r o m
flat
o f
a g e
statistics
a n d
practice
l a w
o f
t h e
w i t h o u t rates, d i d
s o
m a t h -
o f
their m e m b e r s h i p . t h e
t h e
m a t h e -
years
t h e
first
p p .
c h a r g e d
f r o m
insur-
t h e
1 9 6 2 ,
a c c o u n t
m o r t a l i t y
o f
S o c i e t y
t w e n t y
first
t h e
s c e p t i c i s m
s o m e
at
A m s t e r d a m
Y e t
t h e n
( O g b o r n ,
p r o f i t i n g
t h e
s e e m s
a s s o r t m e n t
p l a n s instead
f r o m
t h e o r y t h e
1 7 6 2 ,
i n t e r e s t e d
a n d
E q u i t a b l e
a n o t h e r
available
Far
o f
L o n d o n
universal
w e n t
m o r e
a d v a n t a g e .
insurer
a l m o s t
n o
i n d i f f e r e n c e
a m o t l e y
in
e i g h t e e n t h - c e n t u r y
w e r e
percolating
life i n s u r a n c e f e w
large,
i n s u r a n c e
o n l y
a n d
subject.
m o s t
a n d
this sort, t h e
dealers in a n n u i t i e s a n d t o
real
m e n
r e a d e r
B y
life
established
c o n s u l t i n g
for
for
c o m p e t i t i v e
m a t h e m a t i c a l nil
t h e
p r o s p e r o u s
annuities
for
t h o s e
t h e
o f
in
u p o n
aleatory
a b o u t
in-
m a k e s
also
statistics
business:
( D o d s o n ,
t h e
societies strictly l i m i t e d
t h e
effectively
o n
w i t h
o f
in
p a y m e n t s
beneficiaries
A r m e d
set
o f life
h o l d e r
D o d s o n
translating
g a m b l e r s .
c o m m u n i t y ,
w i t h o u t
t h e s e
W h y
o f
m e t
a n n u i t y
age,
n u m b e r s ,
t h u s
w a s
p r o j e c t
imitators.
e m a t i c a l
t h e
e n t e r p r i s e
rather
t h e
J a m e s
insurance,
a n d
particularly
Lives,
I n d e e d ,
a p p a r e n t l y
t h a n
b a s e d
D o d s o n
spare
realized.
s c r a m b l e d
m a t h e m a t i c a l l y
his
o r
lives."
p u r v e y o r s
s c h e m e s
t o
p o l i c y
variety
p i t c h e d
p e r h a p s
annuities
t h e o r y
w h e r e
A s s u r a n c e
o f
t h e
s e c o n d
h a n d b o o k s
m a r i t i m e a n d
regular
p a i d
part
p r e v e n t e d
s e l d o m
inexplicable,
m a r k e t s
t o
for
b i g
arithmetic,
tables
u s e f u l
w a s
lives"
T h e y
o n l y
like
o f
w r o t e
statistics
"values
h o p e
b u y e r s
a n c e
o f
c o n t r a c t s
T h a t
in
w i t h
lack
v a l u e
r e t u r n
probabilists
it
W h i t e ' s
o b v e r s e
like
tables.
like
t h e
lives;
this
t h e
clubs
s i m p l y
in
s u m
g r e a t e s t
colleagues.
n u m e r a t e
s u m
o f
A n d
t h e
m a t h e m a t i c i a n s
treatises
w e r e
a l u m p
t e c h n i q u e s , taking.
o n
L o n d o n
p e r s o n )
m o r t a l i t y
m u c h
d e p e n d e d
for
in
m a t h e m a t i c i a n s
o f
risk
l u m p
m a t h e m a t i c s
analytic o f
a
o n
d e s i g n a t e d
r e t u r n
t h e
w e n t
p a y s
s o m e
m a d e
b u s i n e s s
Britain
in
H e n c e
their
viii).
s o m e
p a y m e n t s
d e a t h .
t h e
probabilities
risk
large T h e w a s
century. n o t
t o
m e n t i o n
c u s t o m - m a d e
g a m b l e r s , ( a n d
o f t e n
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Classical
c u s t o m - w r i t t e n )
for
o f
m i n d l e s s
irrationality:
s u p e r i o r i t y r e c o g n i z e
o f
in
t h e
this
n e w
probabilistic
"the
P r o j e c t i n g
e f f l o r e s c e n c e c r o o k ,
b y
Lotteries, w h o
a n d
l o t t e r y
m a y
T h e
b e
b y
t h e
cash
e v e n
six
v e r y
v e r y
s u b v e r t e d
t h e
o f
t h e
lifetime
o f
life
a l m o s t
a celebrity
n o t
p e r s o n a l l y
o r
a n c e
t o
resisted e m a t i c a l
f u t u r e
policies
w e r e t h e
o f
o f
l o t t e r y
p r o b a b i l i t y
still
a n d
a n d
X V ' s
it
a
a c q u i r e d t h a n
o u t m a d e
v e r y
legal
c h e a p l y
n e e d
t h e
w a s
o f
q u i c k financial
a n n u i t y
as
t h e
o f
a
b u y e r
-
century. t h e
mistresses.
in
life
o f
T h o s e
a l m o s t
all
flourish
in
life Sir
w h o
life
e x a m p l e ,
t o
L o n d o n
t o
p e r s o n ,
for
b a n n e d
c o n t i n u e d
f r o m
earlier, a third
a
w e r e
also d e d i c a t e d
a n d p o s s i b l y life
5 %
t h e r e -
T h e s e
o f
bit
t e c h -
m o r t a l i t y statistics
as little i n t e r e s t e d
insurR o b e r t
t o o k
in p r o b a b i l i t y
o u t
t h e o r y
tickets.
d e e p e r
r e a s o n s
t h e o r y o f risk. statistics,
t h e
t h e probabilists.
w h e r e
e i g h t e e n t h
L o u i s
in
1 9 2 8 ) .
t h e
w i t h
s o l d
seller,
s u m m a r i l y
e v e r y t h i n g
m a r i t i m e
o n
t h e
usually
m a t h e m a t i c a l
c o n t i n g e n c y
o f o n
w e r e
o t h e r ,
annuities,
o f
b o o k
it w a s
o n
t h e y
t h e
t h e m .
g o e s
interest,
p u r p o s e
c e n t u r y ,
at
o f
s o l d
t a k e n
w e r e
at this t i m e
a c q u a i n t e d
s u c h ,
o f
t h e
b u y e r , a n d
a w a g e r
E n g l a n d ,
m o s t
s u c c e s s i o n
p u r c h a s e r s
T h e r e
bling,
m a d e the
A s
e x c e p t
t h r o u g h o u t
b e t t i n g
t h e
s o v e r e i g n .
c o u n t r i e s
offices
W a l p o l e
a
a l w a y s
o f
m e r c h a n t s
loans at m o r e
( C a m p b e l l ,
s i x t e e n t h
w a s
rate
o r
Societies,
o n e
b u t
t h e
h o o k
probabilistic
a n n u i t i e s
annuities
t h e
p o l i c y
t h e
original
t h e
after
h i g h e r
e n d s . S i n c e
f o r m
t h o s e
for
t e r m s
b y
his
t o
l o s i n g
n o t
i n v e s t m e n t ,
L o n d o n
t h e
life
w a s
o f
c e n t e r s
called
F r i e n d l y
w a s
n e g l e c t
o f
M a n y
o n
u n f a v o r a b l e
clearly
i n s u r a n c e
o f
testifies
i m p r o v e
life
c e n t e r s
D e f o e
( 1 6 9 7 )
inertia
t o
t h e
e v e n
contract:
p u r c h a s e )
D a n i e l
b u t
difficult
also
a n d
d i f f e r e n t
E u r o p e a n
as
t h e
w e r e
case
m a n i f e s t
b u s i n e s s
c u c k o l d r y ,
f o r m
m u c h
h o w e v e r
L o n d o n
Life i n s u r a n c e
cardinal
s u c h
a
t h e
T h e
s o relevant.
o f t e n
this
o f
at
is
A s s u r a n c e s ,
g e n e r a l
u s u r i o u s .
t o
facie
8 - 9 ) .
n o t
i n s u r a n c e
a
t h e
t h e m
w h i c h
a n d / o r
p p .
a n d
a n c i e n t
l o a n s
years'
o n
a n n u i t i e s
a n
n a t u r e
o f p e n s i o n
t h e r e f o r e
w e r e
1 6 9 7 ,
a prima
Projects
S t o c k - j o b b i n g ,
e x p l a i n i n g
d e c l a r e d
a r r a n g e m e n t s k i n d
w h i c h
essentially
at
m o n e y
in e i g h t e e n t h - c e n t u r y
aleatory
( m o s t l y
m a k e
It
s e e m s
i n n o v a t i v e
on
things,
o f
b l i n d e d
Essay
m a n y
A n n u i t i e s
w e r e
o w n
s o
applications.
fire,
n i q u e s .
after
t h e s e
against
t o w a r d s
w e r e
t o
d o
A m s t e r d a m ,
i n s u r a n c e
in
f u n c t i o n
a n d
his
S t o c k s ,
a c c u s e d
t o
b o o m i n g ,
( D e f o e ,
c o n t e x t
interest
a n d
25
m e t h o d s .
L i k e "
f u r t h e r
a n e w
t h e
in
s c h e m e s
the
i n v e n t e d
m a t h e m a t i c a l
research
" B a n k s ,
failure
c o n s e r v a t i s m
L o n d o n
A g e "
o f
T h e i r
d e s c r i p t i o n
e i g h t e e n t h - c e n t u r y for
t h e m ?
probabilities
basis
o f
W h e r e a s
L o n g
parties
i n s u r a n c e
w h y
practitioners
b e f o r e
t o
aleatory
h a d
a g r e e d
i n t u i t i o n s t h e
t h e
that
ran
t h e
a d v e n t
c o n t r a c t s u p o n
t h e
directly
dealers in risk a c t e d
o f
o f like price
risk
m a t h g a m o f
c o u n t e r
as if t h e
a t o
w o r l d
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26
Classical
w e r e
a m o s a i c
ticular
o f
i n d i v i d u a l
c i r c u m s t a n c e s
p r o p o s e d
a w o r l d
t h e
data
right
F o r
t h e
r e q u i r e d
a n d
t o
e m a t i c i a n s o u t
in
trade t h e
-
w i n t e r
r u i n e d
o n
m a r i t i m e t h e y
insurer
c o n d i t i o n
o f
t h o r o u g h o n
t o
annuities
astatistical; case
t o
t h e
e q u a t e d
n u m b e r s
i m p l i e d
r u m o r s
o f
that
m o s t
that
o f
t h e y
if
at
c o n t r a c t s
m e n t
t o o k
their
all
w e r e o v e r
interest
o f in
t h e
ture
tradition
a l o n e
carried
f o r
t o
o f
t i m e
o f
t h e
n e w
h a d in
jurists.
e v i d e n c e , o w e d
t h e
d i v i n e
N
area
D
is
u r g e
T h e
W r i t e r s s i m p l y
i n d i v i d u a l
c h a n g e s
certainty, apparent t h e o r y
t h e r e f o r e a n d
a
p r a c t i t i o n e r s
w i t h the
a n d
n o t
t h e
t h e
t h e flux.
o f
p e r h a p s
t h e
in
beliefs
risk n o t t h e y
o f
C A U S E S
a p p l i c a t i o n
T h e y
particularly m u c h
t o
t h e
historical
S e v e r a l
o f
t o
cargo,
u n f o r e s e e n
t e c h n i q u e s
A
t h e
m a t t e r s
w a s
o n
t e r m .
o t h e r
1 9 8 7 ) .
f r o m
c l a s h e d
it
c o l d
e v e r y
t h e
risk
t i m e
their
j u d g m e n t
m a t h e m a t i c a l
o n l y
I n
g o o d
f o c u s
e q u a t e d
a n d
o n
e x c e p t
a c c e p t
t h e
subject.
its
b r o u g h t
w o r l d ,
o f
risk in question.
l o n g
t h e
a n o t h e r
s i x t e e n t h - c e n t u r y
r o u t e ,
o f
m a t h -
u n u s u a l l y
p r e m i u m s ,
the
o n e
en
thirty-year-old;
advice
t h e
o n l y
t h e
s t u f f
t h e
t h e
O n l y
in
W h a t
underlying
n o t
w a s
that h e l d
ailing
practice
t h e
also
v e r y
t h e
L e v a n t ;
o f
price
a n d
life insurance,
regularities
t h e
w i t h
risk
as
detailed
etc.
T h e
o f
t h e o r y
cancel
s e a s o n ,
c o u l d
( D a s t o n ,
miracles.
a p o l o g i s t s
ture
t h e
pirates,
a c c e p t e d
e x a m p l e
C a t h o l i c a n d
o f
probabilists
risk
inspirations
spectacular lore
o f
the
e q u i p p e d
w o u l d
t h e
t h e
subject
E V I D E N C E
t o p r o b l e m s
C h r i s t i a n
t h e
revealed
1 . 7
A l t h o u g h
t h e
o f
par-
o f
rules
A l t h o u g h
full
n u m b e r s
c o n c e p t i o n
slowly,
early o n
w e r e
minutiae
large
c o n d i t i o n s ;
n e w
probabilists
t o
v i n t a g e .
uncertainty,
practitioners
A l e a t o r y
w a y
antistatistical
w i t h
surprising
t h e
that
o u t l i v e d
p o s i t i v e l y
large
s o
w h o
o n
t o
m a t h e m a t i c i a n s
r e c k o n i n g .
v i e w e d
w a s
it
case
w i t h
a c c o u n t
these
t h e
j u d g m e n t
year's
t h e
m a t h e m a t i c a l
cases w i t h
o n
a c c o r d i n g
that a n y o n e
i n d i v i d u a l
insurance
ship,
n e g l e c t
a
in
advice.
crucial
r e q u i r e d
beliefs, a n d
p r a c t i t i o n e r s
m u t e
business,
t h e
a n a l o g o u s
t i m e
the
in
a p p r a i s e d
e x p l o i t .
g a v e
t h e s e
F o r
t h e
full
versing in
t h e
as local p e r t u r b a t i o n s
w e r e
t h e
in
b e
regularities
c o u l d
replace
that
t a k e
t o
risk, a c c e p t i n g
pirates
that
particular,
h a n d
s i x t y - y e a r - o l d b y
e a c h
stable
s e a s o n e d
run,
w a y l a i d
m a n u a l s
t h e
t o
replace
spry
o f
c h a n g e
h a d
l o n g
the
s h i p
s i m p l e ,
d i s m i s s e d
t h e
o l d
f o r m u l a e
p r o f o u n d
a n d
cases,
a n
p r a c t i t i o n e r s
o f values. T h e y masse,
o f
b y
probabilities
t h e
o v e r faith,
f e d
t h e
t h a n
t h e
relative
century, w e i g h t
a n d
t h e
classical
their
a t t e n t i o n t e s t i m o n y .
h o w e v e r ,
legal:
c u r r e n t
P r o t e s t a n t s
i m p r i m a t u r ,
the
o f w i t n e s s
c o u r t r o o m ,
s i x t e e n t h
t h e
t u r n e d
t h o s e
rather
s t r e a m s late
also
that
o f
t h e
their
J u d e o -
E n l i g h t e n -
P r o t e s t a n t
carried
insisting C a t h o l i c s
a n d
b y
scrip-
that
scrip-
retaliating
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Classical
w i t h o n
a s o p h i s t i c a t e d
the
t h e
existence
critical
sceptical torians m a j o r
c o m p a r i s o n
o f
s o m e
c h a l l e n g e their
o f
sources,
errors,
J e a n
m a d e
C a l v i n
w a r n e d Pierre like
B a y l e
t o
e x p l a n a t i o n s a n d
m o t i v e s
n e w
v i s i o n
H u m e ' s
o f
B o t h
biblical
a
t h e
t h e
their
t h e
G o d
"Essay
large
f r o m
t h e
e v i d e n c e
f r o m
C o m b i n a t i o n s
j u d g e ,
c r e a t e d
for
w a s
t o
rational find
a t t e m p t e d
a r g u m e n t
that
r e p r e s e n t i n g mathematica lished t h e
a n
o f
1 7 1 3 , a
w o n d e r
t h e
w h o l e
d i d
o f
s a m e
in
o f
t h e Ars
t h e b y
f o r m s
veracity
p e r f o r m a n c e
probabilist d o o m e d
( N .
Pierre
b y
a n
1 7 1 3 ,
m a t h e m a t i c i a n s
d e
a n d
o f
t h i n g s ;
c o n s i s t e n c y
a
o n
" m o t i v e
o f
w i t h
usu
e a c h
M o n t m o r t
f u n c t i o n J o h n
a
o f
"space" principia
L o n d o n that
p u b -
a n a l y z e d
1 6 9 9 ) .
J a k o b
a t a n g l e d
e x p o -
o f artis
e v i d e n c e
(J.
conjectandi
i n d i v i d u a l 1 7 0 9 , in
t h e
f o r c e s "
t h r o u g h
sorts
o f
t h e
s a g a c i o u s
s o m e
( H o o p e r ,
De
a n d
f l o u n d e r e d .
B e r n o u l l i ,
"infinity
intrinsic
b y
H o o p e r )
b o t h
for
p r o b l e m
probabilists,
S o c i e t y
( 1 7 1 3 )
Bernoulli's
t h e
christianae
G e o r g e
o f
D a v i d
w i t n e s s e s
t h e
a
1 9 8 1 ) .
n a t u r e
o f
o f
f o r g e
( B u r n s ,
internal
Theologiae
conjectandi
o f
t h e
s u s p i c i o n "
R o y a l
a r g u m e n t s
contri-
b e t w e e n
t h e y
m o d e l
natural
m a n y
o f
w e i g h t e d
first
e v e n t s
h e l p e d
o f
t r e a t m e n t s
F o r
history;
e x c e p t i o n s .
o n e
a n d
B a c o n
singular
this t o p i c
e x p e c t a t i o n
N i c h o l a s
for
f r o m
p o p u -
suspect.
natural
b o t h
e v i d e n c e
A t
his
year
t h e y
a n d
a n d
t h e
a
nature,
Francis
b e t w e e n
d e g r e e s .
o f
( p r o b a b l y
( M o n t m o r t ,
t h e
sifted
"velocity
p r o p o r t i o n " past
o n
o f
a t t e m p t e d
c o m p e t e n c e
sorts
H u y g e n i a n
ii-iii).
as
a n d
N e w t o n i a n
" m i x e d "
F r e n c h
e n t e r p r i s e
o n l y
I V
f r o m
a s s u m p t i o n s
N o t
o f
a n d
"true
t h e
t h e
t o
his-
b e c a m e
a n d
past;
t h e
o f
particularly
resort
t h a n
c e n t u r y
f r o m
o p i n i o n
T o l a n d
Plausibility
v a r y i n g
assent"
article
part
IV.
t h e
G o d
s i m p l y
d e r i v e s
d u l y
o f
d i s t i n c t i o n
probabilities.
o f
In
t e r m s
c o m p u t e d
N o
trary
in
" p u r e "
a s s u m e d b e
" d e g r e e s
legal
b o t h
e l a b o r a t e
i m p e l l e d
b e g a n
B e r n o u l l i ,
belief in
i n t o
a n o n y m o u s
p r o b l e m
sition
t o
a n
( 1 6 9 9 ) .
B e r n o u l l i
jure
t h e m
w a s
m a t h e m a t i c a l
t w o ,
o f
rules
a n d
w i t n e s s e s
in
b u t
d o u b t
a t t i t u d e
fable
y a w n s
literature
e v i d e n c e
t h e
w o u l d
t h r e w
o f
w a s
a n d
T o l a n d ,
integrity,
m e a s u r e s
c o n v e r t i n g
C r a i g
o f
fact
for
t h e
miracles
c h a s m
t e s t i m o n y .
n u m b e r ,
o t h e r .
trick
A
v e n e r a b l e
extrinsic
o n e ;
o f G o d
D e i s t
a n d
Intrinsic
t h e
that
E n l i g h t e n m e n t
e v i d e n c e .
o n
m i x
d e b a t e
learned
miracles
M i r a c l e s "
extrinsic
b o r e
o f
r e v e r e d
o n
a n d
that
s e v e n t e e n t h
c h a n g e d
i n t e n t i o n s ; J o h n
t h e
p h i l o s o p h i c a l
c u e
a g e
miracles.
m o r e
this
b e t w e e n
m a r v e l s
idea his
f r o m
the
c o n c e p t i o n s
the g a p
p r o m i s c u o u s
t e x t s
t r u s t w o r t h i n e s s
N e w
t h e
o f C a l v i n a n d o f
t o
that
a n n o u n c e
f a m o u s
b u t i o n s
t o o k
t h e
t h e
o f
biblical
p y r r h o n i s t s
o f
a c c o u n t s
ridiculed
c o m e t s
a n d
27
D u r i n g
e m e r g e d
n e w
sense
d e c l a r e d
against
original.
p r o b l e m .
as w e l l as a h e i g h t e n e d lar
that
t h e
m e t h o d o l o g i c a l
o f v a r i o u s
pristine
h e r m e n e u t i c s
t o
probabilities
in
w i t n e s s ,
c h a p t e r
1 7 1 3
o b s c u r i t i e s "
w r o t e a n d
9 ) . o f f
arbi-
P r e f a c e ) . face
t h e
p r o b l e m s
o f
q u a n t i f y i n g
t h e
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28
Classical
p r o b a t i v e w i d e l y a n d
f o r c e
h e l d
w r i t t e n
m u c h ?
h a n d
-
a n d
i n t o
b u t
h o w
l i n g e r i n g
t h e s e
t h r o u g h
l e g i t i m a t e
f y i n g
t h e s e
r e p o r t s
o f
o f
t h e
m i r a c l e
as
s o a
p p .
9 8 - 9 ) .
t h e
m o r e
w a s
l a w s
t h e far
H u m e
also
for
m a r v e l s
e x t r i n s i c
b y
intrinsic
b o o s t
t h e
t h e
(Price,
a c c e p t e d
H u m e ' s e n c e ,
causes. w i t h
a
n o v e l
c o m m o n p l a c e c a u s e s t h e s i s "
t o
t h e
o f
f r o m
o f
b r o k e
p r o b a b i l i t y
critics,
i d e n t i c a l
g r o u n d
t w o
s o r t s
effects
causes.
u n d e r l y i n g
p r a c t i c e s like
e x p e r i -
s t e m m e d
causes,
m e t h o d t h e
o f
p h i l o s o p h y
c e n t u r y
as
f r o m
p r o b a b i l i t y
it
i n v e s t i g a t i o n :
f o r m e r
P r i c e
e x t r i n s i c
p a s t
n a t u r a l
o f
T h e
a n d
f r o m
a d m i t t e d
o f
t r i e d
belief.
t h e
i n
o f
b u t t r e s s
a n d
e v e n t s ,
p r o b a b i l i t y ,
t o
-
E n g l i s h
this, a n d
m i r a c l e s
r a t i o n a l
1 8 3 7 ,
t h e i r
t h e
a n d
intrinsic
a
a r g u m e n t
like
i n t u i t i o n s
t o
o f
a n n i h i l a t i o n
p o i n t ,
d e r i v e d
as
k e e n e r
r e c o g n i z e d
o f
m a k e
P o i s s o n
( P o i s s o n ,
t h e
o f
t o
e v e n t .
t h e
w a s
z e r o
d e f i n i t i o n
p e r c e p t i o n
g r o u n d s
essay
s i m p l i -
reliable,
a n
s e v e n t e e n t h
f r o m
really
calculation.
b y
s o
late
t o
w e r e
suffice
o w n
p e o p l e ,
t h a t
n e w
J a k o b
t e s t i m o n y ,
i n t r i n s i c
t h e
p h e n o m e n a
I n
o f
a r e
s u c h
o n e ' s
p r o b a b i l i t y o f
n e w
u n d a u n t e d
f o r
t h u s
d e f e n d e r s
d e g r e e s
t h e
drastically
sincere,
e v e r y d a y
classical
c a u s a t i o n .
s o
a s t u t e
t h e
e v e n
r e p e t i t i o n
n a t u r e
a n d
t o
B u t
e x t r i n s i c
o f
t h e i r
Price,
a b o v e
p r o d u c e
p r o b a b i l i s t s
t h a t
d e d u c e d
t h a t
his
a s s u m p t i o n
b r a n c h
m o d e l
effects
t o
o f
m o r e
a p p e a l
2 2 6 - 7 ) .
t h e
i m p o r t a n t H e r e
b y
t h e
s t r o n g
f r o m
g u i l t - b y - a s s o c i a t i o n
R i c h a r d
p r o b a b i l i t y
m u l t i p l i e d
as
H i s
d i v i n e
u n d e r l y i n g
a r g u m e n t
c r u x
e v i d e n c e .
1 8 1 1 , p p .
c o n c e i v e d
a n o t h e r
t h e
u p o n
n e e d
w o u l d
w a s
a
b e f o r e -
t h e
m a t t e r s
o f
t h e
p r o b a b i l i s t i c t o
o f
w e r e
m i r a c l e s
t h e r e f o r e
b a r b a r o u s
b u t
U n i t a r i a n
t h e
p r o b a b i l i t i e s
-
clearest:
r e j e c t i n g
r e c o u r s e
a n d
a d v a n t a g e
i m p r o b a b i l i t y
t h e s e
p r o o f
p r o b a b i l i t y
b e y o n d
w i t n e s s
c o n v e r s e d
s u c h
h o w
t h e o r y .
p r o b a b i l i t y
n o
o n
p r o b a b i l i t y
[ 1 7 6 7 ]
a n d
r e c o m m e n d
h a d
i n t r i n s i c
e x t r i n s i c
t h e
b y
i n d e p e n d e n t
p r o b a b i l i s t
t h e
a g r e e d
b u t
t w o
p r o b a b i l i s t s
w h e t h e r
g r e a t
is
-
o f
w e i g h t e d
h i s t o r i a n s
o f
h a d
It
n u m b e r
b e
t r a d i t i o n
w h o
e v e r y
a
t o
" p r o b a b i l i t i e s "
at
a l m o s t
e x t r i n s i c
t o
h a n d
t h e
o v e r w h e l m i n g as
t w o
m a t h e m a t i c a l
h a d
credible;
o f
a s k i n g
n a t u r e ,
h a l l u c i n a t i o n
a n d
in
o r a l
t e s t i m o n y
classical
his
w a s
jurists a n d
t h a n
A l m o s t
p r o b a b l y
o f
o f
a p p e t i t e
t o
t h e
e v i d e n c e
legal
t h e
t r i e d
o f
i g n o r a n t
p r o b a b i l i s t
t h a t
i n c o r p o r a t e
c a l c u l a t i o n ?
o l d
c o n s i d e r a t i o n s
miracles
w e n t
in
t h e
m i r a c l e s
a m o u n t
c o u n t e r b a l a n c e later
o f
v e x e d
N o
o f
e x c e p t i o n a l
f o r m u l a t i o n
z e r o .
this
t o
e x a m p l e ,
t h a t
difficulties.
a p p l i c a t i o n s
v i o l a t i o n s is
w a s
q u e s t i o n
H u m e ' s
c a p t u r e
P o i s s o n
s u c h
reliable
t h a n
p r o b a b i l i t i e s
M o n t m o r t
T h e
t o
h a d
e y e - w i t n e s s
m o r e
f o r m i d a b l e
B e r n o u l l i a n d
f o r
F o r
m o r e
t h a t
i n f l u e n c e
m a t h e m a t i c a l b y
w e r e
also
h o w
m o d e l .
k n e w
c o u n t e d
t h e y
a b o u t
t h e i r
r e c o r d s
E v e r y o n e
w i t n e s s e s
e v i d e n c e ;
a s s u m p t i o n s
c o m b i n e d
t h a t
o f
probabilities
o f
w a s
a
f r o m " s y n -
m a t h e m a -
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C l a s s i c a l
tician
d e d u c e d
t h e o r e m s
r o a d
t o
n a t u r a l
clear
u n d e r s t a n d i n g
fallibility b u t
a
o f
v e r y
p h i l o s o p h y , a n d
h u m a n f e w
m e t h o d
f r o m
b o t h
C o p e r n i c a n
e x a m p l e
-
v a r i o u s
success
B e g i n n i n g t h e
certainty.
T h i s
t h e
h a l l m a r k
i n g s
w i t h
r e p l a c e m e n t
as
n u m b e r
t h a t
t h e
a c t u a l
in
o b s e r v e d p
t o
t h e
fixed
h i d d e n
t h e
r u n
l o n g
u n d e r l y i n g c a u s e
o v e r
T h i s B a n a l , t h e
t h e
r e s u l t
w a s
b e c a u s e
as
(J. a
m a n
t h e
n u m b e r
r e v o l u t i o n a r y ,
t a i n t y
t o
t h e
c a u s a t i o n
t h a t
u n d e r s t o o d
case,
t h e y
a posteriori
w a s as
p r o d u c e d
l o o s e l y
o f
t h e i r
just
o r
t o t h e
as
all
u p o n
t h e
c o u l d
V e n u s
o f
t h e
b e f r o m
p r o b a b i l i s t s
w h a t
in
m / N
d e g r e e
t e r m s u r n
w h i c h
t r a c t a b l e
a n
t h a t
u r n
filled
r e p e a t e d
t h e
o f
m o d e l
states
infinity,
d r a w -
t h a t
in
t h e
p r o b a b i l i t y
c o r r e s p o n d s
t o
P t h e
c e r t a i n t y .
1,
f o r
balls
t h e
i n
a n y
6
t h e
u r n
r e p e a t e d t o
c o r r e s p o n d s
d r a w i n g s
a
stabilize
t h e
1 9 6 2 ,
t o
g u a r a n t e e a r o u n d
t r i u m p h
b a n a l in
o f vol.
a n d
a
t h e
t h a t
t h e
o v e r
t h e
o f
Ill,
o f
se
p a r t
in
" t r u e "
variability,
t h e
a n d
it
causes.
in
if
L e i b n i z , a n d
b y
s u r e r o f
b e c a u s e
r e v o l u t i o n a r y .
1, p p .
p r o b a b i l i t i e s
necessarily,
results
t o
n a t u r e per
m i c r o s c o p i c
effects
t h e
l e t t e r
o b s e r v a t i o n s ,
d e v o i d
effects
as
=
f r e q u e n c i e s ,
e s s e n c e s ,
causes o f
I V . v ) .
o f
l i n k e d
essentially
c o n n e c t e d
r e a s o n i n g ,
it
t h e
s e v e n t e e n t h - c e n t u r y
t h e o r e m
balls
i n s t i n c t
[ 1 7 0 3 ]
o f
I m a g i n e
f r o m
a d m i t t e d
s o m e
senses,
b a c k
u b i q u i t o u s
u l t i m a t e l y
1 7 1 3 ,
b o t h
effects
effect
a m o u n t e d
c o n f i r m i n g
b e c a u s e
p r o b a b i l i t i e s
b e e n
m o r e
o f
t h e
o f
w o u l d
h i m s e l f
( L e i b n i z ,
a n d
w o u l d
m i x t u r e
b y
)
t h e o r e m
s e c u r e
t h e
g e n e r a t e d
a p p r o a c h e s
results
B e r n o u l l i ,
k n o w s
t o
c o l o r e d
f r e q u e n c i e s
c u r i o u s
c a u s e
6
h i d
t h e o r e m ,
a p p r o a c h e s
|
e x c e e d
in
T h i s
11
a
n u m b e r
w o r k e r s . "
t h e r e
t h e
v a l u e
a s s u m p t i o n
find
will
a p p r o x i m a t e l y
null.
S o m e t i m e s
" c o n v e n i e n t
m i n d
T h e
as
a r e
t h e
will
fields
/)
0.02.
t h e
r e s u l t
o f
t h e
data.
d a t a
h y p o t h e s i s
I n
scientific
m a t i o n . "
t h e
o f
c a n
c o m p a r i s o n s ,
a b o u t
w i t h
e x p e r i m e n t a l
" n o
t o
is
r e s e a r c h
t h a t
i d e a s "
i n d e p e n d e n t
" f e l l o w
n u l l
o f
t h e
a
d e t e r m i n e p ( \
o n e
v a l u e
f u n c t i o n
o u r
as
as
a
level
P e a r s o n
his
o f
t o
o f
s u c h
is u n d e r
h a v e
a b s o l u t e
v a l u e
p r o b a b l e
n o w a d a y s ,
t h e
E g o n
g i v e s
as
h o w
is, w e
d i s c o r d a n t
a n d
t o
| ( t h e
d a t a
/-statistic
significance
a
s u c h
t h e
d i s c o r d a n t
t o
d a t a
this
o f
o f
p u b l i c a t i o n
r i g h t
p r e s s u r e
p r e s s u r e
it actually
level
h y p o t h e s i s
a g e d
t h e
b l o o d
calculate
p r o b a b i l i t y
o f its p r a g m a t i c s .
level,
t o
significance
" s i g n i f i c a n t "
a i m s
b l o o d
a g r i c u l t u r a l
t e x t b o o k s
this
m u n i c a t e d
y e a r
experts
is m i s s i n g
h a d
is t r u e . T h a t
t h a t
e x a c t
t h e
is
n u m b e r
t h e
t h u s
for
h i g h
p o i n t
o u r
c a l c u l a t e d
t h a t o r
null
t h e
statistical
v a l u e
statistical
p r o b a b i l i t i e s
o f
for
s t e p
h y p o t h e s i s
m o s t
a r e
d a t a
w h i c h
d i s c o r d a n t
error
d a y
w i t h
a v e r a g e
/-statistic
T h e
n u l l
t h e
inference
e v i d e n c e .
T h e 2.5.
a
t h a n
p o i n t s
a b o u t
o n
t h a t
h i g h e r
m a n y
i n
The
t h e i r
o f
a n d o f
o f t h e
o w n
1 9 5 5 ) .
a c h i e v e m e n t
w a s
t o
d e v e l o p
a
p o w e r f u l ,
n e w ,
a n d
c o h e r e n t
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The
c o n c e p t i o n
o f
o f
w h a t
e x p e r i m e n t
at
t h e
a n d
a n t w o
ideas
culture. e v e n
m a i n
B o t h
until
illustrations
is
c h a n g e d
n o t
A
o f
w a s
has
a
N
D
t h e
B e r n o u l l i
a n d
t h e
ever, n i n g
n e v e r o f
d e v e l o p
t h e
a n d
t h e
E d g e w o r t h .
Laplace
s u c h
o f
o n
Bayes'
o f
t h e o f
t h e
a
a n d
n e w
c o n v e n i e n t l y
are
s u p p o s e d
t o
family
distributions;
relation
p a p e r s
n o r m a l
o n
coefficient,
t h e
o v e r
t h e
h e n c e
a n y
o f
fit" ( H e
n o
g i v e n
h e
w a s
d u e
p l a n n i n g
b y
year
D a n i e l p l a n e
tests,
until
t o
itself.
orbital
t h e
s u s t a i n e d testing.
"probability
h o w b e g i n -
e f f o r t T h e
o f
t o
o n l y
causes,"
t h o r o u g h l y
s u s p e c t
a m o n g
b e
in
K a r l
1 9 0 0 ,
w h e n
o f
a
o f
d e v e l o p e d
I n
d i s t r i b u t i o n s
this
training
r e c e i v e d
test
o f
1 9 0 8 , o f
a n d
t o
a
his
a
a n d
like t h e
t o
Francis a i m i n g
m u c h
o f
p u b l i s h e d t o
p r o v e
o w n
m e a n
t h e
b i o m e t r i c
c u r v e
G o s s e t
a n d
s e e n
p r o g r a m
P e a r s o n
data
s u p e r i o r i t y
1948.)
L e x i s
testing,
P e a r s o n
t o
set
c a n
research
significance o f
t h e
P e a r s o n ,
o n
T h e i r
c h a n c e
a n d
significance
Laplace's
b e
Probabilistic
w a s
a f u l l - f l e d g e d
d a t e d
s a m p l i n g
o f
greatly
d i v i n e
discipline
t h e r e
o f
t h u s
w o r k
a n d
a n d
c e n t u r y .
m e t h o d s
o f
f e w
births e v e r y
o r i e n t a t i o n
g e n r e .
in
o f
calculation
W i l h e l m
b e
data,
c o u l d
f e m a l e
statisticians
t h e
a
m e t h o d o l o g y .
o r
social
c u r v e
b a s e d
c h a n c e
t e s t i n g
o f
o f f e r
h o w
o r
b r o u g h t
analysis.
effect
significance
w a s
see
a n
T h e
this
a n d
w e
m a t h e m a t i c s
m a l e
w a s
agri-
S I G N I F I C A N C E
o f
c o n f o r m .
o f
e p o c h a l
rule
" g o o d n e s s
a d e q u a c y o f
t h e
tests
as
E X P E R I M E N T A T I O N
1.4).
in
s u c h
n e v e r
s h o w
E A R L Y
w h e t h e r
o p e r a t i o n s a n d
t o
testing,
n i n e t e e n t h
a l m o s t
e x p e r i m e n t a l
t h e
c o n c e r n i n g
revival
s c h o o l .
t h e y
(see
b e g i n n i n g
a p p l y
o f
d e c i d e
n i n e t e e n t h
statistics,
test
t o
as
m e t h o d o l o g y
m a t h e m a t i c a l
c h i - s q u a r e
o f
t h e
statistical
w h e t h e r
l o n g
century,
e c o n o m i c
It c a n
as
r o u t i n e
f o r m
a n d
a n d
t o
idea
separately
significance
f o l l o w s ,
b u t
v e r y
l o o k i n g
o b s e r v a t i o n a l
m u c h
originality,
e x a m p l e
a
B u t
d e v e l o p
t o
e x a m p l e
i m p r o v e
e v i d e n c e
o f
a p p l i e d
slight e x c e s s o f
is a n o t h e r
f r e q u e n t i s t s
w o r k
t h e
t h e n
d e p e n d e d
S o m e
t e s t i n g
t h e
subjects
w e r e that
d e t e r m i n e
test
t w e n t i e t h
s t a n d a r d i z e d w h i c h
for
b e c a m e
t h e
t h e y
w i t h o u t
b y
b a c k
s e c t i o n
a l m o s t
earliest
p l a n e t s
s t r e t c h i n g
statistics
t o
this
c o m p l e x
C O M P A R A T I V E
p r i m i t i v e
r e s p o n s i b l e
see
t h e
Fisher's o f
t r a n s f o r m e d
synthesis:
for
t h o u g h
I n
t o
Fisher's
d e s i g n
79
that
A N T E C E D E N T S :
h i s t o r y
is p e r h a p s
t o
d e n y
p r o b a b i l i t y
A r b u t h n o t ' s
o f
t o
o n e
b e g i n
r o o t s
1 9 0 0 .
character
T E S T S
c h a n c e
o f
e x p e r i m e n t a t i o n
the
use
h a d
significance
F I S H E R S
T h e
c a n
century,
a b o u t
o f
c o m p a r a t i v e i m p o r t
t h e s e
e i g h t e e n t h
t o g e t h e r
is. W e
e x p e r i m e n t a l
o f
experts
research,
c o m p o n e n t s
a b o u t
t h e
3 . 3
e x p e r i m e n t a l
inference
his
w h i c h t h e
in-
g e n e r a l i z e d
p u b l i s h e d a n d
w o r k
o f
a
his cor-
b e g u n
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in
8 0
The
P e a r s o n ' s s m a l l
l a b o r a t o r y ,
s a m p l e s
T h e
first
w e
o f
a b l e o r
tests
t h a t
t o
v a r i a n c e .
t u r n e d
t o
B e a v e n , P e a r s o n ' s F i s h e r ' s
w i t h
it
u s e
t h e
in
(3.2).
o f
l a r g e
b e
t h e
first
b a s e d
o n
m e n
a n d ,
t h e
e x a c t
h e
t h e
d r a w n
e s t i m a t e
t h e
t r u e
r e m a r k a b l y ,
e v e n
o f
t h e
p o p u l a t i o n
d i s t r i b u t i o n ,
a n d
t h e
G o s s e t
later
w i t h
E .
b e t w e e n
o b s e r v a t i o n
s m a l l
availk n o w n ,
t h e
i n t e r m e d i a r y
a n d
t h a t
t h e
w a s
c o l l a b o r a t e d
f r o m
1 9 0 8 ) .
/-test
G o s s e t ,
a p p r o x i m a t i o n s .
w a y s
e x p e r i m e n t s
as
i n v o l v i n g
( S t u d e n t ,
v a r i a n c e
t h a t
t a k e n
w h e r e
s a m p l e s
B e f o r e
s o
tests
p o s s i b l e
p o p u l a t i o n
c o u l d
m a n y
h a v e
b r e w e r s
m a d e
l a r g e "
w a s
t o
t o
1 9 5 8 )
a b o v e
t h a t
n e e d
q u e s t i o n a b l e
w a s
b o t h
a n y
e x p e r i m e n t s ,
w o r k
m e t h o d s
d a t a
o n
o n
t h e
S t u d e n t ,
/ - d i s t r i b u t i o n
statistics
a c q u a i n t e d
s a m p l e s .
r e m a i n e d
o n
K a r l
a n d
H e
S.
R .
w a s
A . w e l l
g o o d
t e r m s
t h e m .
T h e t h e
a p p r o a c h e s
g o a l
o f
data.
T h e
e v e r ,
o w e d
t h a n
t o
m u c h
m o r e
A r b u t h n o t .
reject
d i s c r e p a n t
b u t i o n .
b y
T h e
p u r p o s e
t h e o r y
t h e
n i n e t e e n t h
t h e
m o s t
t h e
m o r e
t o
n o t
s o p h i s t i c a t e d
t h e
b a s e d
u n l i k e
o f
t h e o f
t h e
u s e
o n t h e
p r o b l e m
o f
m e t h o d
a r e a
o f
i n f e r e n c e
b a s e d
least
o n
h o w s q u a r e s w i t h
o n
data,
b u t
a b o u t
t h e i r
o f
c a u s e s , " firmly
a s t r o n o m y .
w e r e
a n d
least
tests
r e s e a r c h ,
sciences,
m e a s u r i n g
o f
b a s e d
" p r o b a b i l i t y
at
statistics,
significance
h y p o t h e s e s
o b s e r v a t i o n a l statistical
o f
s h a r e
h y p o t h e s e s
h y p o t h e s e s
a w e l l - d e v e l o p e d
r e s u l t s
o f
reject
F i s h e r
m a t h e m a t i c a l
a n d
m a d e
t o
e r r o r s ,
c e n t u r y
c o n t e x t
-
a n d
e v a l u a t e
o f
t h e o r y
t h e o r y
G o s s e t ,
t o
f o u n d e r s
( o u t l i e r s )
o f
t e c h n i c a l
p a p e r :
e r r o r
E r r o r
d a t a
P e a r s o n ,
1 7 1 0
t w e n t i e t h - c e n t u r y
d i f f e r e n t
t h e
d e v e l o p e d
A r b u t h n o t ' s
s u b t l y
i n
b a s e d
reliance
his
o f
"sufficiently
a g r i c u l t u r a l
a n d
for
b e
e i t h e r
w a s
v a r i a n c e
a v o i d
(see
a s s u m e
S t u d e n t ' s
t o
w i t h
t o
t o
a g r i c u l t u r a l
s a m p l e
p o p u l a t i o n
first
t h e
h a d
t h e
p a p e r s
experts
a d a p t e d
if statistics w a s
t h e s e
a p p l i e d
b u t
inference
i n
fact
a t o
distriw a s
i n
allied
t o
M a n y
o f
d e v e l o p e d
m i n i m i z i n g
e r r o r s
o f
o b s e r v a t i o n .
S i g n i f i c a n c e
T h a t
m e a s u r e m e n t s
tries t o t h e
m e a s u r e
t i m e
u r e d
it
m e a s u r e d p e n d u l u m e r r o r
r e j e c t e d s e l e c t i o n
o f
f o r
f o l l o w
a
i n
i n
h a v e
a s t a b l e
c o m e t r e l a t i o n
d o
s y s t e m , t o
n o t
s u b j e c t i v e .
g e t A
m a k e
r i d
g o o d
t h e
like a
o u t l i e r s
clear
a
s m o o t h
l e n g t h
L o n g
a n d
b e f o r e c e r t a i n
is
t h e
first
s o o n
line, t h e
as
o n e
o f a c o m e t
s w i n g .
t h e
i n c o n s i s t e n c i e s .
e x a m p l e
as
t h e p o s i t i o n
c o m p l e t e
s e l e c t e d o f
o f
b e c o m e s
f o l l o w
c u r v e .
s o m e t i m e s t o
r e j e c t i o n
e r r o r
b e t w e e n
c o n t i n u o u s
o r d e r
t h e
a n
p e n d u l u m
scientists
o t h e r s , w e r e
a
t h e
f u n c t i o n a l
t h e o r y ,
a l w a y s
r e p e a t e d l y
t a k e s
p o s i t i o n s
t e s t i n g
T h e
n o r
m e a s -
d o e s
p e r i o d
t h e
o f
t h e
d e v e l o p m e n t
m e a s u r e m e n t s B u t
t h e
o f a n d
criteria
a s t r o n o m e r
o r
f o r
r o y a l
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The
a n d H e
h e a d
o f
s p e n t
his
n e w in
a n d
m o s t
his
m i n u t e
o f
o w n
series
p o s i t i o n s
t h e
it
c o g e n c y 1 7 5 5
t e n t
o f
in
in
v e r y
t o -
I n
t a k i n g t h a n
t h e
part
1 7 9 5 ,
m e t h o d
a n d
h a d
c o v e r e d
b y
first
d a y
o f
first
k n o w n
t h e
G a u s s
s q u a r e s
a s t r o n o m e r s p h e n o m e n a B u t m e n t t h e
m o r e o f
m e a n
a d d e d o f
all
o r
o f
w h i l e
for
t h e
t o
star
c o m b i n e
t h e
t a k e
case
t h e
o b s e r v a t i o n s t h e
S i m p s o n ' s
m e d i a n a b o v e
T h e
t h e p r o b l e m errors w i t h
o f
c o n c e i v e d
o b s e r v a t i o n s
t o
as
c o n t r i b u t i o n
scientists h a d
lead
o f
o b s e r v a t i o n s .
c o n n n e c t e d
t o
t o
as t h e
least
h e
( a b o u t
as t h e
o f a
a
e x -
certain
m e a s u r i n g
t h e
o f t o
o f
t h e
t h e
n e w
Piazzi
h e a v e n l y
Piazzi
o f
g e o m a g n e t i c
g a v e
in dis-
o n
t h e
t h e t h e
n a m e
o f
d e v e l o p e d
calculations
w e r e a n d
it
( T h i s w a s
s i m p l e
t o o l s
o n e ,
b o d y ,
( 1 7 4 6 - 1 8 2 6 )
o f
m o r e
d i s c o v e r e d
o f least squares. H e
T h e s e
o f
d o m i n a n t
afterwards.
series
o b s e r -
p r o c e d u r e
m e a s u r e m e n t s
already
w h i c h
w h a t
f o u n d .
a
s o o n
m e t h o d b y
c o m b i n i n g
b e c a m e
h a d
G i u s e p p e
planet,
b e
r e p e a t e d
q u i c k l y
s i g h t
o b s e r v e r s
t a k e n
u p
a b y
m e t e o r o l o g i c a l
w o r l d . for
G a u s s
t h e
lost
o f
g e n e r a l i z e d
re-identify
s h o w e d
c o u l d
m e t h o d
T h i s
a n n o u n c e d
m i n o r
it, a n d
o v e r
o f
o f
w o u l d
n e w
m e t h o d
1 8 0 1
g r e a t l y
w e l l
r e g a r d e d
q u e s t i o n a b l e .
I n
w o u l d
r e d e f i n e d
case o f
a s t r o n o m e r
i m p o r t a n t l y
m e t h o d
t h e
T h e
in
s o l u t i o n as
t o
later
his
squares.
1 8 0 1 , b u t
uncertainty,
a s s u m p t i o n s ,
least
Italian
a s t e r o i d
s o m e
i n d i v i d u a l
d i s t r i b u t i o n
p u b l i s h e d
it
year
w i t h
1 9 6 4 ) .
G a u s s u s e d
t h e
e r r o r
quantity.
" m e c h a n i c s "
least
m e a s u r e m e n t
o f
a r i t h m e t i c
t h e
o f
k n e w
t h e m
h e
scientists
1 9 7 1 ) .
for p r e v i o u s l y
said). S i m p s o n
j u d g e d
for
d e b a t e d .
in
r e d u c t i o n
his data; h e
t h o s e
his
1 8 3 5 ) .
m e a n
b e
t h e
L e g e n d r e
single
m u c h
for
accuracy
t h e
c o n s e q u e n c e
n u m b e r
a r i t h m e t i c
t o
c o l l e c t e d
o n
h e
e m e r g e d
s a m e
for
t o
h a v i n g
m a i n l y
quantity,
t h e
w a s
close
a n y
data
a t t e n t i o n
c o n c e r n
o t h e r s
h a d
( 1 6 4 6 - 1 7 1 9 ) .
a s t r o n o m i c a l
(Eisenhart,
inaccuracies
a method
b e c a u s e
Ceres.)
o f
rely
(Baily,
in this regard,
(Eisenhart,
t h e
o n e
o u t
is, a b o u t
1 8 0 5 ,
v a t i o n s ,
t h e
practices
little c o u l d
that
n e v e r
are
rare
f r o m
d i s r e g a r d
a single
t h e r e
a
w o u l d
o b s e r v a t i o n s
F l a m s t e e d
e x t r e m e l y
g u i d e l i n e s
o f
J o h n
m e t i c u l o u s
details
c a t a l o g
practical
t e r m s
w h i c h
g a v e
w a s
81
c o l l e c t i n g
s h o w e d
H e
a n d
his
o t h e r s
t h e s e
p r o c e d u r e
o f
quality,
that
a n d
o n l y
w h i c h
size
-
still s t a n d s
e r r o r
t h e
h a n d s .
m e a s u r e m e n t s s u c h
a n d
o b s e r v a t i o n s
1 6 0 0 ,
v a l u e
b e l o w
in
a n d
" i n c o n s i s t e n t "
r e p e a t e d
F l a m s t e e d
details,
p u b l i s h e d
A r o u n d s u c h
o f
a t e l e s c o p e
circumstantial
e y e s
s u p e r l a t i v e
W h o l e
at
experts
o b s e r v a t o r y ,
o f his data. H e
in their m o s t
v e r y
life
catalog.
m a n i p u l a t i o n
t h e m
-
G r e e n w i c h
w h o l e
3,000-star
t h e
as
t h e
inference
statistical
d e v e l o p e d
squares.
s e c o n d
o n e
T h e c a n
i n f e r e n c e
t w o , first n o w
q u i t e o n e b e
is
a n d
for
different, B a y e s i a n
l a b e l e d
t h e
m e a s u r e -
justifications in
d e c i s i o n
t o n e
a n d
theoretic.
Downloaded from https://www.cambridge.org/core. Newcastle University, on 09 May 2018 at 22:47:10, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.005
8 2
The
It is in
G a u s s '
f a m o u s
n o r m a l
G a u s s
b e g a n ,
B a y e s i a n ly
first
G a u s s i a n )
t h a t
p r o b a b l e .
s h a p e d
justification
( o r
s e n s e
t h e
T h e n ,
l a r g e r
h e
m a d e
t h e
case
m a t e s
t h a t
is
is
1 7 9 8 , n o t
g e n e r a l
p u b l i s h e d
w a s t h e
p r o b a b i l i t y ) ,
s h o w e d ,
falling n e v e r
o f f
w h i l e
t h e
m o s t
p r o b a b l e
t r u e
v a l u e
o f
t o
all v a l u e s
z e r o
a t
-
finds
t h a t
is,
b o t h
(in
a
belle r r o r s
u n r e a l i s t i c
least
s q u a r e s
c o m b i n a t i o n
t h e
t h e
e q u a l -
w h e n
a n
T a k i n g
t h e
v a l u e
sides
t h e
S u p p o s e ,
f o l l o w
clearly
h a s
t h a t
a r e a priori
s h o u l d
z e r o ,
it
1809,
p r o b a b l e
c o n v e n i e n c e ) . since
u n t i l
p r o m i n e n t .
e r r o r
r e a c h i n g
justified,
m a d e
m o s t
m e a s u r e m e n t
m a t h e m a t i c a l
t h e n
experts
d i s t r i b u t i o n
q u i c k l y
f o r
o f
is i n
( a l t h o u g h
a s s u m p t i o n g e n e r a l
m e a n
o f p o s t e r i o r
d i s t r i b u t i o n ,
b e c o m e
inference
h i g h e s t
o f
i n
esti-
a
posteriori
p r o b a b i l i t y . B e s i d e s c e n t e r u r i n g
o f
t h e
d i s t r i b u t i o n
p r o c e d u r e
c u r v e . t h e
t h e
T h i s
m a r k ,
e s t i m a t e
is
t o
t h a t
t h e
b y
t h e
s q u a r e
( S i m i l a r
p e o p l e
s h o u l d
b e
It
is
statistical
in
t h e
It
is
this
a n d
o f
o b s e r v a t i o n s
q u a n t i t y
e a c h for n e w
o f
did,
e r r o r false
o f
t e n d e n c y
bell. G a u s s
a n
a v e r a g e
as
reliable
it g i v e s
t a k e n ,
o f
t h e
m e a s -
close
t o
h o w
t o
d a t a
t h e m a c c o r d -
it
f o l l o w e d
c o u l d
a p p r o x i -
o f
t h e
G a u s s '
o f
t r u e
h o w
m a n y
so-called
m a k e s
a m e a s u r e in
b e
d e t e r m i n e
t h a t
h a v e
t o
t h e
o n e
t h e
b e l l - s h a p e d
e s t i m a t e
t o
a
d e c r e a s e s
e s t i m a t e
e r r o r
c a n
a n
u s e d
o f
s h o w e d
f r o m
o b s e r v a t i o n s
a v e r a g e
a
f e a t u r e
p a r t i c u l a r
o b s e r v a t i o n s
p r o b a b l e
o n e
o f
E a r t h
t h a t
in t h e
n e w
t o
c i t e d
t h a t
lies
p r e v i o u s
o f
S u n )
o f
t h e
t o
m a d e
t h e
p u b l i c m e t h o d
u n c e r t a i n t y
a v e r a g e
c u s t o m a r y
n o t a t i o n
e v e n
c h a n c e (x
—
case
B u r e a u
o f
o f
t h e
E a c h
d i f f e r e n t
x
c a l c u l a t e d
U n i t
n e w
o f
x
a)"]
+
h a s
n o
t h e
t r u e
T h i s
o f
a s s u m e s ,
as
h a s
i n s t a n c e , a v e r a g e
1 9 6 1 ,
a n d
p r o b a b l e
a n d
s o
o r
W .
J.
listed
fif-
d i s t a n c e
o b s e r v e d e r r o r w a s
w a s
sys-
p r o v e d
m e a s u r e m e n t . for
basis
v a l u e
c o n s t a n t
d e t e r m i n a t i o n
o b s e r v e r s ,
[ " o n
t h e
( t h e
a n d
l i m i t s
a
similarly.
S t a n d a r d s ,
1 8 9 5
±
i n t e r p r e t a t i o n
t h a t
scientific
A s t r o n o m i c a l b e t w e e n
a,
p r o c e d u r e
all m e a s u r e m e n t s
lay o u t s i d e
b y
t h e
t h e
i n t e r v a l
m e a s u r e m e n t
t h e
m a d e
t h a t
it is a n
d e t e r m i n a t i o n . a n d
a n d
i n t e r e s t i n g
d e t e r m i n a t i o n
t e c h n i q u e s
in
U . S . N a t i o n a l
t h e
realize
a l o n e ,
t h e
e v e r y
t o
e r r o r
a t t a c h e s
d e t e r m i n a t i o n s
t h e
g e t
its
t h e
n o w a d a y s
t r u s t
p r o b a b l e
m e a s u r e d
a l w a y s
Y o u d e n
t h e
m a n y
s i n c e
h o w e v e r ,
t h e
t e e n
o f
o f
t h e
t o
a
d e t e r m i n e s
1 9 8 6 ) .
o f
b e
as
a r e
o u t
m e a s u r e m e n t )
n u m b e r
s e n s e ,
t h e
o f
d i s t r i b u t i o n
o f
m o r e
p r o c e d u r e , w i d t h
w h i c h
o n e
single
single
t i m e s
m o d e r n
n o t i o n
t o
a
t h e
e s t i m a t e
i m p o r t a n t ,
t e m a t i c
t h e
i n t e r v i e w e d
t h e
G a u s s
o f
t o
t h e
reliability
o f
t h e
t o
c a l c u l a t i o n s
o p i n i o n . )
r e m a i n i n g ,
o f
t h e
f o u r
t h e
v a l u e .
o f
q u a n t i t y ,
m e a s u r e m e n t s ,
(i.e. o f
r o o t
say,
d o u b l e
(Stigler,
p r e c i s i o n
w i d t h
m e a s u r e d
k n o w n
c o r r e s p o n d s
t a k i n g ,
m a t e l y
o f
b e
p r e c i s i o n
selves. S i n c e i n g
t h e
a n d t h e
m u s t
t h e
o f t h a t
r e p o r t e d b a s e d
s u b j e c t
o n t o
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a
The
d i f f e r e n t t h e
s y s t e m a t i c
p r o b a b l e
able
t o
t h e n
is o f t e n
B y
o b t a i n
m e a s u r i n g o f
it
t h e
t h e s e
t h o s e l e m
s p e a k s
o r
t h e
large
( O l b e r s , tions,
o f t e n
a n d
explicit
T h e o n l y
in
that
G a u s s ,
t o
for
o f o f
letters
t h e
o f
f o r m e d
m e a s u r e m e n t s o f
t h e
b u l k
probabilistically o p e d
b y
P e i r c e
Peirce's cance. w e r e T h e
rules
m a y
b e
a c c e p t
f r o m
w e r e
a n o t h e r u s e d o r
t o
in
in
data.
a
o f
b y
e v e n
r a w
data.
t r e a t m e n t
1 9 7 4 - 7 6 ) .
o f T h e
H o w e v e r ,
t h e
in
m e a s u r e m e n t s o r
t w o
e r r o r
o f
t h e
this n o t
b e -
that
w a s
n o t
discard
c o m p l e t e l y
s o l u t i o n
afresh?
T h e
s o m e
letters
t h e
s h o u l d
t o
o f
c o u n t
m o r e
t o
o u t s i d e
as
u n u s u a l
d i r e c t i o n s "
a n y
m o r e
e v e r y d a y t h e
b y
u n u s u a l l y an
precise
g i v e
p r o b -
e x c h a n g e d
p r o b l e m
( e x p r e s s e d
w a s
direc-
life,
w h e r e
o f
f o r m a l
r e i g n
this t h e
o f
t h e
t o
test
g r o u p
a n d
o f
l e d
t h e
rejection
o f
A m e r i c a n
h i m s e l f
t o
as
rejecting,
o r
t o o
first
N e w
m o d i f y -
m u c h
f r o m
e l a b o r a t e
outliers
w a s
p h i l o s o p h e r
a
d i f f e r e n -
calculator.
d i f f e r e d
c o n t e x t ,
G a u s s
e l i m i n a t e d ,
projects
residual
t o in
b e t h e
objective,
in
y e s / n o
rules
r u l e - d r i v e n ,
o n e
or
o f
o r
a s i m p l e
s o u r c e
as
a n d
d e v e l o p m e n t
c o m m u n i c a t e
also
o n e
d i s t r i b u t i o n
o r p r o v i d e
a n d
that p e r i o d ,
w h e t h e r
( n o r m a l )
is
b y
gradually
m e c h a n i c a l l y
t h e
d e v e l o p e d
s a m e
It
a n d
a n d
d e v e l -
C h a r l e s
S.
1 9 3 3 ) .
d e s i g n e d
h y p o t h e s i s .
print)
for
father
o t h e r s
m e a s u r e
w a s
t o
situation
m a t t e r s
in
I n
rule
reject a h y p o t h e s i s ,
data
s u c h
w h i c h
R i d e r ,
d i m e n s i o n
tests, t o
b e t t e r
r e c e i v e
j u d g m e n t s
p u r p o s e
u n d e r s t o o d
nificance a n d
t h e
Peirce,
m a k e
t h e
t h e
t h e
o n e
u n u s u a l
o f
o f
o t h e r s . W a s
disinclined
n e c e s s i t a t e d
cases
t h e
o f t e n
e x p e r i m e n t e r / o b s e r v e r
t h e
1 8 5 2 ;
w a s
u s e d ,
a p p e a r e d .
t h e
" W h a t t o
scientist
( H a r t e r , it
E x p l a i n i n g
like
n e v e r
m o t i v a t e d
w e r e
t a k e n
is
o f
rule, a n d
T h e y
T h i s
in
B e n j a m i n
(Peirce,
for
a n
in
b e t w e e n
s q u a r e
G a u s s :
t h e
o f
1 8 2 7 ) .
a n d
labor
w i t h
p a g e s
c o m p a r e d
subjectivity
j o b s
t h e
intuitive
s o
that
it n o t
least
I w o u l d
( G a u s s ,
o r
clear
w a s
O l b e r s .
a s k e d
scientific
w e r e
t h e
e l e m e n t s
d i f f e r e n c e s
a n d
f r o m
h e
rest,
i n c u r r e d
h o w e v e r ,
m a k e
rules
private
tiation habits
has
n e e d
d i v i s i o n
ing,
recalculate
in his a n s w e r
o n e
h a d
smallness
t e c h n i q u e
e r a d i c a t e d
c o m p a r e d
m a d e ,
a d e v i a t i o n ?
t o
c o n t r o l
t h e
i n d e p e n d e n c e
subjective
b e c a m e
a s t r o n o m e r
1 8 2 7 ) .
a n d
it
O b v i o u s l y ,
statistical
s e c u r i n g
laid
large
O l b e r s
t h e
( t h e
vividly
1 9 7 2 ) .
c o m p l e t e l y
residuals
t h e y w e r e a n d
n o t
b e e n
u n u s u a l l y
d e v i a t i o n s ,
t o o
h a d
83
e x p e r i m e n t a l
that
b e e n
o f
m o s t
a n d
large
s e e m e d
m e a s u r e m e n t s
r o g u e s
G a u s s
b y
e s t i m a t e s )
w h e n
o n l y
particular
h a d
s t u d i e s
residuals w e r e
n o t i c e d
t h e
F l a m s t e e d
a n d
cause
indicates
t h u s
e r r o r
e m p i r i c a l m a d e
in
experts
( Y o u d e n ,
e x a g g e r a t e d
1820,
g h o s t
e r r o r
e r r o r
inference
t h e o f
w e r e
tests o f
m o r e t h e
g a v e
m e a s u r e m e n t s
r e m a i n i n g a strict
significance
m e c h a n i z e d m e a n s ,
o n e s .
criterion. tests:
c u s t o m
t h e y
d e c i s i o n s
as in Fisher's
d i s c r e p a n c y t h e
signifi-
t o sig-
b e t w e e n
t h e
o f
t h e
u s i n g
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84
The
w h o l e
tail
area
m e a s u r e m e n t T h u s tics in
in
t h e t h e
error
this
b e y o n d
o f
search
for
t w e n t i e t h
theory.
o f
a n w e l l
o f
M e t h o d
t h e
t h e
like
d u c e d "
o n e
o f
has
u n d o u b t e d l y (Jordan,
d e s i g n ,
t o
research trated
n i z e d o f
o f
that
aspects m e a n s
w i t h
t i m e ,
t o
t h e
m a k e t h e
w i t h
t a k e
b e
o f
c o p i e s
T h e
u n d e r s t o o d
as
a
o f
t h e
statis-
call
(Swijtink,
s t a n d a r d i z a t i o n W i l h e l m
o n
g e o d e s y ,
aspects t o
o f
o u r
large
u s i n g
discipline
e x t e n t ,
o f
a
m e a s u r e m e n t s
a n d
m e a s u r e m e n t s
a n d
m e t h o d
t o o l
d e s i g n
rarely
w a s
i n t r o -
d r a w
testing
causal in
n o t
t h e
h y p o t h e t i c a l
least
consists
e x p e r i m e n t a l t h e
in in
all
closely
r e q u i r e m e n t s d e g r e e
o f
a
t o
b e
original is
illus-
c o m p a r i s o n
T o
t o b e
o f
a
t h e
w h e r e
as
c a n n o t
g e n e r a l l y t h e
d o
cause
e x p e r i -
e x p e r i m e n t s ,
T o
d o
s o
aspects. p o s s i b l e
c o m p a r a t i v e
logic
o p e r a t i o n a l
s i t u a t i o n o n e
r e c o g -
T h e
cause
r e l e v a n t
in
already
a
B u t
c l o s e
w a s
tied
situations.
as
his
h y p o t h e s e s .
c o m p a r a t i v e
causally
g e t t i n g
b e g i n n i n g
s e p a r a t i o n
f r o m
causal
o c c u r r e d . I n
e x p e r i m e n t s
c o m m e n c e d
e x p e r i m e n t
h y p o t h e t i c a l
h a v e
m e d i c i n e .
plots.
general is
s t r o n g e s t
a n d t o
o n l y
traditional
t h r e e
e x p e r i m e n t a l
w h o s e
a p p l i e d
w a s
s t a t e m e n t s .
situations. o f
b e e n
i n f e r e n c e s
o f
synthesis,
p h y s i o l o g y ,
F i s h e r
T h e i r
e x a m p l e s
tradition,
d e s i g n
c o m p a r a t i v e
o f
i n c r e a s i n g
statistical
w h e n
m e t h o d o l o g y
p l a c e at
h a d
1 9 1 0 .
for
h i s t o r i c a l
a g r o n o m y ,
c o n t r o l
w o u l d
t h e m ,
e x p e r i m e n t a l situation.
t h e
t o
t o
t h e
h y p o t h e t i c a l
situations
t o
m a k i n g
l o n g s t a n d i n g
statistics
a d i f f e r e n c e :
e f f e c t
a
e x p e r i m e n t a l
a
m e a n i n g
s o m e
Fisher's
in
desire
invaluable
o f
o f
a r o u n d
e x p e r i m e n t a l
is a b s e n t , m e n t s
p l o t
J o h n s t o n ' s as a n
b e e n ,
t o o .
m a y
analysis.
m o r a l
since
w e
h a n d b o o k
s u p p r e s s i o n
o f t e n
t h e
a d v a n t a g e s
in
as
a
tradition
t e s t i n g
data
t h e
h a v e
h o n e s t
less
t e s t i n g
a n d
statistics
o n e
m o r e
w e r e
Fisher,
b y J o h n s t o n ' s
s a m p l e B y
a n d
p r o b a b i l i t y
o n
o f
" T h e
S q u a r e s
[ D J i s h o n e s t
e m b o d i e d
significance
related
t h r o u g h
e m p h a s i z e d
e x p e r i m e n t s :
B u t ,
G o s s e t
statistical
n i n e t e e n t h - c e n t u r y
h a p p e n s
a t t a c h m e n t s
b e f o r e
o f
m e t h o d s
o f
a w e l l - d e v e l o p e d subjectivity,
I f
has t o g o
characteristic
o f
i n d i v i d u a l
a n d
h e
c o m p o n e n t
also
as
t h e
Least
. .
disciplinary just
o f
discrepancy.
outlying o n e
f r o m
h i s t o r y
o f
1 8 9 5 ) .
m a i n
w a s
t h e
b e c o m e
calculations.
o t h e r
m e a s u r e
rules, s o
derives
in his p r o f e s s i o n .
C o m p a r a t i v e
T h e
t o
w h e n
m e t h o d s
d o i n g
a
objectification
i m p o r t a n t
s t a n d a r d i z e d
nature:
also
p r o c e d u r e s
this
t h e
t h e
socialization
a u t h o r
u n d e r s t o o d
moral
as
m e c h a n i c a l
century,
is c e n t r a l
e x p e r i m e n t a l
u s i n g
o b s e r v a t i o n
f o r m a l
I n d e e d ,
It is t h e
J o r d a n ,
experts
is r e j e c t e d as a r o g u e , a n e v e n m o r e
d e v e l o p m e n t ,
1 9 8 7 ) .
t h e
inference
actual
t h e y h a v e T h e t o
art
this
trials c a n
t o o f
ideal all
similarity.
Downloaded from https://www.cambridge.org/core. Newcastle University, on 09 May 2018 at 22:47:10, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.005
b e
The
Especially in
t h e
t e e n t h
c e n t u r y
s l o w l y
e m e r g i n g
t h e
century,
troversial t h e
t w o
b y
t h e
G e r m a n
fluke,
b u t
o u s t e d
b y
b e g a n
o f
t h e
t h e
t o
test
m a y
w h a t
Fisher's
e r r o r
t h e o r y
a n d
tacit
t o
agricultural
t h e
tradition
e x p e r i m e n t a l
o f
variance,
r a n d o m i z a t i o n s o p h i s t i c a t e d
t h e
little
in
c e d u r e s b e f o r e
a
d e c i d i n g
t h e
in
a n d
R.
A .
3).
t o
w a s
a n d
a
W e
o f
part,
-
find
o r
E x p e r i m e n t a l
d e s i g n
agricultural
F.
J.
a n y
t h e
associate
O n
o n
t h e
o t h e r
t h e s e
p r o b -
m o d e l s ,
analyses,
studies,
agri-
e m p h a s i s
o f
h a d
for-
in
n o w a n
M .
o f
already w e
that
a p p l i c a t i o n
statistical
factor
literature,
b o d y
blindness.
n o
n o w ,
material,
that
f o r m u l a t i o n
tradition
n o
o r i g i n a t i n g
t h e
i n c l u d i n g
i n v e s t i g a t o r
t h u s
E n g l a n d .
t h e m e s
Fisher
Certainly
R o t h a m s t e d
statistical
w a s
c o n s i d e r a b l e
learn.
e x p r e s s i o n s
o f B u t
this
literature
t h e o n
analyze t h e
o f
t h e
i n s i g h t
are
set
o f
t o
data
insisted
o n l y
natural
data
M o r e o v e r ,
t h e
c o m p r i s e s
G e r m a n in
a
o f
it p r o v i d e s .
e x p e r i m e n t s .
d e s i g n
a d d i n g
data
t h e
d e s i g n
q u e s t i o n
Fisher, w h o
d e s i g n
reveals
the
o b t a i n e d .
a b o u t
that w h o l e
p r o c e s s
m u l a t e d
t o
correlations
analysis
h o w
e x p e r i m e n t a l
p.
h a v e
b e t w e e n
w e r e
c o n c l u s i o n s
already
1 9 3 5 ,
like
a
o f
variance o f
G e r m a n
a b o u t
a
c o n -
f o r g o t t e n
1 9 3 1 ) .
w r i t t e n
i n s t i t u t i o n s
G e r m a n
a n a l y z i n g
data
t o
plete
o f
statistical
a t t r i b u t e d
w h o l e ,
a n d
p r e - b i o m e t r i c
c o n n e c t i o n
t h e s e
reliable
these
w i t h
t w e n t i e t h - c e n t u r y h a d
T h e
this G e r m a n
(Fisher,
w a s
b l o c k i n g .
agricultural
m e t h o d
p e r f o r m
s t o c k e d
t h e r e
n o
( 1 9 2 9 ) ,
a n d
n o
u s e
b e c o m e b u t
n o o f
q u i t e
p r o b a b i l i t y
role.
i n t i m a t e
a n d
o r
G e r m a n
p r o p e r
w e l l
F i s h e r
t h e
o f
n i n e -
close
the
d e v e l o p m e n t s
w a s
a c o m p r e h e n s i v e in
w h e n
is a l m o s t
k n o w n
replication,
o u t
h i s t o r y
unclear
the
i n d e p e n d e n t l y
B e h r e n s
p r e s t i g i o u s
C a m b r i d g e ,
w h i c h
U .
t h e
research
t o w a r d s
m e a n s
h a v e
early
at
o f
m u s t
w o u l d
o f
like
w o r k e d
p a r t i t i o n i n g
T h e
a n d
literature
d e s i g n ,
n o t h i n g w a s
at
W .
in
i n t e r p r e t a t i o n .
p r o p o s e d
T h i s
r e m a i n s
k n o w l e d g e
G e r m a n
h a d
c h e m i s t
agriculture,
e x p e r i m e n t e r
l e m s
different,
in
t u t o r
cultural
h a n d ,
d i f f e r e n c e
Fisher
parallels
that,
for
t h e
e x i s t e d
e x p e r i m e n t a l
t e c h n i q u e s
tradition.
e x t e n t
t h e r e
a probabilistic
successful
E n g l a n d .
c o u n t r i e s ,
o b t a i n
b e
a l o n g
m o r e
h a d
S t r a t t o n ,
w i t h
statistical
t o
85
o f agricultural
library at R o t h a m s t e d
literature
m a l
o f
agricultural
part
a l t h o u g h
o f
b o d y
s a m p l e s
in Ireland a n d since
tradition
significance
o f
experts
G e r m a n - s p e a k i n g
a rich
e v e n
inference
a n A
data
h e
t o
p e r f o r m
t o
risk
o f
k n o w s
b e i n g
all,
different logical
k n o w l e d g e
b y a n
e x p e r i m e n t e r
H .
c a n
w h a t
t o
i n s i g h t is m o s t b e
"[statistical aspects
h a d
the o n l y p r o -
d r a w o f t e n
i n v o l v e d p r o c e d u r e
o f o f
t h e t h e
e x p e r i m e n t a t i o n "
R o d e w a l d
o f
e x p e r i m e n t
u n a b l e
r e q u i r e m e n t s
b y
a n d
analyst
that statisticians m u s t A f t e r
a s e n s e
e x p e r i m e n t
if
s t u d i e d . T h i s
t w o
all t h e
is
b e g i n n i n g s
s a m e c o m -
(Fisher,
already
for-
1 9 0 9 :
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86
The
D u r i n g
the
last
decades,
field
have played an important conduct
since
therefore
from
its
trials
one
scientific
answer
one
experts
to
compare
varieties
role in agriculture. T h e
s u c h trials a n d h o w
valid and
inference
can
can derive
conclusions.
see
how
the
trials
the
last
have
kinds
o f
question arises h o w
from The
and
results o f the
question
has
to be conducted
to
fertilizer
one
trials
be
should
generally
answered
(Rodewald,
first, 1909,
p.
12).
S o m e 1 8 0 0
s e n s e
in
the
o f
w o r k
e x p e r i m e n t e r
that o f
b e
a p p l y i n g B u t
his
n e e d
t h e
that o n e
w h i c h
n o
" t h e
natural
w a s
in
also
c o n s i d e r e d
for
h i m s e l f
o f
the
m e n t s b l i n d u s e f u l
t h e
if t h e
in
o f
d e t e r m i n e
subject
w i t h
t h e
m e t h o d o l o g y Subject
as m e d i c i n e n o t
k n o w
a certain its
a t t i t u d e
causal
n o t
m a y
for
t h o s e
field. o f
a b o u t
t h e
different p l o t "
a n
in
( t o
i n d i c a t i o n
this
case
a n d
it
s o
h e
p u r -
replication,
w e l l
t o
n u m b e r
o f
u n d e r s t o o d s a m p l e
w a s
-
r e c o g n i z i n g
o f t e n
a b o u t
t h e
b e
b e c a u s e
b y
size
re-
e v i d e n t
a n d
c o u r s e a n
its
e x p e r i m e n t
t h e y
are
r e c e i v e d
Similarly,
a n
n o t
h e
w a s
It is
o r i g i n
l i m i t e d
w a s
T h e
r a n d o m i z a t i o n .
fields, is o f
b l i n d n e s s
e x p e r i m e n t s .
t r e a t m e n t s
effects.
soil"
replication
three
large
o n l y
m e d i c a l
p s y c h o l o g y ;
w h a t
o f
4.2).
this
blindness
a n d
o n
for
u n d e r s t a n d i n g
r e a s o n s in
o f
variety
climates,
replicate,
e x p e r i m e n t e r
o r
a
k i n d s
t o g e t
a
c o n f u s i o n
a n d
u n d e r
" c o n t r o l
r e a s o n
w a s
r e m a r k e d
Still, J o h n s t o n ' s
T h a t
(see
a n d
a p p r e c i a t i o n
n o t
possible.
e r r o r
t h e
p s y c h o l o g i c a l
century.
h a v i n g
the
d i d
m a i n
hair
e x p e r i m e n t a l
t o w a r d
h e
t h e
H e
U n f o r t u n a t e l y ,
§ 2 6 ) .
e x p e r i m e n t s
c o n n e c t e d
fields
1 9 3 5 ,
r e c o m m e n d a t i o n s ,
subjects d o
b e c a u s e
partially
c o n c e p t
a n
w a s
Fisher's
g i v e n
o n
idea
m o t i v a t i o n
w h i c h
spirit,
d i f f e r e n t
d i f f e r e n t
t h e
similar lack o f
m e d i c a l
p r e f e r r e d
s u c h
t o
d i m i n i s h
3.1. A
i n v o l v e d
n i n e t e e n t h in
close
in
replicated
w a s
agricultural
c e n t u r y . J o h n s t o n ,
soil."
result,
etc.
r e p e a t e d
m o d e r n
lead
a r o u n d
h o r n - s h a v i n g s ,
b e
p l o t s
f o u n d
B a c o n i a n
his m e a s u r e m e n t s
o n l y
t h e
(Fisher,
Fisher's
it is s t r o n g l y
part in
t h e
in
o f
like J o h n s t o n ,
in s e c t i o n
A l t h o u g h
r e p e a t e d
true
b e
t u r n e d
b o n e s ,
o n
t h e
d i d
c o n c l u s i o n
t o
a n d
n o t
H i s
a
c o n t r o l ,
n i n e t e e n t h
a p p l i e d ) .
firm
s e r v e s
c o n t e m p o r a r y
n o t
n o
t o
o u r
d i f f e r e n t
J o h n s t o n
w a s
error
agriculturalists
t h e
e x p e r i m e n t a l
that
replications
t o
e n o u g h ,
that
w a s
in
g r o u n d
u n d e r
t o
physician
d u n g ,
. . . h a v e
diversity
variability
the
the
t o
d u r i n g
n o t
fish,
c o n d i t i o n s
natural
c o n c e p t u a l l y
e s t i m a t e
ferred
t o
t r e a t m e n t
c o m p l a i n e d
n o t
t r e a t m e n t
n o t i c e
o v e r l a p p e d
p o s e
s a m e
trial w a s
B u t
are
already
G e r m a n
a n i m a l
r o t t e n trials
is
s t u d i e d ,
o f
2 4 ) . T h a e r ' s
replication
plots.
o f
§
a t t e n t i o n
for
effects
w e a t h e r
1 8 0 9 - 1 2 ,
T h a e r
t h e s e
that
replication
e n l i g h t e n e d
T h a e r .
c o m p l e t e
d i f f e r e n t
( T h a e r ,
for
e x c r e m e n t ,
c i r c u m s t a n c e s
u n d e r
the
fertilizing
h u m a n " t o
o f
n e e d
A l b e r t
c o m p a r a t i v e w o o l ,
t h e
t o is
lies
n e e d n o w also
e x p e r i subject
receiving. t r e a t m e n t
It
is
m a y
e x p e r i m e n t
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is
The
e x p e r i m e n t e r
b l i n d
t h e
subjects h a v e
i n d i v i d u a l
f r o m
t h e
G e r m a n
m e t h o d o l o g i c a l
G i v e n
the
a judge's what
writer
and
o n
signs with [Wagner]
a general
judgments
and
had
second
then
n e e d
c e n t u r y
o b s e r v e r
for
o f
in
next
and
m e t h o d s take
this
R a d a u ,
i m p o r t a n c e
In
and
b l i n d n e s s
o f
t h e
a n d
m a n a g i n g
so-called
b e t w e e n
I n v e s t i g a t i o n
s u b l i m i n a l
o f
e m p h a s i s
o n
e x p e r i m e n t e r
b l i n d n e s s
w a s
d i f f e r e n c e
b e t w e e n
( H a c k i n g ,
1988).
i n f u s i o n
statistics w a s w o r k for b e
for
t h e
statistics o f
o f
l i m i n a r y
s t e p
t h e
m e t h o d o l o g y
f u r t h e r
r e f i n e m e n t
it p r o v i d e d
rich
relevance.
data t o
a
h a d
o f t e n
e x p l a n a t i o n
illustrated w i t h
t w o
o f
o f
field
Earlier b e e n o n
e x a m p l e s
t h e o f
tests
basis t h e
o f
can
o f
o f
t h a n
easily n u m -
t h e
w a s
t h e
h u m a n
e x p r e s s e d acuity
o b s e r v e r s
w e r e
react
e v e n t s ,
d e v e l o p e d
a c c o u n t
(Bessel,
especially after ( P f u n g s t ,
s o u r c e
w h e r e
it
statistical
o f
f r a m e A n d
it
c o u l d
r e a s o n i n g
w i n d o w - d r e s s i n g , principles.
statistical analysis o f
d e -
i n t o
e x p e r i m e n t a t i o n . w h i c h
for
a n d
a c o h e r e n t
for
t h e
1 9 0 7 ) ,
e x p e r i m e n t a t i o n
physical
the
t o w a r d s
clairvoyance
p r o b l e m s
the
n i n e t e e n t h -
s i m u l t a n e o u s
It p r o v i d e d
m o r e
with
for
in p e r c e p t u a l
i n t o
c o m p a r a t i v e
applications
little
in
p a r a p s y c h o l o g y ,
n e w
t h e m
light
T h i s
e q u a t i o n "
c o m p a r a t i v e o f
these
47).
h u m a n t o
to
judgment
chose
especially i m p o r t a n t
t o b o t h .
field
numbers
m a d e
r e c o g n i z e d
e x p e r i m e n t a l
crucial i m p o r t a n c e
d a y - t o - d a y
e x p e r i m e n t a l
b e
o f
that
o b s e r v e r s
A n
w e
p.
o t h e r s
t i m e s
w a s
-
as
removed.
his
a t t i t u d e
these p h e n o m e n a ,
stimuli
some-
proceeded
the
d i s c u s s e d
a t t e n t i o n .
" p e r s o n a l
h u m a n
1880,
d i f f e r e n c e s
t e c h n i q u e s .
T h e
a n d
p s y c h o l o g i c a l
e x p e r i m e n t a l
t e l e p a t h y
seeing
sceptical
F e c h n e r
a
was repeated and the
also
g e n e r a l
w e
different
R o h n ,
w a s
n e w
t h e
since
the experiment
( W a g n e r
forming
comparing
day
r e s p o n s e
t h e
us
a
influence
also then m a d e
the
o f
characteristic o n
o f
may
m a d e
time
r e q u i r e d
fined
then
without
any
d e t e r m i n e d
1866).
H e
1880, in
experimental
in the afternoon
s e r i o u s
variation
o f
aside
A s t r o n o m e r s
b a s e d
the
n o w
place
e x p l a i n i n g
put
without
p e r c e p t i o n ,
o f
b u t
variation.
in
e x a m p l e
a plot were
day, but
c o m b i n e d
individuals.
else
a judge's opinion,
over
b y an
each plot
s o m e o n e
times
t r e a t m e n t
trials:
fertilizer used o n
several
w e r e
e x p e r i m e n t e r
a subject
fertilizer
seeing
limits o f
also
another
h u m a n
d i f f e r e n t
1823;
the
applied
T h e
finally
interest
a m o n g
t o
that
w h a t
w r o t e
l o o k i n g at it a n y f u r t h e r . D r . R o h n
w e r e
p s y c h o l o g y .
reliability
w i t h
fact
the appearance o f the plants -
T h e
a n d
that
obtained.
were
as a n
o f
W a g n e r
fertilizer w a s used o n
walked
n u m b e r s
examination
change bers
his
in
k n o w
is illustrated
P a u l
can easily influence
then
impression
fertilizers
other
literature.
the
n o t
Its n e e d
the names o f the
a n d p u t it aside w i t h o u t
the
received.
87
d o e s
i m p r o v e m e n t s
given
judgment
experts
e x p e r i m e n t e r
agricultural
p a p e r
opinion,
follows. T h e
get
t h e
fact that k n o w i n g w h a t
different
T h e
if
inference
a
t o
p r e -
T h i s
c a n
e x p e r i m e n t a l
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88
The
data
that
t h u s
w e r e
f r o m
w e r e
t h e
subject
J o s e p h
o f
t h e
t h o s e
that
w h o
t h e
d a r k
o f f
b y
g i v e n
e x p l a n a t i o n H e
o f
a p p l i e d
c o i n c i d e n c e i r o n
t h e
ability
sixty
that
c o i n c i d e u s e d
w i t h
in
t h e
a c c o r d i n g
w h e t h e r
b y
K i r c h h o f f
c o n s i d e r e d
m i l l i m e t e r
as a m a t t e r b y
o f
h e a t i n g
lines
o f
q u i t e
t o
t h e
t h e
sixty
t h e
null
pairs
o n e
d i d
distribution.
d a r k
lines
b r i g h t
h a v e
lines
in
T h e
t h e
t h e
sun.
already
t o
t o
a
justify physical
error?
d e v i a t e
t h e
of)
b e
as
W h y
h i g h l y
(0.5)
6 0
that
this
w a s
t h e
this
t h e
solar
o f
o n e
t h e
i r o n
s p e c t r u m , lines
in
that
w i t h i n
s p e c t r u m ,
s i m p l y
p r o d u c e d
m a t c h
sixty
calculated
( n o t
t h a n
10"
1 7
.
B u t
i m p r o b a b l e
if
7 8 - 9 ) .
o n e :
w a s
t h e
o f
that
f r o m
g i v e n
p r o b a b i l i t y
since
d i r e c t i o n :
in
(fall
h e
m a r g i n s
O b v i o u s l y
w a s
c o n c l u d e d
h i g h l y
a c o n d i t i o n a l
w i t h i n
c o n c e r n
b e t w e e n
o b s e r v a t i o n s
t h e
is
test
solar
his null h y p o t h e s i s
is
h e
t o
line
c h a n c e ,
p p .
less
s p e c t r u m
is s m a l l e r b e
o r
n o t
a s p e c t r u m
b y
a
p r o b -
interval
m a t c h
i r o n
unlikely;
1 8 6 2 ,
w h a t
in
a
t h e
f r o m
w o u l d
h a v e ,
test?
h y p o t h e s i s
t h e
i n d e p e n d e n t
u s e d
t h e
w o u l d
just
t h e
m o r e
lines
If
b e
distribution,
H i s
K i r c h h o f f
o f
is
w a s
distance
, w h i c h
t e r m i n o l o g y ,
t h e m
in
s h o u l d ,
( K i r c h h o f f ,
t h e y
lines
s p e c t r u m
b u r n e r
w o u l d
h e
d a r k
t h e
d i s t r i b u t i o n
a i m
in
n o t
certain
the
t h e
sixty lines
a
his
line
a n y line
T h a t
in
b u r n e r .
that
iron
data w e r e
test
a
w h a t
T h e
that
characteristic
c o u l d
u n i f o r m .
m i l l i m e t e r s ,
the
true
b r i g h t
o f
s o m e t h i n g
w i t h
null
2
B u t
for
s h o w
u n i f o r m
falls
really
B u n s e n
t o
s p e c t r u m
t h e
a line
G i v e n
left
l o c a t i o n
c o i n c i d e
a
a B u n s e n
w e r e
w a s
interval.
t h e
i r o n
s p e c t r u m ?
l o c a t i o n s
in
0.5.
m a t c h ,
i n s t r u m e n t a l f r o m
s o u g h t
q u e s t i o n :
t h e
solar
that
for
o f
o r
w a s
t w e n t y
f o r m
b y
c o r r e s p o n d e d
s p e c t r u m
s p e c t r u m
t h e
lines w a s
a v e r a g e
in m o d e r n
a n d
G u s t a v
h a d
preliminary
t h e
solar
p o s e d
that
p r o b a b i l i t y
h y p o t h e s i s
h u n d r e d
s p e c t r u m
K i r c h h o f f
say,
lines o f
sixty
s p e c t r u m
t h e
R e c o n s t r u c t e d
o f f
a n d
i n f e r e n c e
b y
detail,
significance
p r o b a b i l i t y
i r o n
line
o f
of,
t h e
m i l l i m e t e r
right
filings
correctly)
in
test
t h e
it a m a t c h .
c h a n c e ,
solar
in
filings
Vi
any
t h e
i r o n
lines
a r g u m e n t ,
lines
H e
o f
w e r e
is o n
that
a
p r o b a b i l i t y
i r o n
s p e c t r u m
call
this
t h e
w i t h i n
probability
s t u d y
t h e s e
1 8 6 2 ,
l o c a t i o n s
fell
the
a
g i v e n
I n
c h o s e n
o f
in
data
h e a t i n g
solar
is
solar
d e s i g n ,
statistical
lines
flames.
lines in
l e n g t h
sixty
t h e
m u c h
b r i g h t
t h e
lines
t h e
s p a c i n g
a n d
a n d
o f
c h a n c e .
d a r k
s p e c t r u m
Vi
d a r k
t o
t h e
H i s
as
p a r t
b r i g h t
r a n d o m l y
t o
c o i n c i d e n c e .
o b t a i n s
d u e
w h i c h
t h e
s p e c t r u m
t h e
calculation
p r o p o r t i o n a l
in
e x p e r i m e n t a l
e x a m p l e
d e s c r i b e d
w o u l d
o f
sixty
t o
first
a probabilistic
w e
a series fact
first
Fisherian
p h e n o m e n o n .
w h a t
c o n t i n g e n t
a
d a r k
s o d i u m
b e t w e e n
a n d
o f
experts
a m b i g u i t y
O u r
lines
w i t h
o f
s a m e
s p e c t r u m
such identifications
o f
t h e data.
F r a u n h o f e r ,
o b s e r v e d
p r o d u c t
t o
o b s e r v a t i o n a l
K i r c h h o f f
t o
n o t
inference
a
t h e uni-
that
t h e
that
t h e
p e r c e p t u a l
a n d
t h e
o b s e r v a t i o n s
d a t a
s u g g e s t
this
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The
correlation. nificant
T h u s ,
findings,
K i r c h h o f f b y
u s i n g
t h e m s e l v e s .
Little
b u t
similar
a r g u m e n t s
F o r
instance,
o f
t h e
is
a r g u e d
in
a n g u l a r
s e p a r a t i o n
natural
c o n c l u s i o n
certainty
a
o f
p a p e r
stars
nearly
t o g e t h e r ,
e v e r s o m e
this
o t h e r
B o t h
p r o b l e m raised
that
r e p e a t e d
K i r c h h o f f f o u n d
o n e
t r u m .
T h i s
a n c e
o f
t h e
t h e
assertion
b e
tails. A l l
t h e
basis o f t h e
their
t h e
biased
files
t h e
d a r k
lines
all t h o s e
all, t h a t
fact
is n o t
a
g a v e fluke
w o u l d
. . .
p l a c e d
t o
w h a t o r
t o
b o t h
t h e
s t u d i e d
J o h n
-
F o r b e s H e r s c h e l
c a n i m a g i n e spectra t h e
a
that
until
solar
h e
s p e c -
m i l l i o n s
o f
a h u g e
p r e p o n d e r -
able
e x p l a i n
m u c h
t h a n
h a v e
o r
1 7 6 7 ) .
t h r o w i n g
w a s
t w o
o f
E d w a r d
o f
g a v e
K i r c h h o f f
e x p e r i m e n t a l
p h e n o m e n o n
that
t o
stars
b e e n
o f
as
n e x t
gravitation,
w h e n
a n d
fallacy
a n d
l a w
Similarly, w e
s a m e
" T h e
o f
sciences.
h a d
chance.
consist
h a d
files
o f
t o
1 8 0 3 ,
small
particular,
d a t a
in
o f
( M i c h e l l ,
calculation
1 9 8 2 ) .
t h e
t o
m u t u a l
o b s e r v a t i o n a l
part
d u e
g e n e r a l
In
b e f o r e .
M i c h e l l
p r o b a b l e ,
C r e a t o r "
after
t h r o u g h
g i v e n p r o o f ,
consist
o f s o m e
r e a s o n i n g ,
f r e q u e n c y
b e
really
o b j e c t i o n s .
c o i n c i d e n c e
t h e
n o t
h i g h l y
d o
t h e
G o w e r ,
in
h i g h
sig-
o b s e r v a t i o n s
b e e n
as a p p e a r
t o
t h e
h i g h l y
K i r c h h o f f ' s h a d
t h e
is
M i c h e l l
c o m m i t
o f
p r o b a b i l i t y
in
t h e
calling
that
o f
m a t c h e d
t o
a n d
o n
t o
s e a r c h e d
closely
o r
o f
b y
o f
a s t r o n o m e r J o h n
stars
c h o s e n
arises
(see
it
w h e t h e r
certain
w e r e
o f t e n
1 8 4 0 s
t i m e s
h e a d s
tiny
test
w o u l d
sixty
invite
that
basis
o b s e r v a t i o n a l
that
i n f l u e n c e
a p p o i n t m e n t
h a v e
that
g a v e
t o g e t h e r ,
o w i n g ,
o b j e c t i o n
m a y
c o i n c i d e n c e s t o
b e
o r
t h e
o r i g i n
1 7 6 7
is,
t h e
t h e
s u g g e s t e d
E n g l i s h
d o u b l e
n e a r
u n d e r
m o s t
it i n
t h e
in
s u c h
v e r y
t h e
this
stars,
o n
c o i n c i d e n c e s
H e r s c h e l
h e n c e
that
m a y
a n d
just
c o i n s
f r o m
a r g u m e n t s
h y p o t h e s i s
c o n c e r n i n g
null
w a s
t h e
89
o f close pairs o f stars c o u l d
a n d
l a w
t h e
that
a b o u t
p u b l i s h e d
p l a c e d
cause
test
W i l l i a m
in general,
m o r e
a
binary
experts
rejected
k n o w n
b e f o r e
e x i s t e n c e
inference
t o
m o r e
a n y
t h e
c r e d e n c e
calculation
if it w e r e
n o t
d u e
o f
t o
a
cause. I n
t h e s e
e x a m p l e s
w i n d o w - d r e s s i n g , e x p l a n a t i o n p o w e r s
o f
d r u g s
is o f t e n
a t i o n
o f h o w
o r
t h e
b y
causes
statistics
o f
Fisher
unification
real
inferential
fertilizers
p r o v i d e d
d e n i e d
d i s c u s s i o n B u t
t h e
o f
t h e
is
f r o m
m a d e t h e
g e n e r a l
causal
p r o v i d e d
n o
e x p e r i m e n t
is n o t
o f
d a i m s p a n a c e a .
T h e r e
t o
t h e
i n t o
o n l y
w h i l e
b y
deal
w i t h o f
claims.
s u c h
It
causal
e v i d e n c e
detailed
K a r l
t h a n
physical
t h e
Fisher's p r o g r a m
p o s i t i v i s m causal
m o r e
carried
I n v e s t i g a t i o n
available.
it p o s s i b l e
little
w a s
e x p e r i m e n t s ,
e x t r e m e
a n d
b u r d e n
different.
m e a n i n g f u l n e s s
p r o v i d e d
e v i d e n c e .
c o m p a r a t i v e
o p e r a t e
e x p e r i m e n t a t i o n
s e p a r a t e d s i m p l y
a n d
r e a s o n i n g
o r direct o b s e r v a t i o n a l
h a v e
parative
statistical
e x p l a n o f
c o m -
p r o b l e m s .
P e a r s o n ,
m a d e
w e
a
It
w h o
s y s t e m a t i c
possible. Especially
statistical analysis
in
t h e
social
that h e
sciences,
i n s p i r e d
has
t h e b e e n
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9 0
The
highly t h e
t r o u b l i n g
i d e a
o f
c r u s t e a n
w h a t
B e d
c h o l o g i s t s ' effect,
F i s h e r i a n
p h e n o m e n a g e n e r a l
p o p u l a t i o n ,
t h a t
t h e
c a u s e
i n d i v i d u a l ,
t h e y
d e s i g n
w e r e
t r o v e r s y is
causal
a r e
w i t h J e r z y
d i s c u s s e d
3 . 4
in
t h e
T H E
W i t h i n
b y
t h e
N e y m a n
a n d
f o l l o w i n g
b e g i n n i n g
o f
t h e
d r a w
d i f f e r e n t
a p p r o a c h e s
o f
R.
v i e w s :
t h e
B a y e s i a n s ,
t h e y
a r e
p r a c t i c e s .
T h e y
effort.
t h a t
b e e n g o
I n
n o
i n t o
w o r d s
" c o h e r e n t , " t h e o r i e s .
I n
s e n s e
t h e
s c h o o l s
l a d e n
bias,
a r e
d e c l a r e d
d e e p
f e r e n t
m o r e
a n d
f r o m
a p p r o p r i a t e
s h o u l d
o f
a n d
t o
t h e
a
effect
a p p l y
its
o n
s o n
o n
t o
a d m i n i s -
e x p e r i m e n t a l i n f e r e n c e
o f
H i s
c o n -
K a r l
P e a r s o n ,
N
M
e a c h
c a n
o u t c o m e o f
a
N e y m a n
Y
A
N
o f
a
f o r
t h a t
fiercely
t h e
s u c h
as
o f
a p p r o a c h e s
basic
c e n t r a l a r e
t h e r e
h a s
s c h o o l s T h e
a n d
dif-
v a l u e -
" u n b i a s e d , "
c o n c e p t s
c h a r g e d
o f
intellectual
s e v e r a l
issues,
"efficient,"
earlier r a n g e
o f statistical i n f e r e n c e . a b o u t
as n a m e s
a w i d e r
a l t h o u g h
d i s t i n g u i s h
v e r y
P e a r s o n ,
o v e r
t r e m e n d o u s
h a v e
T h e
E g o n
a d v a n c e
a c c o u n t
v i e w s
d a t a .
a n d
b r e a k t h r o u g h ,
p r a c t i c e
s p e e c h
rival
E
d i s t i n c t
statistical
c o n s i d e r a b l e
issues
a n d
e n l i s t e d
V S .
i n
w i t h
t h e
a n d
v a r i o u s
inefficiency,
i n c o h e r e n c e .
statistical
s o m e
b e e n
i m p l i c a t i o n ,
r e a s o n i n g
a l l - e n c o m p a s s i n g
fact,
a n d
d i s a g r e e
o r d i n a r y
is
p s y c h o -
r e f e r e n c e
statistical
s e v e r a l
f r o m
o f J e r z y a
s p e a k
T h e
f o u n d a t i o n s o f t e n
h a v e
B y
w i n n e r .
t h e
T h e
d e s i g n
p r o g r a m s .
F I S H E R
c e n t u r y ,
F i s h e r ,
i n v o l v e
c a n
s t a t e
a l t e r n a t i v e P e a r s o n ,
6 ) .
P E A R S O N
successful
o n e
t h e
o f
E g o n
u n i v e r s a l
necessarily
analysis
D
s y s t e m a t i c t h e
n o t
t h e r e o f
p s y -
c o n c e n t r a t e s
i n c i d e n c e
v i e w s
c o n c l u s i o n s
A .
all
It
Fisher's
his
G e s t a l t
u n i v e r s a l
statistics,
t w e n t i e t h
t o
f o r
t h e
t o
P r o -
c h a p t e r
i m p l i c i t
d o
t h e
a
t h e i r
c l a i m s
fit
e x p e r i m e n t a l
p e o p l e .
i n
e x a m p l e ,
s e c t i o n .
N
h o w
all
w i t h
C O N T R O V E R S Y :
a b o u t
o f
t o
t o
t h e
(see
s e a r c h
i n t e r e s t
a d v o c a t e s
e m e r g e d
a n d
b u t
field
t h e
as
for
demonstrate
F i s h e r i a n
o f
t h e s e
f o r e m o s t
A
S i n c e
o n
s u c h
t o
t h e
i n c r e a s e
S i n c e
a c c e p t e d ,
criticized
o f
s t a t e m e n t s ,
o f
1987a).
largely
o u t
a n
n a r r o w e d
s i m p l y
e q u a l l y
o n l y
p s y c h o l o g y ,
A l t e r n a t i v e s ,
relies
a p p l y
is p r e s e n t .
( D a n z i g e r ,
s h a r p l y
r u l e d
I n
s t r i k i n g l y
a b a n d o n m e n t
r e q u i r e
trators
w a s
a n
is w a s
e x p e r i m e n t
t h a t
t h a t
e s t a b l i s h i n g
t h e
u s e
b e e n
w i t h
observers.
statistics.
p s y c h o l o g y
a s s o c i a t e d
w h e n
t o
virtually
experts
t h o u g h t f u l
e x p e r i m e n t
e n d e a v o r
e x p e r i m e n t a l
logical
s o m e
a n
o f
h a v e
o f t e n
t o
inference
t h e o r y ,
if c e r t a i n w o r k i n g
a p p l y
it o f
h a s
n o t
w h i c h
c o n d i t i o n s
t h e
a r e
statisticians
d i f f e r e n t
(yet)
a p p r o a c h e s
p r o v e n
c u r r e n t
satisfied
a d v o c a t e t o
t h e
a n
s a m e
p o s s i b l e
p o s i t i o n s ( b u t
see
a r e
o f
c o m e special
B a r n a r d ,
e c u m e n i s m set
t o
d a t a
i n ( G .
t o
a n
cases,
1 9 8 0 ) .
w h i c h E.
P .
I n o n e
B o x ,
Downloaded from https://www.cambridge.org/core. Newcastle University, on 09 May 2018 at 22:47:10, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.005
The
1 9 8 6 ) .
I n
s c h o o l s .
o t h e r F o r
m e n t a l
a r e a s
i n s t a n c e ,
t o
t h e
1 9 7 8 ;
S w i j t i n k ,
s c h o o l
h a v e
( L e h m a n n , T h e r e c a t i o n s
1 9 8 2 ) .
line
c o n q u e r e d
t w o
" f r e q u e n c y "
t h e
e x p e r i m e n t a l
" s u b j e c t i v e "
c a t i o n s
t o
s o m e
in
I n
t h a n
b y
R.
A .
c o n c e n t r a t e
o n
t h e
b e
d i s c u s s e d
v i e w p o i n t s . sciences t h e
f e w e r
f o l l o w i n g
f o u n d e d
w e
a n d
i n s o f a r
T h e s e
t w o in
s c i e n c e s
o f
C a m b r i d g e
W i t h
a r e
this
t h e
o n e
o f
t h e
e l e m e n t s
M e n d e l i a n
a n d
i n h e r i t a n c e , 4).
m a n .
w a s
least
a n
i n d e e d
o f
t h e
t h e m
t o
a c c u m u l a t e
t r i e d
t o
F i s h e r ' s t h e
b i r t h
r a t e
s u b s i s t e n c e
h e
w e a l t h . f a r m i n g ,
t h e y
B e f o r e since
6
r a n g e
h a v e
a p p l i -
see
W e
t o
t h a t
w e
a p p l i m o d e r n
o f applicability
o f
h a d . v i e w s
o f
o f
s c h o o l
W e
will
t h i n k i n g
t h e
v i e w ,
t w o
t h e
s c h o o l .
B a y e s i a n
statistical
i n
t h e
t i m e .
at
will
c o n f l i c t i n g least
i n f e r e n c e
i n u s e d
t h e in
v i e w s .
t o
i n f e r e n c e
H e t h e as
a
s t u d y
h a d
f a r m i n g
r e c o n c i l e
t h e
e v o l u t i o n
a n d
o f
t h e
t h e
rise
a n d
h e
(see
h e r e d i t a r y o n
fall o f
societies
a c a d e m i c
w a s , i n his v i e w ,
social
i n h e r i t a n c e
s u p e r i o r i t y a n
c h a p t e r
j u d g e d
b i o l o g i c a l a n d
biology. a n d
statistician
o n
e m b a r k e d
a n d
r e v o l u t i o n
h e l p e d
m o t i v a t i o n ,
w h o s e h e
i n
w h e n
a n d
physics, m a t h e m a t i c s ,
e x p l a i n e d
t h o s e
i n r o a d s
t h e o r e m
will
t h e
F i s h e r
abilities
d r i v i n g
effects
a m o n g
his
his
t h e
o f
a p p r o a c h e s o f
u n d e r g r a d u a t e
t e r m s
h e
b e c a u s e
w e
t h e
rationality.
c h a p t e r
p o i n t s
a l e a d e r
o f
B a y e s '
in
t h e s e
A .
s t u d i e d
b e c a m e
b i o m e t r i c
a c c o r d i n g A s
F i s h e r
h e
f r o m
o f
p e n e t r a t e d
m a d e
u n d e r s t a n d i n g
f o r m
R o n a l d
g e n e t i c i s t s
t h e
n o t
E u g e n i c s
m e a s u r e s o f
U n i v e r s i t y ,
g r e a t
T h e
a p p l i -
d e s i g n a t e d
h u m a n
t e s t i n g .
d o m i n a n t
o f
c o n c e p t s
N e y m a n - P e a r s o n
t o
( R u b i n ,
i n f e r e n c e
h a v e
h a v e
c o n f l i c t i n g
significance
b o o k .
m i x e s
this b a c k g r o u n d ,
t h e
as it is r e l e v a n t
Sir
A t
o f
o f
t o
t h e
p a y i n g
fields
u s u a l l y
a n d
T h e r e
s e e m s
o f
e i g h t e e n t h - c e n t u r y
a b o u t
e m p h a s i z e
analysis
o n l y
7.
h i m s e l f
will
a n d
t h i n k i n g
c h a p t e r
B a y e s
M e t h o d s
B a y e s i a n s
r e s e r v a t i o n s
F i s h e r
d i s c u s s e d
social
in
e x p e r i -
c o n d i t i o n a l
t h e
j u d g m e n t
o f
t o
N e y m a n - P e a r s o n
b e t w e e n
a p p l i c a t i o n s
d i f f e r e n t
c o l l e c t e d
t h e
o f
t r a d i t i o n a l
s t u d y
a r e
w i t h i n
B a y e s i a n s ,
B u t
legal
r e c e n t
life
h a v e
t h e o r e m t h e
as
o p p o s e d
N e y m a n - P e a r s o n ,
w h e r e a s
s u c h t h e
e v e r y d a y
a n d
n o t .
e x p e r i m e n t a l
Bayesians o f t e n B a y e s '
o f
s c h o o l s .
b e t w e e n
i m p o r t a n c e
o b s e r v a t i o n s
c l e a v a g e
r e c o v e r e d
p r o b a b i l i t y
t h e
cations
h a v e
o f
t i m e
t h e
i m p o r t a n c e
F i s h e r
h a v e
l o n g
statisticians
v a r i o u s
sciences,
s c h o o l ,
discuss
t u r n
t h e
s c h o o l s ,
a n d
o f
b y
a
r e c o g n i z e
t h e
r e m a r k a b l e
9 1
c o n v e r g e n c e
f o r
w h i c h
Similarly,
10).
s o m e
w e r e
b y
c h a p t e r
experts
b e e n
n o w
r e c o g n i z e d
a
e c o n o m i c s
b u t
p r o c e d u r e s
1 9 8 6 ,
is
h a s
B a y e s i a n s
r a n d o m i z a t i o n ,
a t t e n t i o n
will
t h e r e
inference
i n
e n a b l e d career,
a e u g e n i c
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w a y
92
The
o f
life, in w h i c h
tor
(J. F .
t o
t h e
a n c e t o
B o x ,
o f
F i s h e r
R o t h a m s t e d
established
d i f f e r e n t
field
t h e
p h o s p h a t e
e x p e r i m e n t s ,
F.
l o o k s
o f
ments,
p u b l i s h e d
data
o f
part,
o v e r
o n l y
based w i t h
o n
in
a v e r a g e
yield
p e r
t h e
right
t e c h n i q u e s 2 5
o f
t h e
a
a n d
Fisher's
w a y s
t o
basic
p o s e s
t h e
b y
t h e
in b y
w a s
e x p r e s s
t h e
o f
Fisher m u s t
probability. a p r i o r w a s
a
w i t h a
T h e
w e r e
p r e s e n t e d
a n d
verifiable
in
inferthat
t o
s o l d
b o o k
t h e
n e w
d u r i n g
t h e
international
o f
( 1 9 3 5 ) , c o m p a r a t i v e
t h e
a n d
o f
( 1 9 2 5 ) ,
Experiments
h a d
factorial r e a c h e d
a
1 9 6 2 .
o f
statistical
a p p r o a c h in
t h e
Bayes'
insisted t o
a l t h o u g h
in statistical
d i s t r i b u t i o n h e
Fisher
w i t h
Workers
h y p o t h e s e s
o f
t h e
i n f e r e n c e s
itself,
efforts
t h e
u s e
frequentist, b e
o f
w i t h
m o s t
e x p e r i e n c e ,
H i s
w h e n
t h e
c o p i e s
h y p o t h e s i s
p r o b a b i l i t y
theoretically
a n d
of
in
f r o m
u n c e r t a i n t y
o f
F o r
successful,
c o n c e p t s
satisfied
1 9 1 7 ) .
principles
provisional.
u n c e r t a i n t y
a p o s t e r i o r
learn
d e v e l o p i n g
n o t , h o w e v e r ,
S i n c e
w e
field
Experi-
d o n e
increasingly
d e a t h
o f
I n d e e d ,
r a n d o m i z a t i o n ,
similarly
t y p e s
Rothamsted
Research
Design
t h e
Fisher's
that
r e m a i n
t h e
o f
The
o f
C o n t i n u o u s
agriculturalists
a n
soil
f a m e . Fisher's first
2 0 , 0 0 0
t o
b l o c k i n g ,
o f
t o w a r d
a n d
w h i c h
ability j u d g m e n t
It
w a s
nearly
t h e
c o n f r o n t a t i o n s
for a n d
b o o k ,
a c c o u n t
always
availability
h y p o t h e s e s .
third
t i m e
belief
d i r e c t e d
data. Fisher w a s
e x p r e s s e d
Methods
o n
b e e n
station
c h i e f
agricultural
R o t h a m s t e d
t h e
e x i s t e n c e ,
replication,
m u s t
m e a s u r e
t h e o r e m ,
H i s
h a d
t h e
at
R o t h a m s t e d
station.
of the
4.4).
v a r i o u s
o f
vari-
factors
also
b e c o m e
a n d
o f
statistician
effects
(Hall,
daily
biologists
o f
t o
tabulated,
o f
see
fac-
Fisher
causal
a m m o n i a .
t h e
little
m e a n s .
w o r k
Statistical
c o n f o u n d i n g .
k n o w l e d g e w e r e
t h e
b o o k ' s
s y s t e m a t i c
e d i t i o n
e n c e
in
o f
b y Fisher's rapidly g r o w i n g
1 9 5 1 ) .
e x p e r i m e n t a t i o n :
s e v e n t h
w a s
o f
t h e
Book
h o w
It p r o v i d e d
i n t r o d u c i n g
( Y a t e s ,
p r o v i d e d
d e s i g n ,
a n n u m
p o s t
led
analysis
1 9 1 8 ;
a w e a l t h
The
that
L a b o r a t o r y .
j o i n e d
o f
o f statistical analysis, w i t h
years
a u d i e n c e
arose
t h e r e
in
e d i t i o n
c o m p a r i s o n
m e t h o d o l o g y ,
successful
p r o v i d e d Fisher
d o m i n a n t
d i f f e r e n t
b o n e s ,
e x p e r i m e n t a t i o n
challenge.
that
b u r n t
t h e
o f f e r
G a l t o n
m u r i a t e
is s t r i k i n g
o f
statistical
first
it
years
visitors attracted
w a s
1 9 1 7 ,
a j u d g m e n t a l
just
s e c o n d
a n
i n v e s t i g a t e
o r
w h e n
o f
c r e a t e d
t h e
m e a l ,
o f
Fisher,
r e f u s i n g
t o
1 8 4 3 ,
sixty
ential p r o b l e m s
o n
t h e
n e w l y
s u l p h a t e in
t e c h n i q u e
1 9 8 0 ;
at
b o n e
b e g u n
t h r o u g h
t h e
1 8 3 0 s
data, still largely u n a n a l y z e d o n e
B o x ,
Station,
late
w i t h
t h e
t h e
o f inheritance
c o n t r i b u t i o n s
P e a r s o n
c o m b i n a t i o n s
m i n e r a l
t o
t h e
a c c e p t e d
K a r l
in
a n d
(J.
E x p e r i m e n t a l u n d e r
qualities w e r e
his investigations
separate
correlations
1 9 1 9 ,
statistician
It w a s
t o
experts
b u t p e r s o n a l
variance,
c o m p o n e n t s
In
m o n e y ,
1978).
c o n c e p t
o b s e r v e d
w a s
n o t
inference
a n y
in
o u r
infer-
e v i d e n c e t h e
light
b a s e d
o n
light
o f
o f
Bayes' data
is
t h e o r e m
p r e s u p -
o v e r
t h e
p o s s i b l e
that
e v e r y
c h o s e n
p r o b -
d e g r e e
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o f
The
a p p r o x i m a t i o n
b y
inference
s a m p l i n g
its
can, a c c o r d i n g
t o
i s a priori
distributional
i n f o r m a t i o n
is,
t h e
cases
o b s e r v a t i o n s p o p u l a t i o n
a p p l i e d
are
o f
c o m m o n .
F i s h e r
t o
cases.
prior
ance,
lead
w o u l d
d e n c e
is
just
Fisher's
a
Bayes'
test
m o d e l i n g
( t h e
that
n o t
is
a
c o n f i d e n t
in
t i o n
o f
o f
w h e r e
h y p o t h e s e s ,
It is e s p e c i a l l y t o
e n c e
a
class
W e that
will
t h e
a
o t h e r
o n e
h e r e
Fisher's
b e l i e v e d
that
tainty o f
h y p o t h e s e s
f r o m
a
small
t h e
in
n u m b e r
t h e
t o
e x p r e s s
priori
m u t u a l l y o f
i g n o r -
s t r e n g t h
o f
evi-
w i t h
a
light
t h e
b e
o f
t h e
t h e
B a y e s o f
u s e
w a s
o f
t h e
w i t h o u t
t o
T h i s
p o i n t
t h e
h y -
m a k e
o n e o t h e r
t o
t o
special
o f
refer-
correct. n o t
m e a n
R i c h a r d
o f v i e w ,
e x p r e s s
Bayes'
Fisher's
w h a t
d o e s
m e a n i n g f u l
u s i n g
f u n c -
probability.
t h e o r e m .
o n l y w a y
d o e s
o f
b e i n g
Bayes'
d r a w
test
u n c e r t a i n t y
instance,
f r e q u e n t i s t
data. T o
o b s e r v a t i o n s
o f
F o r
a s s u m -
t h e
r e s p e c t
testing.
c o n t r o v e r s y .
signifi-
data,
c o n s i s t e n c y
f r e q u e n c y
significance
A
g o o d
p r o p o s e d
t e r m s
fact,
a
in certain
in
w i t h
all
as a l i k e l i h o o d
e x p r e s s e d
t h e
that
h y p o t h e t i c a l
c o n s i d e r a t i o n s
applies,
a
a
p r o b a b i l i t y
s u c h
o f
d i f f e r e n t
significance
a r g u m e n t
clear
test.
F i s h e r
u s e
h a v e
t h e
data. O n l y
q u e s t i o n e d
o f
A
o f
b e
are, in in
n o t
that
light
m o d e l , "
g i v e n
it is n o t
less
b y
in
t h e
T h e r e
d o e s
s u g g e s t
d e g r e e
f r e q u e n t i s t
t a k e n t h e
o n l y
t h u s
a s s u m e
significance
theoretical
has
t o
t o
a p p r o p r i a t e
o n e
uncertainty,
c a n
h a v e
are
a
s h o u l d
o b j e c t i o n s
p r o p e r l y .
fiducial
since
o f
m a k e
p a r a m e t r i c
m o d e l
m a n y
o f
a
state
w h e r e
u n -
n o
w a y
s a m e
w r o n g
w h e n
c a n
a n d
r e p r e s e n t
c a u s e d
r o u t e
v e r y
s u p e r -
v e r y
researchers
i n f e r e n c e
that
specific
h y p o t h e s i s
analysis
a
the
c o n s i s t e n t l y
h a v e
o n e
o f probabilities.
p e r f o r m e d
M i s e s , h i m s e l f a m a j o r p r o p o n e n t w i t h
d i f f e r e n t
are
is i m p l a u s i b l e
"full
o n l y
t o o l s
can
a n d
a n y
f r e q u e n t i s m ,
deal
b e
a n d
t h a n
n u a n c e d
in t e r m s
b e l i e v e d ,
particular
w h i c h
f r o m
c a n n o t
m o r e
t h e
f r o m
t h e r e
s a m p l e d ,
o b v i o u s l y
i g n o r a n t
statistical
t h o u g h t ,
so-called
that
are
subjectivism,
e x p e r i m e n t s ,
w a s
in
Fisher h e r e
h e
o n ,
a n d
his
a l l o w
h i g h l y
e x p e r i e n c e
calculate
are
b e i n g
r a n d o m
t h e o r e m
u n c e r t a i n t y
assign
a c c e p t i n g
a d h e r e n c e
his
a r g u m e n t
t h e p a r a m e t e r s
situations,
o f
r e p r e s e n t
past
p o p u l a t i o n at
Bayes'
cases w h e r e
p o p u l a t i o n
cases
e x p r e s s
in
e x p r e s s e d
t o
W h e n
t o
light
is g o i n g
o n e
t h o s e
1 9 6 2 ) .
taste.
h y p o t h e s i s )
p o t h e s i s .
m e t h o d s
o f
t h e
exist
u n a c c e p t a b l e
e x p e r i m e n t
p e r m i t
will
(Fisher,
in
d r a w n
w e
t o
u s e d
T h e s e
T o
p r o g r a m
w e a k
null
t h e
t h e r e
c o m p a r a t i v e
w h a t
b e e n
w h e r e
Bayesians,
t o
I n
a b o u t
c a n c e
a n
c a n b e
w a y s
situations. idea
t h e
T h e
uncertainties d i f f e r e n t
t o
m a t t e r
in
rule.
F o r
set
t h e
Bayes'
probabilities
research
u n d e r s t o o d
that
probabilistically.
inconsistent
that
itself
h e l d
b e
a b o u t
k n o w
has
i n f o r m a t i o n ,
i g n o r a n c e
o n l y
specification.
also
o t h e r
Fisher,
w e
d r a w n
k n o w n
distributional that
w h e r e
93
r e f e r e n c e
t h e o r e m
that
experts
v o n
a g r e e d B u t
h e
u n c e r -
c o n c l u s i o n s t h e o r e m ,
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as
94
The
Fisher in
w a n t e d ,
1 9 5 1
that
M i s e s , the
" t h e
[ 1 9 2 8 ]
1 9 5 7 ,
u n d e r s t a n d s u p p o r t
p.
s i m p l y
t h e
F o r
t h e
o n e
can
that
(1)
T h e
b u t i o n a m p l e pair
w a s
b u t i o n
s a m e
t h e
3.2,
t h e
for
all
pairs.
It
" r a n d o m
o b s e r v a t i o n s
t o
lack o f
sibly
as
t h e
t o
m a t r i x " ( 2 )
a
d e g r e e
e m p h a s i z e d
lead
f r o m
f r o m
t h e
s i t u a t i o n
h y p o t h e t i c a l
o f
t h e
W e o f
b e o n
d e v i a t i o n
s a m e
that
o f
p o s s i b l e
f r o m
t h e
has
s u c h
as
o b s e r t h e
hy-
T h e r e
are
t h e
p o s s i b l e
a
m e a s u r e W e
as
b o t h
since is in
t h e
h e r e
s a m e
that
b o d y
c o n c e r n s
w h i c h
t h e i m p o r t a n c e
o f
s h o u l d
h y p o t h e s i s .
t h e
B u t
a n d
a w e a b e
o f
data.
t h e
p o s -
since
it
"causal
this p o i n t
t h e
if
n o t
s a m e
reflect
o f
d e s i g n ,
c o u l d
ineffective,
/-
is n o t
instance,
first
it
T h e
u n k n o w n
s p e a k s
t h e
t h e
t h e
variance
t h e p o p u l a t i o n
o f data
a
distri-
variance.
F o r
o f
o b s e r v a t i o n s
o f
u s i n g
b o d y
n o r m a l
o n e
e x -
w h i c h
u n k n o w n
repeatedly. field,
in
r a n d o m
a l t h o u g h
distri-
m e m b e r
a
u n k n o w n
o b s e r v a t i o n s null
o f
agricultural
e a c h
i n d e p e n d e n t
t r e a t m e n t
t o
t h e
a n d
t h e n
a n d
r e p e t i t i o n s
will r e t u r n
test
a u n i q u e
p o p u l a t i o n ,
p o p u l a t i o n
t h e
o f
that
pair,
are
that,
u n r e l a t e d
a
w i t h
a n d
is
1 4 9 ) .
null h y p o t h e s i s .
in
b u s h e l s )
t h e
zt
h y p o t h e t i c a l ,
series
t h e
s a m e
s a m p l e d
s a m e
t h e
p o p u l a t i o n , "
t h e
o f
h y p o t h e s i s ,
stated
z e r o
h e r e
s a m e
t o a q u i t e
p o p u l a t i o n
o r d e r i n g
m e a n
o f
implausible.
f r o m
in t o
p.
f r o m
o r d e r i n g
J e r z y
n u m b e r s
1 9 4 1 ,
e n o u g h
instance,
distribution,
e x p e r i m e n t
is o p e r a t i v e .
T h e
w i t h
in principle
t a k e n
h y p o t h e t i c a l
refers
tive
t h e
rain m i g h t
called
b e
c o u l d
r e p e a t
c o n s i d e r e d F i s h e r
t o
g r a i n
a n
null
t h e
particular
k n o w n
variance.
w e r e
has
a
o f
o f
features
specification
F o r
f r o m
158).
in
i n f e r e n c e
h y p o t h e s i s
is
t o
o r d e r .
t h e
d i f f e r e n c e s
d i s t r i b u t i o n
h a v e
that
T h e
t h e
h y p o t h e s i s
(yield
null
d e v i a t e
that
statistic.
null
m e a n
in
a l l o w
o b s e r v a t i o n
u n k n o w n
will
real o n e
test
o b s e r v e d
a n o r m a l
statistic
for
m u s t
a
d e v i a t e s
c o n c e p t s
n o t
I n a test o f significance,
h y p o t h e s i s , f r o m
p.
( N e y m a n ,
h y p o t h e s i s
o b s e r v a t i o n
t h r e e
r a n d o m
w i t h
null
their d e v i a t i o n
h y p o t h e s i s
s e c t i o n a
o b s e r v a t i o n s
probability
a t h e o r y
essential
f o r m
his f o l l o w e r s
fiducial
e x a m p l e ,
t h e
t h e
o f
( v o n
c o u l d
c o n f e s s e d
1 9 5 7 ,
c o n f r o n t s
t h e
H e
[ 1 9 2 8 ]
d e f i n i t i o n s "
past"
o f prior
M i s e s ,
o n e
t h e
influence
t h e o r y
p r o c l a i m e d
b e l i e v e d ,
a n d
as follows.
c o n c l u d e
h e
F i s h e r
as, f o r
e x p o s i t i o n ,
h e
is a l r e a d y
vanishes.
" t h e
w a y
a n d
b y
3.2,
here:
t h e s e
f u n c t i o n o f
f r o m
c a n
as t o
characteristic
t h e
s e c t i o n
w h e t h e r
null
h e l d :
s a m e
this
the
u s e d
( v o n
c o n t r a d i c t o r y o f
c o n c e p t s
u p
t h e o r y "
t h e
far a particular
take
w o r d s
. . .
s a m p l e s ,
d i s t r i b u t i o n
s u m m a r i z e d
o n e
o b s e r v a t i o n s
will
in
see
t h r e e
h o w
b e
large
n o t h i n g ,
t h e o r y
since h e r e
beautiful
in
f r o m
s a m p l e
O n l y
cautiously,
p u r p o s e s
t o
p o t h e s i s t h u s
m a n y
less
g i v e n
v a t i o n s
1 5 9 ) .
experts
m u c h
small
inference,
m u t u a l l y
significance
t o o
p o s t e r i o r
n o n - e x i s t e n t b y
o f
l i k e l i h o o d
still
d e f i n e d
the
t h e
"the
o f
N e y m a n ,
o n
g e t t i n g
h e y d a y
basis o f objective
a s s u m p t i o n s
o f
m e a n t
inference
their
later. rela-
o b s e r v a t i o n s
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The
c a n
d e v i a t e
sary
t o
t i o n ,
in
d i f f e r e n t
c o n s i d e r
a n d
p r o c e s s
t h u s
d i f f e r e n t
i n d e p e n d e n c e , test
b a s e d
t h e
test
a n
o n
o n e t h e
a n d
the
testing,
kind, and
in
accomplished
(3)
A s
>
j
o b s
o f
t h e
;
0
H
W e
F i s h e r
o f
g a v e
o b v i o u s
t h a t
d i s c r e p a n c y c o m e s
n o t
Scientific
( F i s h e r , A l l a
b e t w e e n
a n
significance
in
1 9 5 6 ,
all, t h e
u s e f u l
w i t h
r e s p e c t
ancy. 3.2,
S o ,
b e
actually
t o w e
t h e h a d
less
m o r e
clear. f o r
It
a n d
s h o u l d
l o w e r test
a
experiments q u e s t i o n
r e m a i n s
Sellke, b e
statistic
t h e
o r
w i t h o r
w h e t h e r w h e t h e r
u n s e t t l e d
a
ever
(Fisher,
f r o m
it
t h e
called
w i t h
his
w i t h
different
same
t h a n
level
( M a r t i n - L 6 f ,
m e a n i n g f u l 1 9 7 4 ;
a a n d
d i s c r e p -
o f
s e c t i o n
o b s e r v a t i o n s t h e
is
is
o b s e r v a t i o n s
t h e
significance
t o
experiment
t h e s e
statistics
o t h e r
level
r e s p e c t
e x p e r i m e n t 1 % ,
t h e o r y .
a g r e a t e r
test
a n y
f e a t u r e
l i k e l i h o o d
i n d i c a t e
o u t -
a p p r o x i m a t i o n "
t h e
t h e
t h e
Methods
o f
say,
o n
Statistical
significance
in
,
o f
s h o u l d
F i s h e r i a n d a t a
o b $
s o m e t h i n g
d e p e n d
a n
j
e x p l a n a t i o n
§ 7 ) . W h y
as
h y -
u s e
a q u e s t i o n a b l e
s a v e
6).
f r o m
v a l u e
1 9 5 6 ,
this w a s
1939, p.
its o b s e r v e d
o r i g i n a l
of
b e e n
n u l l
d e r i v e d
o f
has
t h e
h y p o t h e s i s
of,
re-
w o r t h
d e v i a t e s
u n d e r
1 9 3 5 ,
level
be
C o n s t r u c -
thinking
f o r m
h y p o t h e s i s
w i t h
can
t h e
level
Fisher,
are
c o m p a r a t i v e
t h e
for
a o f
hypotheses
T h e
will i n d e e d
in
c h o i c e
w h a t
since
o d d s
w h e t h e r
significance
d i s c r e p a n c y ,
t h a t
significance
o b t a i n e d ,
a
o r
o f data
o b s e r v a t i o n
b o o k
d i s c r e p a n c y
d i s c o r d a n t
T h e
d e v e l o p e d ,
B e r g e r
t h e
a n d
it is a t
r u n s ,
f o r
experience
fundamental
d e f e n s i b l e
i n d e e d ,
test
o n
c u s t o m
his later
v e r y
r e m a i n s
same
based
(Fisher,
c o n c e d e d
" n o t
A
w i t h
m a d e . Across
m e a s u r e b e
m o d e l .
o b s e r v a t i o n s
w o u l d
is
if
o f
I n
o f
r e m a i n s ,
this process
satisfactory,
o b s e r v a t i o n
t o
a
p r o c e s s :
o u t l i e r s .
m o t i v a t i o n
p . 6 6 ) , a n d ,
m e a s u r e
o f
w a n t s
is t h a t
1 9 6 8 ) . T h e
p r o b a b i l i t y
this
d e v i a -
o f tests o f significance.
p a r t i c u l a r
t h a t
o f
h y p o t h e s i s
testing,
that
this
t h e
k i n d s
n u m b e r
statistic s b e y o n d
v e r y
F i s h e r
q u e s t i o n
h y p o t h e s i z e d
test
o b s e r v e d ?
testing,
a
n e c e s -
t h e
deciding o n
w h e n
u s e d
n o t
m o r e
Inference,
theory
r e j e c t i o n
w a s
think
k n o w l e d g e
m u c h
earlier
n e e d e d
actually
to
b e
o n e
( B r a d l e y ,
w o r t h
m a y
a n d
m e c h a n i c a l
before
t h e
t h e
o n
n u l l
be given a mathematical
F i s h e r
i n
a
O n l y
h o w
n o t e d
this
t o
m u c h
respects.
o f
r u n
It
d i f f e r e n t
if t h e
b a s e d
l o n g e s t
exercised
tail area
) .
test
illusion
with
h y p o t h e s i s .
r e f l e c t i n g
h y p o t h e s e s
an
n u l l
i n s t a n c e ,
mathematical
h y p o t h e s i s ,
tests
o f
b u t
o f
a
93
c o i n - t o s s i n g ,
a
r e d u c e d
be
m e a s u r e
significance
and
null
together
w h a t
t h e
can the p r o b l e m
a
n u l l
p o t h e s i s p(s
o f
o f
b e
m u s t
F o r
c h o o s e
to a self-contained
same
t h e
a n d
n o t h i n g
tive imagination,
f r o m
i n d e p e n d e n t
l e n g t h
experts
o r d e r i n g s ,
tests.
m a y
c a n n o t
It is, I b e l i e v e , d u c e d
like
statistic,
art,
r e s p e c t s
d i f f e r e n t
b e h a v e s
inference
a
s i t u a t i o n
m e a n i n g f u l m e a s u r e
S e i d e n f e l d ,
c a n 1 9 7 9 ;
1 9 8 7 ) .
r e c o g n i z e d
that,
a c c o r d i n g
t o
F i s h e r ,
r e j e c t i n g
t h e
n u l l
Downloaded from https://www.cambridge.org/core. Newcastle University, on 09 May 2018 at 22:47:10, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.005
96
The
h y p o t h e s i s tion. T h e b u t
is n o t
latter
r e q u i r e s
a n
e q u i v a l e n t
c a n n o t
o b t a i n i n g
i m p r o v e m e n t
c o n d i t i o n s . results t h e
s h o u l d
for
" n o
t h e
b e
n o t
in
1 9 3 5 ,
§ 7 ) .
fication
I n
fail
natural
a
selective t w o , t h e
statistical
h y p o t h e s i s B o t h
f r o m
t h e
this
a n d
in
his
i m p l a u s i b l e ,
a n d
Experiments
h a s
s a m e
v e r y
t h e
p h e n o m e n o n : w h i c h
a p p r o p r i a t e
o n l y
in
t h e
s a m e
g a v e
A n d
" [ T ] h e c a n
just
as t o
d i s p r o v e
c r i t e r i o n
o f
f o r
" t h e o r i e s
p p .
4 0 - 1 ) .
t o
tests
1 9 3 5
a n
. .
o f
e x -
f r o m
F i s h e r ' s t o
t h e
the
p a r t , i d e n t i -
d e m o n s t r a t i n g
significant w e
is
(Fisher,
testing
h a s l e d
I n
e x p e r i m e n t
r e s u l t "
o n
h e
suffice
p h e n o m e n o n
p r a c t i c e
o f
signifi-
c a n
result.
A s
F i s h e r i a n
a w e
will call t h e
hybrid
significance
N e y m a n - P e a r s o n - W a l d
in
t h e
t h e
facts
e x p r e s s
just
as
t h e
s h o w n
" p r o v e d
w a y
s c h o o l
t h e
a c h a n c e
b y
o f
o f
science s y s t e m
w h i c h
m e t t l e "
a n
P o p p e r
a n d t o
a
b e
unfalsified
o f
o u t
t h e
1 9 6 8 , t o
t h a t
p .
e x i s t
c a n n o t
falsifiability "it
m u s t
as b e
e x p e r i e n c e , " [ 1 9 3 5 ]
" d e g r e e
h y p o t h e s e s
[ 1 9 3 5 ]
d e f i n e d
h y p o t h e s i s "
b y
( P o p p e r ,
n o t i o n
b e
n u l l
u s e d
r e f u t e d
n a t u r a l
said
n o n - s c i e n c e :
b e
( P o p p e r ,
t h e
a
[ 1 9 3 5 ]
e x p e r i m e n t
v e r i f i a b l e "
n e e d e d
m a y
o f
carries
( P o p p e r ,
of
Discovery.
m a y
w h o
b e
p u b l i s h e d
Scientific
effect
a n y o n e
o n l y Design
b o o k
d e m o n s t r a t i o n
d i s p r o v i n g
is futile,
e m p i r i c a l l y
t o
of
e x p e r i m e n t
t h a t p e r f o r m i n g
P o p p e r
Logic
c a n
F i s h e r ' s
r e m a r k a b l e
p r e s c r i b e d "
" E v e r y
scientific
t h e i r
plausible,
P o p p e r ' s o f
h y p o t h e s i s
s i g n i f i c a n t physical
b e t w e e n
d e g r e e
n u l l
a n o t h e r
n u l l h y p o t h e s i s
. . . never
a
r e p r o d u c e d
w r o t e :
e m p i r i c a l
I n d e e d ,
as
K a r l
r e g u l a r l y
t h e
t h a t
b e
scientifically
16), m e a n i n g
a r e
a n d
n e v e r
m e s s a g e
d e m a r c a t i o n
a n
f o r
t o
b e
g i v e
p o s s i b l y
u p
a
w r i t i n g
e l e m e n t s
c h a r a c t e r i z a t i o n
F i s h e r
1 9 3 5 , p .
o r a t i o n "
so-called
1 9 3 5 :
e x p e r i m e n t
o r d e r
p o s s i b l e
m i x e s
i n s i s t e n c e
c a n
year, s a m e
(Fisher,
a
t h a t
itself,
significance
o f w h a t
t o
o f
c o n d u c t
statistically is p a r t
l e d
testing.
in
4 5 ) .
single
t h e
h a s
reflect
p h e n o m e n o n .
o f his early w r i t i n g s
e n c o u r a g e d a
t o
o t h e r
c o r r e c t l y
significant
C a r e l e s s
o f
t h a t
h o w
statistically
3.5, this p r a c t i c e
s h o w n
t h a t
k n o w
say
phenomenon.
i n f e r e n c e
i d e a s
a
m a y
d i s t i n g u i s h e d
basis
in s e c t i o n
w e
u n d e r
o r
n o n - s i g n i f i c a n t
in
n a t u r a l
q u e s -
e x p e r i m e n t ,
Experiments
significant a n y
o r
also
e x p e r i m e n t
i n
e x p e r i m e n t ,
l i t e r a t u r e
of
c a u s e
single t h e
b u t
Design
o f
t h e
l a b o r a t o r i e s
F i s h e r
h a s
w h e n
t h e
o f
The
w e
u s
r e a d i n g
a n d
let
h o w e v e r
w h e n
g i v e
of
o n
w i t h
t o
p a s s a g e ,
t h e
p h e n o m e n o n will s h o w
o f
this
w i t h
o f
o f
test
r a r e l y
c o m b i n e d
as
b o o k
e x p e r i m e n t ,
o t h e r
t y p e
o f
basis o f o n e
results
t o
c e r t a i n
his
d e m o n s t r a b l e
demonstration
P o p p e r
o r d e r
significance,
will
t h e
i n
efficacy
significant,
t o
t h e
t h e
at
o n l y
a
t h e
significant
d e m o n s t r a t i o n
w h i c h
i n
o n
r e p e a t e d
w h i c h
i s o l a t e d
p e r i m e n t a l l y
t e s t i n g
is
p u b l i s h e d
A l r e a d y
a c c e p t i n g
e x p e r i m e n t a l
r e l a t i o n
theory
m o r e
it,
w i t h
results.
w r o t e :
o f
t o
experts
established
T h e r e f o r e ,
f r e q u e n c y
c a n t
b e
inference
1 9 6 8 ,
o f h a d p p .
1 9 6 8 ,
c o r r o b s t o o d 4 0 - 1 ) ,
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The
F i s h e r s o
also vacillated,
w e l l
k n o w n
nificance said
t o
t h a t
b e
u p o n
a b o v e
d i v e r s e , F o r
t h e
a n d
t r e a t m e n t
h a s I f
t h a t
false,"
is
in
h y p o t h e s i s T h e
t h e
n o t
h a s
m e a n
The
a r e
o f
belief
of
T h e s e T h e y
w o r d s ,
d i d
in
m o s t
o f
it
sig-
m a y b e
F i s h e r
n e v e r
b e
this
t h a t
t h e
false.
t r e a t m e n t
t h e
t h e
h y p o t h e s i s
n u l l h e
l e a r n i n g
t h e
n a t u r e
a c c r u e d "
false
is
t o
t h e
b e
n u l l
n u l l
if
t h e
E f f o r t s
F i s h e r
a
d i d
c a t e g o r i c a l
s e v e n t h . . .
[ 1 9 3 5 ]
h y -
e x e c u t i o n
e v e n
r e p o r t s ,
(Fisher,
effect.
effective.
e x p e r i e n c e ,
c a n n o t
t h e
h y p o t h e s i s "
p r o g r e s s
a n
d i s t r i b u t i o n .
F u r t h e r m o r e ,
a d d e d
b y
o f
i n
h y -
belief
statistical
s a m e
e r r o r s
" t h e
t h e
s u b s t a n t i v e
t r e a t m e n t
a
as: null
h a s
t h e
t h e
t o
r e q u i r e d .
A s
is
a r e
r e a d e r .
substantive
" a d o p t i n g
r e j e c t e d
n u l l
still b e
t h e
f r o m
w r i t i n g s
h y p o t h e s i s
as
s y s t e m a t i c
w h i l e
far
call
his
h e r m e n e u t i c
n u l l
s a m e
c o n c l u s i o n s
n o t
call
The
Design
for
h a v e
d o n e
h i m
as
" t h e
significance
" a n
m o s t
m u c h
t o
e d i t i o n
c o n c l u s i o n s i n t e r p r e t i n g
I 9 6 0 ,
d e t a c h e d
i n v e n t i v e
o f
s i m p l e
t h e
size
t h e i r
( Y a t e s ,
§ 1 2 . 1 ) .
f r o m
t h e i r
h e
o f
f u r t h e r t h e
p r o m o t e d
t h e
t i m e ,
( E d w a r d s ,
1 9 7 2 ,
a n d p .
1 9 2 5 ,
b y
Statistical
a g r e a t in
o f
e m p h a s i s
for
o n
tests
w i t h
fiducial
a statistical
effects b y
r e a d e r s .
Methods
c o m p a r i s o n
e x i s t e n c e
controversial.
F i s h e r ' s
h i g h e s t I n o w
h a v e
t h e
F i s h e r ' s
t h e y
p r a c -
s t u d i e d ,
m e a n s
o f
a
b u t
single
1 9 5 1 ) .
t o statistics r e m a i n
g e n i u s
tests
o f
u p
social scientists a d o p t e d
e s t a b l i s h e d
d e v e l o p
p i c k e d
Experiments
relatively
r e s u l t
n o t
b o o k of
assessing
e x p e r i m e n t a l
h a s
o f t e n
earlier
in c o n s e q u e n c e ,
t o
w h o
w e r e
w e r e
Fisher's c o n t r i b u t i o n s
a d v a n c e "
a test
7 3 ) .
B u t
m o s t
t h e
is
" i n
s o
t h e
d r a w n
statistical
is
1 9 7 7 ) .
e q u i v a l e n t
m a y
his
in
w h i c h
c l a i m e d
significant
w o r k
in
h o w e v e r ,
a n d
intervals. P a r t l y
m e r e l y
it
e v i d e n c e
b o t h
Workers,
t h a t
a n d
are
d i s p r o v i n g
i n d u c t i v e
n u a n c e s ,
significance,
tice
fallacy,
basis.
f o u n d ,
Research
t h e
at
1 9 5 5 , p .
t h e
t h a t
is n o t
t h u s
o r
is
a c c e p t
t r u e
Experiments,
e m b o d y i n g o t h e r
o r
t h a t
p r o v i s i o n a l
e v i d e n t i a l
o f
t h e
t h e
m a y
c a n
h y o t h e s i s
t h e r e
effect,
r e s u l t
O n e
s a m p l e s
m a k e
e v e n
f o r m u l a t e d
i n d e e d
t w o
" r e j e c t i n g
Design
a l w a y s
a n d
t h e
"it is a
f r o m
e s t a b l i s h e d ;
( C o x ,
t o
h y p o t h e s i s
t h i n g ,
n o
b y
a d o p t i o n
I n
this
t h e
t h a t
credit:
c o n c l u d e
(Fisher,
F i s h e r
p e r i o d . "
d o e s
t h e
o n e
d e s i g n
r e p l i c a t e
o f
t h a t
F o r
t r e a t m e n t t o
effect,
statistical n u l l h y p o t h e s i s
p o t h e s i s . o f
-
o f
s o m e t i m e s
fact,
s o m e
t o
is t h e r e b y
t r a n s p a r e n t
" r e j e c t i n g "
a c t u a l
97
r e m a r k . r e a d i n g
o n e
e x a m p l e ,
s t r e n g t h e n e d "
a l w a y s
n o
experts
n o n - r e f u t a t i o n
h y p o t h e s i s
o r
F i s h e r
p o t h e s i s .
B u t ,
null
o n e
n o t
g a v e
a s t a n d a r d
this
is
i n s t a n c e ,
it
b e
c o n f i r m e d
e l a b o r a t e d T h e
as t o
a n d
inference
l i k e l i h o o d
o r d e r , "
t h i n k
A . W .
b u t
g r e a t l y
E d w a r d s ,
t h e o r y ,
also
i l l - f o u n d e d ,
c o n t r i b u t e d
F.
h a i l e d
w r o t e
t h a t
t h o u g h
t h e y
t o
scientific
2 1 2 ) .
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The
98
J .
E g o n
S.
P e a r s o n
G a l t o n a g r e e d
actively,
statistics.
I n
W a r s a w
years,
at
also
w i t h
l e d
eclectic. T h e y
F i s h e r
first
p r i n c i p l e s .
b e c a m e
i n d u c t i v e
r e c t i n g
d e a t h
s a m e
in
a n d t h e
as
l i v i n g
lish
F i s h e r ' s
tific
t o
o f
"I
a m
v i e w
P e a r s o n
a n d
a
it
t h a t
w a s
t o
t h e o r y
o f
w e r e
b y
his
t o o
t h e o r y
1 9 2 2 b ) .
B u t
t o w a r d s
L e b e s q u e " ) ,
strictly
p r o v i d e
B o t h
t h e m
a t t i t u d e
o f
o f
s o m e t i m e s t o
(Fisher,
s t u d e n t
o f
c o u p l e
B o t h
it s e e m e d
E u r o p e a n
in
city,
statistics.
b e c a u s e
m o d e l
issues
i n t e l l e c t u a l
t h e o r e m .
p a r t
dis-
s a m e
n e x t
ideas, especially
t r i e d
a n d
d e d u c e d
this
i n
"statistical
d e b a t e
this
t h a t
t h e i r
real
scientific
" t h e
f r o m
w h i c h
in
a n d
m a n y
h e
t h a t
k n e w
r e p o r t e d f e u d ,
w i t h
b u t
F i s h e r
k i n d , "
felt f r o m
w h a t
later
i n f e r e n c e
w h i c h
h e
w o r k .
v e r y
t h a t
h e
t h e y w a s
H i s
t h e
as
e d i t e d ,
F i s h e r
w e a k n e s s in
o f
a n y t h i n g
little" a n d c o u l d
m a r k e d
t o
S.
n o t
w a s
e x p e r i e n c e
P e a r s o n l o n g
d e c l i n e d since
t h r o u g h o u t
a n d
f r o m
h a d
P e a r s o n
this
a n d
scien-
u n w i l l i n g n e s s o t h e r s , see
t r i e d
t o
a v o i d
a b o v e a
p u b -
F i s h e r
3 ;
b y
w a s
t o
p .
stay
f r o m
d i s a g r e e m e n t
f o r g a v e
1 9 5 6 ,
t o
r e p r o a c h
i n s u l a t i o n
p o s s i b l y
l e a r n
u p
t h e
his m a t h e m a t i c a l
(Fisher,
E.
this
self-criticism,
c o r -
f r o m
w i t h o u t
h a d
n e v e r
R i g h t
s a m p l i n g
F i e r c e
P e a r s o n
as
N e y m a n - P e a r s o n
r e c u r r i n g
r e f l e c t e d
p r o b l e m s . K a r l
h a d
o f
" r e p e a t e d
w o r k
t h e o r y
significance.
m a t h e m a t i c i a n s
i n c a p a c i t y h e
o f
c o n c e p t s
years,
t e r r i b l e his
tests
b e h a v i o r . "
m e r e
P e a r s o n ' s
possibility
i n v o l v e d
s e c o n d
N e y m a n - P e a r s o n
o n
k e y
w e r e
F o r
in
t h a t :
( 1 9 6 7 )
t h e
t h e
i n Biometrika,
f l o w e d
o f
w o r k
" i n d u c t i v e
w i t h
e r r o r s
t h e
e m e r g i n g
o w n
o f
sciences,
N e y m a n
t h e i r
n e w
t h e
i n f e r e n t i a l
b e c a u s e
statistical
say,
p o i n t
t h e
P e a r s o n
w o r k
h e l d
w o r k
b i o l o g y ,
in p a r t
s o n
U n i v e r s i t y
in
p e r s o n a l
in
f a t h e r ' s
a n d
t h e
t h e
B a y e s '
c o n t i n e n t a l
t o
r e j e c t e d
statistics.
o u t
h e
a d m i t
a
S.
his
" e r r o r s
c o n t a c t
n e w
slight;
a
o f
w o r k ,
N e y m a n - P e a r s o n
h e
a n d
n a t u r a l
p o i n t e d
E .
p e r c e i v e d
1 9 6 2
s u c h
n o t
t o
as
u s e d
u s e
Fisher's
o f
h a d
u n i f i e d
i m p r o v i n g
N e y m a n
t h e
all
a
p o p u l a t i o n , "
t h a t in
( h e
t h e
at
O v e r
o f
his
f u n d a m e n t a l
A g r i c u l t u r e
a
at
F a t h e r
l e c t u r e r
s c h o o l
a n d
b y
o f
m o s t
L o n d o n .
P e a r s o n ' s
c o n c e p t
w h o
H e
n e v e r
a n d
t h e o r y ,
o f
t h e
f o r m e d
n e w
w o r k e d
L o n d o n .
y o u n g
in
a n d
b e h a v i o r . "
F i s h e r
his
l a c k e d
k n o w n
w h o l e
K a r l
his
r i g o r
t h a t
a
o f
C o l l e g e
criticism
N e y m a n ,
a
P e a r s o n
i m p r e s s e d
a n d
m a t h e m a t i c a l
N e y m a n ,
P e a r s o n
P e a r s o n ,
s o m e
a s s u m p t i o n s ,
w e r e
e s t i m a t i o n
especially
t o
S.
C o l l e g e ,
L a b o r a t o r y
w i t h
B a y e s i a n
E g o n
K a r l
a b o u t
E g o n
F i s h e r ' s
dissatisfied
i n v o l v e d
o f
a n d
t h a t
o f
C e n t r a l
G a l t o n
experts
a n d
U n i v e r s i t y
t h e
N e y m a n
a g r e e d
at
s o n
h o w e v e r ,
at
t h e
f r i e n d s h i p
t h e
1 9 2 5 , J e r z y
a n d
a r r i v e d
N e y m a n
w a s
L a b o r a t o r y
inference
t h e
b i t t e r
e v e n
also
in
4.4).
g e t t i n g
fray,
a n d
p e r s o n a l
t o n e .
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The
A l r e a d y F i s h e r
i n
h a d
statistic
n o
late
v a l u e
vations.
B u t
f e a t u r e
o f
F i s h e r
significance basis
b y
c h o o s e b e
F i s h e r
h a d
d e f i n e d
w h e n
k i n d . "
T h e i r
e r r o r ,
t h e it
t r u e . o f
false.
T h e
test
o f
j e c t i o n
a n d
R .
G i v e n r a t i o n a l t h e
o f
d e s i r e d h e r e
a n d
-
first
s m a l l o f
t w o
s h o w s
t h e i r
sets
a n d
statistics
i d e a
it t u r n e d
o f
o f o u t
If
t w o
t h e
a n
o f
b e
d e f i n e d .
h y p o t h e s e s
R
u s e
a r e j e c t i o n b o t h
-
a
r e g i o n
t o
t h e o f
m e t h o d s
o n e
d i s t r i b u t e ,
a r e
called
in
h i m ,
n u l l
h y -
t h e
first
k i n d
a n d
R ,
p ( R ;
t h a t
b y
a
o f
a n d
s e c o n d
o f
k i n d ,
i d e n t i f y w h i c h
for
a
I n
(If
rejects
o f
,
1—p.
a
t h e
first
a n d H]
called, r e j e c t i o n
a n d
p
a r e
k i n d ,
t y p e - I I
o r
e r r o r .
strategies,
a
i m p o r t a n t t o
k e e p
t h e
R
t h e
r e g i o n case
a
r e -
Hx
a r e t h e
t h e
H2
a c c e p t s
o f
b y
reject
a n d
o f
c o n s i d e r e d
p r o b a b i l i t y
l e m m a o n e
t o
is
basis
so-called
w a n t s
s i m p l e
specify
viz.
m o r e
r e j e c t i o n
t h e
t h a t
t h e
o n e
t h e
o n e
o r
t h e s e
o n
H2)
is,
e r r o r
o f
Hl
t h e
R , o n e
o u t s i d e
a n
exists.
h e l d ,
distri-
N e y m a n
a n d
h y p o t h e s e s
is
c o m p l i c a t e d . )
a b l e
o f
t h a t
h y p o t h e s e s ,
f u n d a m e n t a l
a l w a y s
m o r e
a n d
s e a r c h
o f
m e a n s
t h e y
a n o t h e r
a c c e p t i n g
t o
test,
for
set
a
o f
a c c e p t a n c e / r e j e c t i o n
o n e
a
h y p o t h e s i s
H , )
First,
s u p p l y
N e y m a n - P e a r s o n
t w o
t h e
t o
t h e
" e r r o r
o b s e r v a t i o n s ,
p o w e r f u l .
s i m p l e
w e r e
t h e
o f
latter
h y p o t h e s i s
is
t h e
o b s e r -
u n d e r s t o o d
r e j e c t i n g
a s s u m e d
m a k i n g
statistical
b e c o m e
o f
t h e
t h e
w i t h
t-
a
i n d i c a t e d
o f
a n
is
t h e s e
p ( R ;
o f
N e x t ,
s u c h
it
is,
o b s e r v a t i o n
e r r o r
m o s t
t h e y
a n
o b s e r v a t i o n
p o w e r
a n
o f
set
a n
small. is
t h a t
w i t h
c h o i c e ,
also c o n s i d e r
h y p o t h e s e s
a
m a k e s
P e a r s o n
t h a t
b y
o b s e r v a t i o n s
t h a t
t h i n g s
N e y m a n
o v e r
is, t h a t
t h a t
-
a n d
t h a t
so-called
P e a r s o n
c o m p o s i t e ,
k i n d
size
for
test
c o u l d
s h o u l d
b l a m e
m a k i n g
A s
t h e
t h e
p r o p o s e d
o f
called
o b s e r v a t i o n
p r o b a b i l i t y
h y p o t h e s e s ,
t h e
a n
t h e
e r r o r .
t h e y
k i n d "
c o n v e n t i o n a l l y
t h e o f
o n e
p r o b a b i l i t i e s a n d
a n
T h i s
g i v e n ,
m a k e s
s p e c i f i c a t i o n
b u t i o n s
o f
a r e
p r o c e d u r e
t w o
e r r o r
o n e
t o
o f
as p r o v i d i n g
m e c h a n i s m
e x a m p l e
is d e f i n e d
size
T h e s e
this
a n d
T h e
t h e
e r r o r ,
a r e
test
as
t h a t
b e y o n d
h y p o t h e s i s
o f statistical e r r o r :
t h a t
s i m p l e s t
statistical A
a r e a
dissatisfied
n u l l
a r g u e
( s u c h
level
P e a r s o n
single
a
l e d
t r u e .
say R . If o n e
H2.
o f
s e c o n d
o t h e r .
if
m o r e
F i s h e r ' s
m a k i n g
H2
respectively,
t y p e - I
o f
t h e
, a n d
respectively,
t h u s ,
o f
a g a i n s t
rejects
r e g i o n
t h e
p r a i s e
a c c e p t
H2
t h e
tail
a n d
k i n d
fact
h y p o t h e s e s
r e g i o n ,
a c c e p t s
o f
p u r p o s e
H i
o n e
i m p l i e d
I n
o b s e r v a t i o n , a n d
in
t h e o r y
t w o
o n e
is
" e r r o r
is
testing,
it
o n l y
t h e
m o r e
a n d
t o
statistics
significance
N e y m a n
rarely
test
t h e
a l t e r n a t i v e s .
if it
o f
b e g a n
as
c o n c e i v e d
s u c h
r e a s o n a b l e
p o t h e s i s
w h e n
r e p l a c i n g
P e a r s o n
c h o o s i n g
statistic
b e c a m e
9 9
a n d
c h o i c e
for
t e s t i n g ,
T h e y
a m o n g
his
o r
test
experts
N e y m a n
f o r
3.2),
t h e
w h i l e
logical
w o u l d
basis
i n
o f
rival h y p o t h e s e s . t o
1 9 2 0 s ,
logical
d i s c u s s e d
o b s e r v e d
this
t h e
inference
e x p l a i n
tail a r e a
a c e r t a i n w e r e
t o
b o t h
t h e
t r a d i t i o n a l
m e a s u r e
size a n d
significance
m a x i m u m
m a t h e m a t i c a l l y
c h o i c e s u s i n g
p o w e r .
e q u i v a l e n t .
F o r
T h e
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tail
The
100
a r e a is, f o r t h e
t h e
usual
p r o j e c t i o n
o n
t h e
t u r n s
o f
g r o u n d s
o u t
that
o f
a n
B u t
let
us n o w test
h y p o t h e s e s
u s i n g
in industrial
o f
a n
a
b y
m i l l i m e t e r s ,
as
n
in
m i l l i m e t e r s
r a n d o m
s h e
w h i c h
d e p e n d e n t
is
n o t
s a m p l i n g e a c h
o f
m e a n
the
f o u n d
d e c i s i o n s a n d
t h e
in
2
,
a n d
a c c e p t
a p p a r e n t
E a c h
o f
t h e
u n n e c e s s a r y H2
is
a n d
true, t h e
g r e a t e r set
its
m a d e r u n
in
m i l l i m e t e r s m i z e s
p at
has
in
s h e
t h e
t h e
it
t o
a
o r d e r
t h e
h e r
c o n s e q u e n c e s ) : lot
t h e p r o d u c t i o n
t o
t h e
a n d
t w o
m i l l i m e t e r s that
t h e
fluctuations, d e t e r m i n e
t h e
d i a m e t e r
a n d
m a k e
either o n
1 0
d i s t r i b u t e d ;
m e a n
t o
8
r a n d o m
k n o w s
m o d e l
w a n t s
say
a
8
say
t h e s e
as t h e
p r o d u c t i o n
is
t h e
m e d i c a l
b e t w e e n
s h e
this statistical
w h o l e
the
n o r m a l l y
a l l o w s
statistic, s u c h o n
value,
takes
d i a m e t e r
m e t a l
that
d i a m e t e r ,
d e c i d e
o f
c o n t r o l
p r o d u c e s
s h e
e x p e r i e n c e
T h i s
quality
o p t i m a l
d a y
t o
statistical
i m p o r t a n t
certain
d e v i a t i o n
m e a n .
s t o p
is
Fisher's
t e s t i n g
w h o
a p p r o x i m a t e l y
a
at
m a y t o
that
the
(H2).
N o w
s h e
m a k e s
s e c o n d o v e r t h e
w h i l e
t h e
o n e
t o
t h e l o o k
for
actual o f
t w o
a c c e p t
m a r k e t ;
t h e
m a y
A n
error
t h e o f
p r o d u c t i o n t h e has
kind, e r r o r
If
true, s h e
t h e error
t h e
r u n
plates t o
is
cause
S i n c e
this
error, w i t h
H ,
p r o c e s s .
suffer.
m a k e
0 . 1 % .
w i t h
c o n t r o l
H2
a p o s s i b l e
i n s t r u m e n t s
flawed
the
i n v o l v e s
p r o d u c t i o n
fact
1 0 % , a n d
e q u i v a l e n t
unreliability in
a
m a n u f a c t u r e r
a c c e p t s
d e c i d e s
a c c e p t e d
the error o f
size, s h e
justified
b e t w e e n
o f
a n
cause
past
practical
r e p u t a t i o n
p r o b a b i l i t y
w a s
in
is
B a s e d
i.e. t o
d e f e c t i v e
danger,
b e
t h a n
F u r t h e r m o r e ,
theory,
It
E v e r y
s t a n d a r d
t h e
latter
e x c e e d
w h e t h e r
a s a m p l e
,
s h e
delays
firm's
if s h e
2
k i n d .
t h e o r y
c o n s i d e r s
i.e.,
the
d e c i s i o n s
If
t h e
o f
place H
c a n
m o r e
for
H]
o r
the
t o
cause
m a l f u n c t i o n i n g .
t w o
c o n s e q u e n c e s .
o n
s a m p l e ,
t o
a n d
differences
t h e
this w o u l d
t h e
i m p o r t a n t
i.e.
m a j o r
n o t
F r o m
h y p o t h e s e s . the
( w i t h
reject H
reject H , o f
t w o
her,
k n o w s
d i s t r i b u t i o n s
first
i n s t r u m e n t s .
d i a m e t e r s
f u r t h e r m o r e
line,
a m a n u f a c t u r e r
p r o d u c t i o n
(H2).
o f
the
u n a c c e p t a b l e .
interest
fluctuation
real
n o t h i n g
a test statistic are
o f
I m a g i n e
since
f r o m
( H , )
o f
the
s h o u l d
definitely
that
1 0
o f
m a n u f a c t u r e r
h y p o t h e s e s o r
c h o i c e s
m e d i c a l
m u c h ,
plates
o f
application
plates
T h e
t h e
N e y m a n - P e a r s o n
typical
t o o
error
s o m e
t h e
u s e d
o n
h y p o t h e s e s ,
h y p o t h e s i s .
e x a m i n e
t h e s e
i n s t r u m e n t s .
o f
a v o i d i n g
a n d
are
millimeters,
s a m p l e
o f
m a n u f a c t u r i n g .
that
d i a m e t e r
r e g i o n
Fisherian
experts
alternative
rejection
alternative
significance
o f
a
m a n y
c h o i c e
plates
c h o i c e s
inference
h a v i n g
c h o o s e
a
calculations
t h e
o f
first
s o m e
patients,
first
k i n d
faultless a
a l t h o u g h
s e e m s
t h e
r e q u i r e d
t o
h e r
k i n d ,
w o u l d
t h e
a n d
t o
t h u s
b e
( H \ ) , w h e n
d i a m e t e r
o f
r e g i o n
s h e
s a m p l e
t h e
a b o u t that
b y varying the
kind,
cause
H ,
latter
rejection
s e c o n d
t h e
a c c e p t s
d i f f e r e n t
will
t o
false alarms. Since o f
this
h a r m
o f
w a s
v e r y
d e c i d e s size
1 0
m i n i s a m p l e t o
that
set will
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The
g i v e
h e r
initial
a test
p h a s e
o f
o f
m a t h e m a t i c a l cal.
If
the
w h o l e a n d
a n d
A s
s a m p l e
falls
N e y m a n o r
t o
b e l i e v e
o u t
o f
t e n
t h o u g h
it
days is
o n l y
c h o o s i n g
a n d
as it
d e r e d ,
w i t h
p o s e d w e
m e n t .
H , t h e
w i t h
m e a n
w e
n e e d
this
w e
effect H2
z / s
p o w e r .
t h e
w o u l d
states
b u t i o n
that
w i t h
k e e p
t h e
0.05.
O u r
t h e
task
m a x i m u m
is,p(R;
H2)
g i o n
a
in
P e a r s o n
w e
r e g i o n
H o w e v e r , line
S i n c e
in
s u c h m o s t
this a
a n d
in
a
p o w e r f u l
t o
a
t h e
errors)
a n d
m e c h a n i -
rejected
is
H2
n o t
s h e
is
t o
a n d
t h e
a c c e p t e d
s t o p
t h e
r e g a r d
true.
m u s t
it
b e l i e v e
e x p e c t
that
as
B e c a u s e in
o n e
p r o d u c t i o n
b e h a v i o r a l severity
v e r y
H ,
e v e n
is
false,
o f
for
s e c t i o n
m a k i n g
t o
t h e
null is
t w o
h y p o t h e s i s
o u r
at
d e f i n e
, w h e n
o f all p o s s i b l e
i m p l i e s
o n e - s i d e d rejection
t o
act
a n
r e g i o n
tail
r e g i o n .
areas If w e
e x a m p l e ,
the
h y p o t h e s i s
a
w e
is
h a r d s p a c e
c o r r e s p o n d R
H , )
t o t o
=
T h a t
f u n d a m e n t a l
exists in this t h e
t o
take
that size.
T h e
this
c h o o s e
A s
distria n d
t h a t p ( R \ o f
F o r
p o s i t i v e
a n o r m a l
o b s e r v a t i o n s ,
p r o j e c t s
that
h y p o t h e s i s .
s u c h
w h i c h
treat-
d i s t r i b u t i o n
small.
an R
H e r e
t e r m s ,
conservatively,
r e g i o n s
p r o -
Fisherian
o f
T o
w o n -
yield.
( a v e r a g e )
as possible.
space,
w e
statistical
f r o m
R
t h e
certain
n o r m a l
true,
that s u c h
/-statistic
a
Statistically
rejection
i n d e p e n d e n t
t h e
has
it is
as large
in
o t h e r
o b s e r v a t i o n s
a rejection
m a d e
a
o n e
plot.
w a n t
t h e
or,
that
T h e r e
t r e a t m e n t
t r e a t m e n t
0.3. W e Hl
o f
f r o m
least
t r e a t m e n t
3.2.
for
inference.
w h e t h e r
ineffective,
o f
indicate
in increasing g r a i n
o b s e r v a t i o n s
u =
n i n e
o f
scientific
J o h n s t o n ,
effective
, t h e
that
b e
i n t e r p r e t a t i o n
features
suitable
n i n e - d i m e n s i o n a l
that
-
g i v e
i n d e p e n d e n t
situation,
w a y
is
this
o f
is q u i t e
if it w e r e
necessarily
c h e m i s t
P e a r s o n
h a v e
as
e x a m p l e ,
e x a m p l e
rejecting
t o
act
a N e y m a n - P e a r s o n
s h o u l d
o f N e y m a n
is
the
H ,
m e a n o f
t o
relative
less
t r e a t m e n t
are
p o w e r
1—p
validity
o t h e r w i s e
h y p o t h e s i s
for
t o
i n t r o d u c t i o n
is n o w
=
b e
o f grain p e r
z ' s
a
t h e s e
causally
g i v e
p r o b a b i l i t y
situation.
t o
t h e
p o s i t i v e
a, w i t h
l e m m a
B u t
h y p o t h e s i s
bushels
H2
after
in t e r m s o f costs, t h u s p r o v i d i n g a basis
i n d e p e n d e n t
the
p r o c e d u r e
m a r k e t ;
n o t
the
m a y
b e
explicit
take
o f 0.3
t h e o r y
0. T o
t h e
t h e p o s s i b l e
r e g i o n ,
a l a r m
s e n s e
a n d
h y p o t h e s i s ,
u =
will
m a k e s
agricultural
are
false
b e e v a l u a t e d
that
is t a k e n
w e r e .
t h e
states
that
a
r e t u r n
as o n e
t h e
m e a n s
1 0 % ,
S h e
it
it
=
will
fertilizer
t a k e
p
rejection,
N e y m a n - P e a r s o n w e
a c c e p t
m o s t
set
if
a n d
o n ,
t h e
( a b o u t
costs o f
rejection o n
t o
p r o d u c e
c a n
size
this,
A t
has
t o
actual s a m p l e
j u d g m e n t
h e r e
t h e
101
s t o p p e d .
satisfactory.
k i n d s o f e r r o r
see
is
e x a m p l e ,
a c c e p t a n c e
F r o m
i n t o
T h e
respective
is p l a c e d
it.
p r o c e e d
this
t h e
e m p h a s i z e d ,
m a n u f a c t u r e r
I n
lot
p r o d u c t i o n
t h e
b u t
a b o u t
experts
p o w e r .
p e r s o n a l
calculation.
p r o d u c t i o n
t h e
true,
this size a n d c o m b i n e d
statistical m o d e l
inference
s i m p l e
rejection t o
visualize.
o n a b e
re-
t h e
real
N e y m a n t h e
set
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o f
1 0 2
The
o b s e r v a t i o n s r e g i o n
o f
w i t h
r e g i o n
d i s t r i b u t i o n
=
n
0 . 3 3 ,
say
a
l o w : t o
=
p o w e r
a b o u t
W e
t h e
c o u l d
m e n t .
o f
this
called
d i s j u n c t i o n first
in
a
"jut =
a n d
A l t h o u g h
b y
w h e n
c h a n c e
i f i t is
i n
are,
a
s e n s e
t h e
sensitivity
o f
t h e
t h e y o f
o n e
t h a t
o f
this
f o r
is
a s m a l l e r
t h a t
p l o t s
u s e f u l
i n
e x p l i c i t
w e
i n
a,
will
t h e
t h e
fail
in
d e s i g n
0.3.
e x p e r i -
d e s i g n
w h a t
e x p e r i m e n t a l
|i
d a n g e r o u s l y
i s , i f fi i s a b o u t
o f
/-
h y p o t h e s i s
a l t e r n a t i v e
o p t
t h r e e
a
n o n - c e n t r a l
b e c o m e s
in -
q u i t e
m a k e a n
t o
n u m b e r
t h u s ,
p o w e r
if t h e
0.3,
false
t h e
h a v e
alternative
w a n t
JJ =
fact
i n c r e a s i n g
t h e
0 . 9 0 ;
I f w e
will
so-called
If
is a b o u t
0.99.
a
i n
scientific
0
o r
u
s e c o n d
this
is
=
p a r t l y
a
t h e
w r o n g
a n c e
b e t w e e n
d a t a
a n d
c a n
p r o v i d e
t h e
a n d
p o w e r
a g r i c u l t u r e , t h e
p r e s e n t
m a r k e t
h e l p f u l ,
since
utilitarian p e n d e n t
o f
T h e r e
are
t e n t .
First
l o o k
at
t h a t
ditionally
h a s talk
s a m p l e
size
t a l k e d
a b o u t
P e a r s o n
a r e
as
o f
o n e
a
o f
a n
F i s h e r ' s
( C o x ,
o f
t h e
b e e n
called
a b o u t
t h e
f o r
t h e
t h e
t h u s
b e
1 9 5 8 ;
in
a
yield.
n e e d
o f
o f
a
rival
a
p o w e r , a n
m o r e
this
a n d
P e a r s o n
m o r e
m u s t b y
b e
t r u e ,
a n d
w h e r e
t o
c o m p l e t e
h a s
d e s i g n .
f r a m e w o r k
s u c h
b y
t h e
b e
t o o
a
s e m i -
a r e
i n d e -
o f
g r a i n .
t h e y
a n d
o n e
o n l y
it
trap o s -
r e q u i r e d i n f o r m a l l y
T h e for
t o
b e e n
t h a t
m a k e s t h e
h a d
c o n s i s -
a l r e a d y
T h i s
h a d
in
o f
p o i n t ,
a l l o w s
calculate
F i s h e r
e x p e r i m e n t a l
b u s h e l s
p r o c e d u r e
e l i m i n a t i o n . "
test,
t h a t
b e l i e v e d
It a
c h o i c e
n o t
e v e n
w h i c h
h y p o t h e s e s .
scientific
o f f s e t
c o m p l e t e
h y p o t h e s i s ,
h a v e
science,
m a y
T h u s
t h e
d i s c o r d -
a
t h e
just
c o n c l u s i o n s
a n d
t e s t i n g
b e t w e e n
o f
B u t
o f
b r e a k - e v e n
a r e
fertilizers
N e y m a n
h o w
i n t o
a
fluctuations.
w e
t h e
o f
that.
will o f t e n
a p p l i e d
b y
fertilizer
s h a r p
" i n d u c t i o n
g i v e s
d e f i n e d
d o
t r e a t m e n t
clear
a n
t h e
e r r o r s
c a n n o t
w e
g o
assert
t h e
m e a s u r e
it is n o t
case
t h e
p r i c e s
o f
t o
o f
m i x e d
h y p o t h e s e s
sensitivity
a w a y
t h e
significance
d e s i r e d
science
t h a t
t o
p o w e r
i n
t o
o f
w e
simplistic
c o n s i d e r a t i o n s
w h i c h
c h o i c e
t h a t
Similarly,
a g r o n o m y ,
i n
w h e n
o u r
n e e d
i n c r e a s e
i n t r o d u c t i o n as
t h u s
w a n t
i n t e r p r e t a t i o n
o f
t r u e
m a y
m a r k e t
rarely
c o g e n c y
a p p l y i n g
t h e
w a y s
t h e o r y
t h e o r y
I n
s u b j e c t
s u c h
t h e
o f
o f
p r e s e n t
t e s t i n g
a c c e p t e d
t o
is
costs
t h r e e
F i s h e r ' s
test.
a l t e r n a t i v e
t h e s e
t h e
utility
a
p r i c e
s c i e n c e
a n d
h y p o t h e s i s .
o f
p r e s e n t
its
it r e m a i n s
w e
t h e
c o n s e q u e n c e
t h e
t h e
a n d
loses
h y p o t h e s i s ,
c o n t e x t size
a p p l i c a t i o n
0 . 2 1 , "
k i n d
u s e d
sible
b e
t h e
1 9 5 7 ) .
test
w e
calculate
i n v o l v e s
test,
p o w e r
as a d i s j u n c t i o n ,
m a d e
t h e
o f
e x a m p l e
w h e r e
t h e
T o
1.86,
1 9 7 7 ) .
H o w e v e r ,
as
size.
it
a b o u t
h y p o t h e s i s ,
a n d
is
o f
w o u l d
C o n s i d e r a t i o n s
C o h e n ,
t h e
T h e r e
alleviate
a p p r o a c h
r i g h t
t h a n
L i e b e r m a n ,
p o w e r
p o w e r
n u l l
e x p e r i m e n t ,
a n d
b e c o m e s
t h e
0.6.
t h e
experts
l a r g e r
c o m p l i c a t e d ;
0 . 2 1 , t h e
0 . 0 1 ,
reject
is
( R e s n i k o f f
t h e
=
/ - v a l u e
a p p r o x i m a t e l y
r e j e c t i o n
is t h a t
a
inference
N e y m a n -
p l a n n i n g
e x p e r i m e n t .
Downloaded from https://www.cambridge.org/core. Newcastle University, on 09 May 2018 at 22:47:10, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.005
a n
The
S e c o n d ,
t h e
calculated original h a v e a
f r e q u e n c i e s
o n
t h e
m a t h e m a t i c a l
t h e r e f o r e
a
h y p o t h e t i c a l
first
k i n d
belief
if
her
that,
in
s e n s e
b e
sively
t h e
s a m p l e d
u s e d
d i s c e r n
t o
in,
sive
that
"the
e v i d e n c e
c o g e n c y ,
o f
is
T h i r d ,
in
B a y e s i a n
d i s c o r d a n c y
called
that
o f
t h e
w h e r e a s tive
i n f e r e n c e "
h y p o t h e s i s esis,
as
N e y m a n , h a d
b e e n
a r g u e d ,
is
p o t h e s i s t o
a
o f
basis
o f
as
t h e o r y
a
strictly are
e x a c t
data w a s
w i t h
exist
T h e
t h e
null
p e r h a p s , e r r o r
o f
Recall
t h e
data c a n n o t
still t h e
Fisher's
a p p r o p r i a t e
in a n y
reality,
realistic
b e i n g
T h e r e f o r e ,
e x c l u -
after
t h e
statistics)
m a y
r e s p e c t
t o
t h e
r e l e v a n t
w h i c h
b e
m o r e
analysis). T h i s
in particular
w i t h
p.
r e m a r k
o n
9 2 ) ,
t h e
l e d
a
t h e
r e p e a t e d
b e
F i s h e r
c i r c u m s t a n c e s ,
c o n f u s e d
deci-
force,
that
o r
O s k a r
s a m p l i n g
I n d e e d ,
if
t h e
i n f e r e n c e
c o n c l u s i o n
that
m u c h .
f r e q u e n c y
o f g e t t i n g
it,
p r i n -
is
B u t
t o
t o w a r d s calls
t h e
this is
( H a c k i n g ,
b o u n d t h e
it right.
t o
b e
o n true.
w h i c h
t h e
o r
o f
m a y
t h e
o n e
a n d
o r
it.
N e y m a n
action,
h y -
h y p o t h e s e s " m a y
b e
o n
a
t h e at
i n f e r e n c e
is
is
i n f e r e n c e
b a s e d c a n n o t
p r o m i s e
m a k e s
b e
l o o k e d
i n f e r e n c e
c a n
a
p e r h a p s
s e n t e n c e s w e l l
t o
W h a t
reject
o f
a
h y p o t h -
o n
d e d u c t i v e
t h e o r y
d e c i s i o n
" i n d u c -
t h e
b e h a v i o r
I n d u c t i v e
N e y m a n - P e a r s o n S u p p o s e
sets
test,
a c c o r d i n g
a c c e p t
v a r i o u s
V a l i d
If
o f a n y
a
a s a m p l e
d e p e n d
a particular
t h e o r y
t o
inference,
assertion
1 9 8 0 ) .
p r e m i s e s
o r
i n f e r e n c e
t h e
s a m p l e .
t o w a r d s
c a n n o t
t h e
f r o m
a p p l y
inference,
T o
take
m e a s u r e s
refrained
t h e
quasi-
i n t e r p r e t a t i o n
p o w e r
a t t i t u d e
behavior.
Fisher's
b e t w e e n
r e a s o n i n g
N e y m a n - P e a r s o n
t h e
o f
relation
science
i n f e r e n c e
if
that
a n d
i n d u c t i v e
a d e c i s i o n
o n e
size
m e n t a l
inductive
a t t i t u d e
W h e t h e r
g u a r a n t e e
evidential
their
o n e
is a p r o p e r t y
i n d u c t i v e
called
o f
as
s o m e h o w
h y p o t h e s i s ,
c o n c e p t s
h a v e
s a w
significance
b e
t o
P e a r s o n
behavioristic
level
t o
t r u t h - p r e s e r v i n g : its
o f
therefore,
b e t t e r
a s s u m p t i o n s ,
true,
o f
t h e
probabilities
a n
faultlessly).
in
(ancillary
a n d
and,
particular
o f
c o m m i t
o b j e c t i v e
1 9 5 6 ,
level
a p u r e l y
w a n t e d
taste.
t h e
are
s a m p l e
attack
a certain
1 9 5 7 ) .
a n d
i m a g i n a t i o n . "
n o t
N e y m a n
is " a n act o f w i l l o r
( N e y m a n , m a t t e r
frontal
k i n d
d i s t r i b u t i o n s
p o p u l a t i o n
" n o
w h i c h
d e t e r m i n e s
really
runs
s e c o n d
( a l t h o u g h ,
(i.e., a c o n d i t i o n a l
(Fisher,
w h a t
t h e
t h o u g h t
a s s u m e
w i t h
w i t h
significance
c a n n o t
t h e
n e v e r
t h e
the
a n
Fisher
will
has
is i n f e r r i n g
that
o f
a n d
p r o b l e m ,
always
s h o u l d
a
interpretation.
Fisher's
first
1 9 7 6 ) .
o f
statistical i n f e r e n c e e p i s t e m i c
o f
calculated
e v i d e n c e "
place
v i e w
a n d
features
( K e m p t h o r n e ,
t h e
statistician's
o b t a i n e d ,
has
t h e
analysis o f e x p e r i m e n t a l
i n f r e q u e n c y
s u c h
K e m p t h o r n e ciple
b e
o f
i n t e r p r e t a t i o n
process
a s u b p o p u l a t i o n
c a n
o f
applications,
t h e
certain
probabilities say
o f
103
s a m p l i n g
m a n u f a c t u r e r
repeatedly,
p r o d u c t
is
r e p e a t e d
p r o d u c t i o n
the
experts
errors
f r e q u e n c y
the
for
t h e
specification
scientific
s a m p l e
o f
o f
direct
o n e :
statistical m o d e l
t o
basis
inference
is
t o
h i g h assert
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104
The
o n e
o f
t h e
, t
o r
H
H
1
at
least
m a d e a n
p o s s i b l e
"
2
o f
rule
a s s u m i n g a n d
i n g
still m a y
able
t o
t h e
that,
call
as a t h e o r y
a role
i n t o
t o
play.
q u e s t i o n
a n d
N e y m a n - P e a r s o n
least H2
t h e
d i s c o r d a n t
,"
t h e
,
for
it
right
is a l s o
t h r e e
t o
1 9 5 7 ) .
v a r i o u s
r e i n t e r p r e t e d
c e d u r e s ,
a n
Fisher
Russians
[who]
1 9 5 5 ,
his
tests
p o i n t
l i k e n e d
o f o f
are m a d e
t h e
o f
n o t
a
true
s t a t e m e n t is
significance tests
m o d e l ,
test-
that
t h e w i t h
w h o l e b o t h
H ,
data
are
t h e
t h e
d i s j u n c t i o n
t h e
third
b y
t h e
" H ,
k i n d :
rejected
t e r m s
v a l u e d
m o d e l
e a c h
o f
t h e s e
h a d
m i s -
a c c e p t a n c e
p r o -
N e y m a n o f
e x p e d i e n c y
o v e r
truth.
science
technology has I think m a d e
it easy t o c o n f u s e
for drawing correct conclusions, with
us
production,
N e y m a n ,
for
his
m a t h e m a t i c a l l y is
less
t h a n
their
size
a n d
o f
errors,
c o n f u s e d
w i t h
significance tests latter f r o m
a n d as
scientific
a b o u t .
o n l y
p h a n t a s y research"
o f
s e n s e
a
' w o r s e
tests v e r y circles
( 1 9 5 6 ,
p.
1 9 6 5 ,
in
d r e w o f
[i.e. 1 0 0 ) .
p .
9 9 ) .
field
n o
"
tests since
line
a n d o f
in
b e t w e e n
P e a r s o n ,
m a t h e m a t i c i a n s ] P r o p o n e n t s
o f
prolet
a
p o w e r
a c c e p t a n c e as
costs
n o t
b e
tests
o f
significance ridiculed
because
o t h e r
in
their
m u s t
his
rather t h e
"are
is w h a t
a n d
application
the
r a t h e r at,
s u c h
a n d
w h i c h
great
70).
A l t h o u g h
role
sciences,
b o l d
N e y m a n
limited
p.
Fisher's
useless,'
play
t h e a
1955,
utility c o n s i d e r a t i o n s
t h e s e
i n f e r e n c e
o f
t h a n
require
a r g u e d ,
(Fisher,
s o m e
H a c k i n g ,
Fisher
h y p o t h e s i s
h a v i n g
"the
Fisher
m o n e y
that
c o n t r o l
i n d u c t i v e
are
t h e
(see
quality
saving
said
specifiable
p r o c e d u r e s p o s s i b l e
part,
or
those aimed
can
organ-
. . [While] in the U.S. also the
cess appropriate say, s p e e d i n g
o r
g i v i n g
w r o n g
the ideal that research in pure
plan for the nation.
importance o f organized
are
t o
familiar w i t h
five-year
i m -
t h e o r y
and should be geared to technological performance, in the comprehensive ized effort o f a
is
r e g i o n ,
qualification
b e l i e v e d in
p
w e l l - d e f i n e d .
Fisher
H e
a n d
rejection
h y p o t h e s i s
a s k e d
significance
N e y m a n
small
is d i s c o r d a n t
is
that
o f
still n e e d
reject
1 9 5 6 ) ,
v i e w
p r o b a b i l i t y
N e y m a n - P e a r s o n
m a y
error
" i m p r o v e m e n t s . "
i d e o l o g i c a l
I n d e e d ,
(e.g.
w o u l d
h o w e v e r ,
w i t h
inference,
that
a n
o f
o f
a s s u m e d
q u e s t i o n ,
probability,
a n d
t h e
statistics
a v o i d
a s s u m p t i o n
is c h o s e n
latter
test will a c c e p t
t o
t h e
asserting
i n d u c t i v e
w e
If
c h o i c e
T h e
w h o l e
w r o n g
p u b l i c a t i o n s
o f
true.
F o r
practice,
t h e
Its
" c o r r e c t i o n s "
t a k e n l y
In
o f
."
2
a
a n d
o b s e r v a t i o n
i m p o r t a n t
a n s w e r
( K i m b a l l , I n
w i t h .
a n
I f b o t h
a c c e p t s
t h e
If o n e
2
m a k e s
b e
"H
h y p o t h e s i s
d e s i g n
if o n e
disjunction. H
1—(5.
t o
e v e n
o r
true
f r e q u e n c y
p r e m i s e s
t e s t i n g h a v e
a n d
h i g h
" H , "
t h e
e x p e r i m e n t a l
w i t h
s h o w s
h y p o t h e s i s
1—a
experts
h e r e
will assert
o f
t h r o u g h
i n f e r e n c e
p o r t a n t ,
o n e
m i n i m u m
small,
results,
c o n c l u s i o n s ,
is t r u e ,
t h e
inference
t h e
d e r i v e d
r e m o t e
f r o m
c a m p ,
h o w -
Downloaded from https://www.cambridge.org/core. Newcastle University, on 09 May 2018 at 22:47:10, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.005
The
ever,
a r g u e d
t h e y
h a d
p a p e r
that
s i m p l y
p r e s e n t e l e m e n t t h e
lapse
is t h e o n e
o f
i n v o l v e s
o f
Fisher's
o v e r b l o w n
u p
t h e
witnesses.
T h e
that
a n s w e r ,
P e a r s o n
" d o e s n ' t
itself
t h e
t h e
p o t h e s i s
o f
A s
o f
g r e a t
for
tests
B a y e s i a n s
a n d
u n r e s o l v e d h a v e h a v e
o f
class o f o f
a
u s e
" T h e
o t h e r .
in
are
a
tests
title o f
t o
the
m e .
T h i s
h y p o t h e s e s ,
I f
this
c o n c e p t u a l
is
n o t
a
d i s t i n c t i o n "
p .
t a u g h t
less
significance
test
n e e d
a n d
as
i g n o r e d
b y
is
n o t
c o n c e p t u a l
t o
as
m o s t
r e g i o n ; t h e
in
t h e
that
a
w h i c h
t h e
H e r e
test
w h a t
e x -
say
.05,
original
c o s t - b e n e f i t
h y -
m a d e
a
c o n s i d e r -
c o n c e i v e d
m e r e l y
it
will
G o s s e t
first
I n
r a n d o m l y
. 0 0 0 0 1 :
that
a n d
Fisher.
d r a w n
t h e y
l o w
h a v e
o n e
l i k e l i h o o d
a m b i g u i t i e s ,
a n d for
P e a r s o n
e x i s t e n c e
t e x t b o o k s .
-
for
t h e
A s
that a n d
f r o m
c u s t o m e r -
t h e
o f
all o f
t h e s e
p e r s o n a l
in-
t e x t b o o k s
e x p e r i m e n t e r
F i s h e r in
e n d e d . b e t w e e n
t h e
in
t h e
B a y e s i a n s
a
n o t
r e l a t i o n s h i p
r e m a r k a b l e
j u d g m e n t
N e y m a n
c a m p s .
probability,
s u p p r e s s e d
t h e
their
l i k e l i h o o d s . "
is e s p e c i a l l y
t e s t i n g
w e l l
it
b o t h
h a d
say
w h o
t h e
a rejection -
m a n
t h e
c o m p l e t e l y
for
for
characterized
for p e r s o n a l
statistic;
p r o b a b i l i t y w e r e
o r
n o t
a n d
it
issues,
o f
2 4 3 ) .
c o n t r o v e r s i e s ,
h a v e S o
small,
c o n s i d e r
t h e
"that
ratio
v i g o r o u s
it,
as
n o t
b e
b r e w e r s ) ,
h y p o t h e s i s
p.
a l t h o u g h
u r g i n g t h e
t o
1 9 3 8 ,
p u t
is
parties
t o
stating
a r e a s o n a b l e
i n c l i n e d
8 3 )
s a m p l e
"childish"
research
t h e
spirit
n e v e r
B o t h
b y
w i t h
G o s s e t
as
G a u s s ,
c l a i m e d
is v e r y
w i t h
P e a r s o n ,
n o w
m o r e
t h e
d e b a t e
w e s t . "
a n d
s a m e
alternative
s a m p l e
frequentists.
b e e n
c o n c e p t i o n s ,
a n y
t h e
G u i n n e s s ,
f r o m
t h e
p o s i t i o n
c o n c e r n e d
c h a n c e
is
in
w a s
t h e
that
t h e
S.
c o n t r o v e r s i a l
in
p o l e m i c ,
Laplace
for
letter
m o r e
h e a t e d
h y p o t h e s e s
p r i o r
t h e
rather
w e r e
less
a n d
if
as
G o s s e t
test
a
t h e r e
w a s
sciences. T h e
m o d e l
his
( 1 9 6 5 ,
b u t
t h e n , n o
in t h e
t h e
N e y m a n ' s
"actively
p r o v e
(E.
s u c h
rival h y p o t h e s e s ,
H a c k i n g
D i s p u t e s
that
w h a t
m y s t e r i o u s
t h e
for
f r e e d o m
w o r k e d
m u c h
t r u e "
m a t t e r s ,
T h e s e ,
sults
v e r y
n o t
ations.
w h i c h
o n
b e c a u s e
instance,
tests o f statistical
learn
b r a n d e d
S.
m a n
e v e n
o c c u r r e n c e
p o i n t
a
necessarily
b e
H e
W .
p u b l i s h e d
if
is
o f
u s e d
that
s t r o n g
t h e
appears
t o
F o r
w r o t e :
talent
past,
( G o s s e t
G o s s e t
s h o w
will
t h e
as
p o p u l a t i o n
t o
. . . y o u
o f
h i m
c l a i m e d
plain
I h o p e
consistent.
N e y m a n
b e t w e e n
intellectual
a u t h o r i t y
s c i e n c e s "
is
t h e n
application,
" F o r
significance,
rhetoric.
h e r o e s
natural
d o e s
o f
o f
q u e s t i o n
that
r e m a r k a b l e
[for]
d e s c r i b e d
f r o m
tests
p e n ,
m o r e
t h e
e l e m e n t
d i s t i n c t i o n
a n d
" h o r r i f y i n g
F i s h e r
o n
fields
1 9 7 6 b ) .
for
called
t h e o r y
105
in
significance?"
a n
a p p a r e n t
experts
d i f f e r e n c e
a c o n f e r e n c e
s o m e o n e ' s
B e c a u s e
a n d
n o
Fisher's
tests o f
h a n d ,
( N e y m a n ,
lacked
t o
a n d
session
w a s
m a d e
p r e s e n t e d
o f h y p o t h e s e s
o n
t h e r e
inference
t h e
c h o i c e
c h o i c e
in
t h e
alternative c o n s e q u e n c e ,
o f
a
c h o i c e
statistical scientific
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106
The
r e s e a r c h e r s
in
m e c h a n i c a l
w a y ,
t h e s e
m a n y
T h e
f o r
sciences,
e f f o r t
especially
a n d
o r
B a y e s i a n I n
t e s t i n g
e x p e r i m e n t a l 1 9 3 5
t o
social ing,
of
it
t h e
w a s
t h e
w a s
o u t
s a y i n g
l o o k e d
level, t h e
t h r e e
a n d
b y
a n d t u a l u s e
B u t ,
a
m a j o r
t h e
h y b r i d
t e n d e n c y
issues
p e r f e c t l y
t h e
s o c i o l o g y ,
a n d
t h e o r y ,
w h i c h
h y b r i d
s o
w h i l e
as
o f
b e
b d o k ,
a n d
d i s t i n g u i s h i n g
in
r e s u l t s
a n d
since o f t e n
o v e r l o o k e d
t o
t h e
b y
p u t
t h e
o n
t h e o r y
t e s t i n g ,
in
a m o n g
w r i t t e n
i n
t h e
s t u d e n t s
in
t h e
se.
test-
f r o m
t h e
call
this
W e
a n d
it g o e s
w i t h -
P e a r s o n
w o u l d
h a v e
m a r r i a g e . t h r e e
levels
n o t
b e
a n d
u s e r s
-
m a t h -
t h e
first
s e p a r a t i n g a p p l i c a t i o n ,
b o t h e r e d
T o
s a m e
O n
issues
t h e o r y
g r e a t
i g n o r e d
significance
per
o n
1 9 5 7 ) . t h e
l i k e l i h o o d
F i s h e r
e x p e r i m e n t e r s .
T h e
in
t h e
c o n c e p t s
f o r c e d
n e e d
H o g b e n ,
o b t a i n e d .
o f
w i t h
b e t w e e n
statistical
c o n t i n u e s
c o n t r o v e r s i a l
p e o p l e
a n d
a n d
t e a c h
t h e o r y
u n d e r s t o o d
s o c i o l o g y
p a r t
i n f e r e n c e ,
t h e i r
t h e
significance
t o
f o u n o n
o n l y
stress
"statistics"
t h e
t h e
" c o o k b o o k s "
N e y m a n
r e s o l v e
( n o t e d
w e r e
o f
f o r m u l a e
b y
t h e s e
statistics, w e r e
d i f f e r e n c e s
in
u s e d
c o n c e p -
p l u g - i n - a n d - c r a n k - t h r o u g h
rules.
s e c o n d o n ,
level, w r i t e r s c o m m e n c e d
s h e l v e s
t h e o r y
N e y m a n - P e a r s o n m e t h o d ,
t o
q u e s t i o n s
i m p a c t I n
d e b a t e
m e r g e d
w r i t e r s ,
a c c e p t a b l e ,
n u m e r i c a l
statistical
t o
c a n
t h a t p r a c t i c a l - m i n d e d
t h e o r e t i c a l
s a m e
b y
t h e
t h e
statistical
o f f s p r i n g
t e x t b o o k
s c h o o l s
o n
T h e
this
q u a s i -
m a t h e m a t i c a l
m o s t
w i t h
F i s h e r ' s
t a u g h t
n o r
o n
t h e
1 9 2 5
t h e
w a s
F i s h e r
i n t e r p r e t a t i o n o f
first,
a n d
a
w h a t
intervals,
t o
t o g e t h e r
statistics."
n e i t h e r
s a y i n g
t h e
o f
t h a t
o f
f o r
his
in
a
sciences.
n o n - s t a t i s t i c i a n s ,
o f
w a s
this s e e m e d
b y
t h e o r y "
statisticians,
t h e r e
m a i n l y
largely
i n
S O L U T I O N
practically
d u e
o f
r e s o l v e d
" h y b r i d
c r e a t i o n
e m a t i c a l
p r o b a b l y e d i t i o n
historically
f a v o r
social
A l t h o u g h
silently
t o
t r e m e n d o u s
b e e n
p r o v i d e d ,
t h e o r y
a
c o n f i d e n c e
h a v e
is
first
h e
as
t h e
w i t h
T h e
t h e
" r u l e s
N e y m a n - P e a r s o n c o m p r o m i s e
this
p r o v i d e
b e c o m e
s u c h
Experiments.
1 9 6 0 s ,
sciences
w h i c h
in
d e s i g n
Design
statisticians, 1 9 4 0 s
p a r t ,
t o
t h e
h a s
i n f e r e n c e
tests
S I L E N T
h a d
a n d
t e s t i n g
a t t e n t i o n
T H E
h a s
b i o l o g y
statistical
a n s w e r .
statisticians
d e v e l o p m e n t s
e x p e r i m e n t e r s . significance
o n
a p p l y
a d e q u a t e
really
t e s t i n g
significance
o t h e r
f u n c t i o n ,
o f
h y p o t h e s i s
p s y c h o l o g y ,
his
t o
H Y B R I D I Z A T I O N :
d a t i o n
o f
g i v i n g
p r o c e d u r e s
i n t e l l e c t u a l
t o o l ,
experts
l e a r n e d
w i t h o u t
n u m e r i c a l
3 . 5
fields
inference
a n d
f r a m e w o r k .
t e x t b o o k s
p e a c e
s h e l v e s
c o m b i n e s
u n r e s o l v e d
o f
in
is
r e s e a r c h
issues
a n d
libraries
f r o m
p r e s e n t e d
c o n t r o v e r s i a l
e d u c a t i o n ,
n e g o t i a t i o n s
c o n c e p t s It
for
t h e
c r e a t e d n o w
p a y
F i s h e r i a n
a n o n y m o u s l y a n d
p s y c h o l o g y ,
a l t e r n a t i v e
as
a
h y b r i d t r i b u t e .
a n d
t h e
statistical a p p r o a c h e s
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The
t o
scientific
i n f e r e n c e
N e y m a n - P e a r s o n significance i d e a s
t h e o r y
t e s t i n g ,
b o o k s
w e r e
o n
readily w e r e
n o t
o f
i d e a s
w e r e
t r o v e r s y , w e r e
m u c h
n o t
p s y c h o l o g y ,
Statistics
w h o
is
w i t h
as
t h e
t h e i r
t h a t
a b s t r a c t
p a r t i e s
( w i t h o u t
n a m e s
a n d
o f
e v e n
at
t h e
in
-
w h i c h
list
is
e v e r y
t h e
v i e w e d
s o c i o l o g y a n d
t h a t E.
a l t h o u g h
c o n -
c o n c e p t s
u n u s u a l
p h e n o m e n o n logic
S.
s o m e
o f
t h e o r i e s
m o n o l i t h i c
t h e s e
s a m p l i n g )
crucial
v e r y
t h e
Fisher's
e x i s t e n c e
T h e
c o m p e t i n g
a l m o s t
t r u t h ,
d i s p u t e .
w i t h
N e y m a n
t h e m ,
h i n t e d
f r o m
r a n d o m
o f
issues
f o r
b o t h
a l o n g
t w e n t y - f i v e
c r e a t o r s
t h e m
c o n c e p t s
e d u c a t i o n ,
t h e
t e x t b o o k s
p r o p o s e d
t r e a t e d
N o n e
o u t
w h e r e
in
K e y
i n t r o d u c e d
c h e c k i n g
t h a t
m e n t i o n e d
s p e l l e d
are
p s y c h o l o g y ,
p r e s e n t e d .
less
p o w e r
f o u n d
1 0 7
i g n o r e d .
m e n t i o n i n g
f o r
w e
e v e n
i d e n t i f i e d
r e s e a r c h e r s
as
i n s t a n c e ,
statistics
P e a r s o n t h e i r
s u c h
F o r
available,
experts
c o m p l e t e l y
w i t h o u t
as i r r e c o n c i l a b l e .
t h i r t y
like
a r e
inference
i n
fields
a n d
t h e
d i s c u s s e d .
o f
i n d u c t i v e
i n f e r e n c e . T h e
h y b r i d
t h e o r y
c o n s t i t u t e
w h a t
t h e
o f
level
is
c o m e s
"scientific"
significance
N e y m a n
a n d
f r o m
n o n - s i g n i f i c a n t
a
P e a r s o n
a n d
n o t
t h e
a n
p a r t
e p i s t e m i c
t h e
w h a t
is,
F i s h e r
in
t h e
o l u t i o n "
t h e
t h e o r y
tests
p r e s s u r e
t o
1 9 7 0 ) .
a n d o f
e x p l a i n I n
o f t e n
G o s s e t ,
N e y m a n ,
tests
a n d
t h e
w i t h o u t
s t a n d i n g
o f
u l t i m a t e
p u r p o s e
o f
o f
e x p e r i m e n t
F i s h e r ) ;
t h e
h a s
h e
will
a n
w h e n
level
t h e
t h e n a n
in w h a t
M u r r a y ,
a n d
h a n d s
h a s
1987).
d e f e n d o f
t h e
i n t o
P e a r s o n
a
h a d
t h e i r
b e e n B y
n o t
m a d e
a n d
t h a t
called
t h e
g i v e n a b o u t
( c o n t r a r y t h e
n u l l
t o
d a t a ,
at
w i t h
h y p o t h e s i s
o c c u r s
fields,
u s i n g
t h e
w a s
n e i t h e r
m a j o r
in
b e h a v i o r a n d
" i n f e r e n c e
w e l l
t h e
o f
e s t a b l i s h e d tests
felt
( M o r r i s o n
a n d
t h e
d r a w i n g
r e s u l t
r e v -
u s e
h y b r i d
a l t h o u g h
s t r i k i n g l y
n o n - s i g n i f i c a n c e
t h e
e d i t o r s ,
ritual,
a significant
j o u r n a l s
significance
a g a i n s t a
o f
m i d - 1 9 5 0 s ,
levels
d e v i a n t
all w a r n e d
significance
a r e
d i d
significant
t h e
e d i t o r s
m e c h a n i c a l
s o m e
r e s e a r c h ,
b y
e x p e r i m e n t e r s
I n
n o t
P e a r s o n .
r e j e c t i o n
r e s e a r c h e r s
b u t
c o n f u s i o n
a r e
t h a t
e x p r e s s i o n a n d
c o n c l u s i o n s
i n s p e c t i n g
r e p o r t
specify
( f o l l o w i n g
e r r o r s
p r a c t i c e
d a t a
t o
i n t e r p r e t a t i o n
e n o r m o u s in
h e l d
m u s t
d r a w
t y p e - I I
i n s t a n c e ,
n o t e ,
T h e y
a n d
a r e
w r i t i n g s ,
b e h a v i o r i s t i c
t o
F o r
n o t
F i s h e r ' s
i n s t i t u t i o n a l i z e d
a n d
m u s t
t y p e - I
led
N e y m a n
j u d g m e n t .
statistical
t h e
c o n v e n t i o n a l
d e g e n e r a t e d a n d
c o n d u c t i n g
level,"
curricula,
r e s e a r c h ,
t h e o r y
f r o m
w a s
( G i g e r e n z e r
s o c i o l o g i c a l
H e n k e l ,
w r i t i n g s
u n i v e r s i t y
significance in
t h e
r e s e a r c h e r
a n d
o f t e n
t h a t
T h e
level.
0 . 0 1
p r e s c r i p t i o n s
"objective."
c o n v e n t i o n a l
t h e
o f
N e y m a n ' s
h y p o t h e s i s .
at
list
( f o l l o w i n g
T h i s
significance
n u l l
h y b r i d
in
a
" r e j e c t e d
T h e a n d
o f
t h e
n o r
o n .
h y b r i d ,
s t r i n g e n t
t o
say,
s o
a
t h a n
r e s u l t
e x p e r i m e n t e r s
m o s t
r e s p e c t
b e f o r e
i n t e r p r e t a t i o n .
m e a n i n g
p r e s c r i p t ) ,
o f
a n d
r a t h e r
N e y m a n - P e a r s o n ) ; b e c o m e
w i t h
F i s h e r ,
i n f e r e n c e s
n a r r o w
u n d e r -
s e e m
b e
s i g n
o f
t o a
t h e
b a d l y
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108
The
inference
c o n d u c t e d
e x p e r i m e n t
-
6.3).
practice
n e g l e c t i n g
T h i s
d e r i v e d
directly
Experiments: p e r
p a r e d
f r o m
"It
cent,
is
i g n o r e
t o
usual
all
e l i m i n a t e
t u a t i o n s
w h i c h
results"
( 1 9 3 5 ,
§ 7 ) .
n o t i c e
direct
c o n t r a d i c t i o n
t e s t i n g a n d s a m e
say,
a n
t h e
social
rejected
f u r t h e r
F i s h e r
S i n c e
t h e
sciences.
w i t h
a
clearly
for
t o
their
B u t
relation
that
b e p u b l i s h e d , w h i c h o f
results
d e c l a r a t i o n o f
a
t y p e
o f
t h e
s u b m i t t e d
that
" t h e
for
i n v e s t i g a t i o n
in
b y
this
t h e
t h e
fluc-
practice
o f
is
in
significance
p r e s e n t e d
t h e
d e m o n s t r a t i o n
of,
c o n f i r m a t i o n f o l l o w
that
literature
w a s
n o t
o f
t h e
q u e s t i o n "
b y
n o n -
will
has
c o r -
led
t o
h e e d e d
in
p u b l i c a t i o n
sensitivity
p r e -
e x p e r i m e n t a l
e x p e r i m e n t
Fisher's w r i t i n g s
5
in
w o u l d that
t h e
this r e a d i n g
r e q u i r e d
s o
o f
of
are
a n d ,
b e t w e e n
e x p e r i m e n t a l
it
t a k e
t h e y
p a r t
s a n c t i o n
results.
laboratories,
w i t h
t y p e
g r e a t e r
b e e n
Design
t o
that
(see
h a v e
The
standard,
i n t o
p h e n o m e n o n
i m p l i c a t i o n
t h e
s e n s e
o f a natural p h e n o m e n o n ,
also
N e g a t i v e
facile
t h e
m a y
Fisher's
this
t h e
s e e m s
o f
in
t h e
r e a c h
insignificant
o t h e r
results. T h i s
in
t h r o w n
t h o u g h t
f r e q u e n c y
t o
p u b l i c a t i o n
e x p e r i m e n t e r s
h a v e
p s y c h o l o g i c a l in
for
o f
results
p a s s a g e
d i s c u s s i o n
analysis
h e
c h a n c e
n o n - s i g n i f i c a n t
fail
causes
d e m o n s t r a t i o n
[is] s u b s t a n d a r d p.
f r o m
his
n o
significance,
w h i c h
results s h o u l d
reflect
o f
results
e x p e r i m e n t s
significant
level
t o
a l m o s t
c o n v e n i e n t
statistically
section.
significant rectly
t h e
o f
i n t e r e s t i n g
similar
a n d
H e r e
n o
w i t h
ill-considered
c h a n c e
t a k i n g
v e r y
a n
as a s t a n d a r d
t o
m e a n s ,
o f
h e n c e
experts
are
o f t e n
e x p e r i m e n t
( M e l t o n ,
1 9 6 2 ,
5 5 4 ) . A s
a n
h y b r i d o n l y
a p p a r e n t l y
t h e o r y
f o r
v i v e d
o n e
that
( M e e h l ,
t h e
f r o m
d e s i g n s
a n d
for
W h a t
is
discipline
a n d
o f
h o w
d o
t h e
s t a n d a r d s
universally
b e c o m e s
m u c h
t h e
its
i n c e p t i o n
in
t h e s e
is o f
b e
t h e
t h e
discipline?
o f
o f
T o
o f
c o m b i n e d ?
A r e
t h e
fact, if
a n d
o n e
sur-
a n d
t h e
a n d
q u e s s u b -
aspects
N e y m a n
o f a n d
e x p e r i m e n t a l
b i o l o g y
really a
g o o d
sciences? w i t h i n
e a c h
d e m o n s t r a t i o n the
has
h a r d
w h a t
a n d
1 9 8 6 ) ,
P o p p e r i a n s
t h e
Fisher,
scientific
It
a n d
If
a c k n o w l -
statistical significance
social
c o m p l e t e
data,
s c h o o l ,
1 9 6 3 ) ,
t h e
1 9 4 0 s .
( B o x ,
unlike.
s u p p r e s s i o n
c o n f i d e n c e
In
s a m e
c o n c e p t u a l l y
in agriculture
in
t h e
N e y m a n - P e a r s o n
t h e
t h e
e c u m e n i s m
t o
S a v a g e ,
ideas
defined. less
since
scientific
statisticians
r e m a r k a b l e
k n o w l e d g e ,
b e t w e e n
t h e
can
statistical
are
p e r m i t s
t h e
o f
d e f e a t e d
a n d
relation
b o d y
a p p r o a c h e s
a p p r o a c h e s
e x p e r i m e n t a t i o n
m o s t that
objectively m e t h o d s
all
b y
easily
different
w i t h i n
e n t e r p r i s e
d e v e l o p e d
has
d o m i n a n c e
i m p o r t a n c e
appeal,
it
attacks
L i n d m a n ,
if any, is t h e
scientific
m o d e l
Its
all
p r o p o n e n t s
( E d w a r d s ,
tions. W h a t ,
P e a r s o n ,
t h e
d i f f e r e n t
1 9 7 8 ) .
stantial
reasons,
applies
attacks
B a y e s i a n s
t h e
s u r v i v e d
practical
in w h i c h e d g i n g
has
n o n - c o n t r o v e r s i a l
social-science
h a v e
standardization l o o k s
across
o f
n o w
b e e n
statistical
disciplines.
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I n
The
e c o n o m e t r i c s , tively
rare,
o f t e n t h e
t o
t a k e
a n d
b e e n
t h e
a p p l i e d
t a u g h t
w i t h i n
t o
ematics.
v i e w
T h e
p r o v i n c e
3 . 6
u s e
o f
statistical
m e t h o d s
o f
o f
w i t h
t h e
basis
p l i n e s
f o r
a n d
a n
a p u b l i c a t i o n
U
Statistics
t o
W e s t - G e r m a n
i n t e r n a t i o n a l
B e s i d e
h a v e
t h e i r
b e i n g o f
t h e
R o y a l
tics, o r
d e p a r t m e n t s , a r e find
Statistical
in
statisticians
w h e t h e r
t h e
m o d e l e d
u s i n g
1 9 7 8 ;
D e G r o o t
T h i s a s p e c t s . a s k
h o w
T w o
o f
o f
b e c o m e o f
affect,
s o
s e e n
b y
m a t h -
practitioners
else's
c o n c e r n ,
t h e
I N T E L L E C T U A L
s u p p o r t s
a
Theory
f r o m
t h e r e
as
t h e
o v e r
1 3 0
Journal
of
in
as
a n d
m a n y
M o r e
c o u r t s ,
c o m b i n e d
in
(see
o l d e s t
7.4;
f o r
statiso t h e r
Statisticians a n d
a n d
t h e
Society
m a n y
a r c h e o l o g y .
t h e
t h e
Statistical
i n
for
c o u n t r i e s
o f
w o r k
o t h e r
S o c i e t y
d e p a r t m e n t
g o v e r n m e n t .
t h e o r y
o n e
t h e
statisticians
in
n o w
i n d u s t r i a l i z e d
a s e p a r a t e
e c o n o m i c s ,
und
B e r n o u l l i
1834
p r o b a b i l i t y
lists
Aligarh
are
o f
Abstracts,
Wahrscheinlichkeitstheorie
f o u n d e d
b e
disci-
Method
I n d i a n
M a n y
w i t n e s s e s
o f
p r o f e s s i o n
(ISI),
statistics,
a n d
b e c o m e
r a n g e
and
I n s t i t u t e t h e
s u c h
h a v e
h a v e
w h o l e
t h e o r e t i c a l
s h o u l d
w e
o f
statistics
call a u t o n o m y a
d i s c i p l i n e per
disciplines
like
a u t o n o m o u s ?
statistics,
b e e n
l o g i c a n d
e n o r m o u s
Statistical
I n f e r e n t i a l
as e x p e r t
b e c a m e
o t h e r
G r a d u a t e
m o r e
it is
d e b a t e d
c o u r t s also
w e
c a n
b e
E g g l e s t o n ,
1 9 8 6 ) .
t h e m
statistics
statistics
a n d
al.y
a n
1885),
i n d u s t r y ,
f r o m
t o
( f o u n d e d
o f t e n
e v i d e n c e
et
b y
h a s
m a t c h e s
r o u t i n e l y
m a t h e m a t i c s ,
fur
for
n o w
p r o f e s s i o n a l i z a t i o n
a p p e n d a g e
t u t i o n s
a c t i n g
i d e a s
It
Y
Zeitschrift
as p s y c h o l o g y ,
w a y
b e
t h a t
1 9 8 5 ) .
h a v e
s o m e o n e
Statistical
Society,
science,
M
P r o b a b i l i t y .
biostatistics.
s u c h
c o n s u l t a n t s
ISI
o r g a n i z a t i o n
f o r
O
t h a t
statistics,
a n d
U n i v e r s i t i e s
e v e n
N
o r g a n i z a t i o n s ,
Statistics
o w n
L o n d o n .
t o
t h e
statistical
M a t h e m a t i c a l
as
e x t e n d s
I n t e r n a t i o n a l
d e v o t e d
Gebiete.
O
j o u r n a l
m a i n l y
verwandte
T
a n d
j o u r n a l s
t h e
c o u l d
a c c o m p a n y i n g
p r o b l e m s
t h e
sciences
c o m p a r a -
analysis.
i m a g i n a t i o n
P R O F E S S I O N :
t h a t
a b s t r a c t i n g
o f
o f
( M c C l o s k e y ,
inference
m a t h e m a t i c s
t h e
e x p e r t i s e
statisticians. T h e
t e s t i n g
r e g r e s s i o n
is
specialists.
a n d
p r a c t i c a l
lack
biological
S T A T I S T I C A L
i n f e r e n c e ,
a
is
e x p e r i m e n t
t o o l s as c a n o n i c a l , g i v e n
A
Statistical
t o o l
w i t h
statistical
h i g h e r
statistical
T H E
a n d
109
c o n t r a s t ,
statistical
h y p o t h e s i s
social
t h e i r
experts
s t r i k i n g
e c o n o m i s t s
t h e
u n c o m f o r t a b l e
m o s t
s t a n d a r d b y
p s y c h o l o g i s t s '
s t u d e n t s
t h e
inference
a n d
m a n y
a s k
o t h e r
h o w
I n
a n d a n d se,
o f
i n f l u e n c e . w h e r e
s o c i o l o g y ,
o r
s e c t i o n
3.7,
statisticians
disciplines
statisticians
a n d
it
I n
w e
w e r e o t h e r
this
earlier
b i o l o g y .
h a s
c o n s i d e r a b l e
t o
social
s e c t i o n
h a d
T h a t
s e v e r a l
b e e n
is, h o w t h e
r e a c h
w e a n d i d
instio u t
t o ,
i n s t i t u t i o n s .
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110
The
W h e n c e n e e d s w a s
this
d i d
t r e m e n d o u s
it
satisfy?
it c h a n g e d
t i o n s
in
d e p t h ,
w e
experts
i n f l u e n c e ?
H o w
itself i n
inference
d i d
t h e
it
c h a n g e
p r o c e s s ?
will i n d i c a t e
W h a t
scientific
a n d
skills,
g u i d e
s o m e
a n d
c o n s i s t s
a n a l y z e
a n d
t h e
since
o f t e n
it
o u t s i d e T h e
in
tacit
d e v e l o p e d
b y
t h e
m e t h o d s
w o r k i n g
as a
M o s t ,
m o s t ,
u s e
f r o m
b u t
t h e
ability
a n d
tician,
since
o n e
n o t
of
a r e
e v e n
( T u k e y ,
1 9 6 8 ) ,
a r e
o f t e n
t h e m !
T h e
t w o
stract
t h e y
1 9 7 7 a )
p a r t l y
c a n
b e
historical w e r e
a r e
a p p l i e d
e v e n t s
idea,
b u t
t h e
f o r
d o
k e y
q u e s issues.
f o r m
o f
n e t w o r k
n o t
o f
u s e
t h e
v e r y
a b s t r a c t ,
r e c o g n i z e d
t h a t
in, m a n y
t h e s e
like. T h e y
n o t
e v e n
as
a b s t r a c t
o f
statistics
p r o b -
t h e
statis-
e x p l o r a t o r y
tests
( B r a d l e y ,
d o
t h e y
n o t
u s e
s o
a b -
a r e
d i f f e r e n t
t w o
d e v e l o p m e n t
clients
t h e
b u t
t h e y
b e c a u s e
a r e
i n t e r r e l a t e d
o f
statistical
a n d
for
c o n c e p t s ,
s u c h
fact
skills
abstract.
k n o w l e d g e
t h e m ,
a n d
skills
a n d
o f
t w o
t o
k n o w l e d g e ,
a n d
M a n y ,
Still, t h e s e
statis-
d a t a ,
T h o s e
a n d
t h a t
T h e i r
this
i n d u s t r y ,
o f probability\
o f
o f
goals.
scientists
a
k n o w l e d g e
g a t h e r e d ,
basis
a n d
m a t h e m a t i c a l
b y
w h i c h
t h e
h o w
i n f o r m a l ,
b e
j u d g m e n t .
n e t w o r k
h i g h l y
to, a n d
a n d
k n o w l e d g e
t h e
data,
d i s t r i b u t i o n - f r e e
t h r o u g h
s e m i n a l
o n
f e l l o w
model.
c h a r a c t e r i z e d
c o n c e p t s
w h a t
t h e s e
t h e
a n d
a p p l i c a t i o n
for
c o n c e p t
o r
a r e
s h o u l d
in g o v e r n m e n t ,
t h a t
a n s w e r
specialized
d a t a
s u b j e c t i v e
z statistical
m e t h o d s
t h e
a r e
t o
o f
specialized h o w
u s e s
t h e
c e n t r a l
t h e
in
c o n s u l t a n t
single
t o
f o r m a l
t h e o r i e s ,
o f
a n d
i n v o l v e d
t h i n k
i n f e r e n c e s
o f
n e e d e d
all, u s e
c o n c e p t
m o d e l ,
analysis
basis
statistician
w e
a b o d y
T h e
m a k e
d e g r e e
t r y i n g
i n s t i t u t i o n s ,
e n v i r o n m e n t ,
t h e
b y
d e t e r m i n e t o
t h e
a
a c a d e m i c
ideas.
t o
data,
o n
o f
c h a n n e l s
k n o w l e d g e
w o r k i n g s .
i n v o l v e s
r e s u l t
d e f i n e d
a n d
k n o w l e d g e
m e t h o d s
n o t
T h e
c o m p l e x
d e c i s i o n s
i n c l u d e
d a t a
a
s u m m a r i z e
p r o p o s e
d o
b y
its
disciplines
o f w h a t
is c h a r a c t e r i z e d
its d e v e l o p m e n t
ticians
t o
discipline
t h e
W i t h o u t
S p e c i a l i z e d
A
w e r e
s i t u a t i o n s .
c o n c e p t s as
a
w e r e
scientific
discipline. T h e
c o n c e p t
o f p r o b a b i l i t y
m a t h e m a t i c i a n m a t i z a t i o n p o r a t i n g [ 1 9 6 4 ] t o
a n d
that. a
u s e d
B u t
n o t
u s
f r o m O f
t h e
t h e i r
N .
c o n c e p t w a s
a p p l i c a t i o n .
w h e n
t h e y
a t t r i b u t e
set
t o
p r o b a b i l i t y a n d
l o n g
b e f o r e
A n d
implicitly it
(Shafer,
tied
t h e i r
t o
1 9 7 8 ) .
t o
S.
T h i s
N . o f
i n
w h o l e
f u n c t i o n s p e o p l e
b o o k
1 9 3 3
t h e
h a v e
p a p e r
S o v i e t
a n
a x i o -
b y
i n c o r -
( M a i s t r o v ,
h a d
r e f e r r e d
is a t e s t i m o n y
a p p e a r s
s o m e t i m e s t o
b y
B e r n s t e i n
h i n d s i g h t
p r o b a b i l i t y his
1 9 3 0 s
d e v e l o p e d
K o l m o g o r o v ,
w h a t
I n
early
t h e o r y
c a l c u l a t i o n s
a s s u m e
t h e
f u r t h e r
d u e
t h e
o f p r o b a b i l i t y . o f t e n
in
w h o
t h e o r y
c o u r s e ,
u s e
d e f i n e d
K o l m o g o r o v ,
c o m p a r a t i v e
i d e a s
1 9 7 4 ) .
l i m i t e d
t o
o f
A .
w a s
s e e m
t o
b e
t o
o n l y
i n c o h e r e n t
p r o p e r t i e s
w e
" G r u n d b e g r i f f e
d o d e r
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The
inference
W a h r s c h e i n l i c h k e i t s r e c h n u n g , " w h a t
p r o p e r t i e s
d e f i n e d
as
a
t h e i r
a
i n t o
t h e
tive
n o t i o n ,
t h e
b e t w e e n
n o t
t h e
w a y
results
h e o n
Cantelli,
o f
a b l e
t o
t h e
l a w
o f
m a t i c s
w e r e
o t h e r s
(see
o f
S o v i e t
d i a s p o r a
i n
in
n o t
t h e
U n i t e d
I n
c o u n t r i e s ,
t h e
a t e d b a s e d
m a i n l y
in
H e
t o
of
Statistics.
p r o b a b i l i t y w h i l e
in
all o v e r
it
t h e i r
British
t h e o f
a n d
t h e
b y
a
t o
M a n y
o f
t h e a
W i t h
t h e s e
a n
b e t w e e n I n
m a n y B o r e l ,
p r o b a b i l i s t s ,
K h i n c h i n ,
o f
a n d
m a t h e m a t i c a l
r i g o r b y
in
m a t h e -
C a u c h y
a n d
t h e n ,
t h e
a n d
b o r d e r s
t h r o u g h
n o w
this
b e -
e v e n t ,
p r i n c i p l e s
o f
E
p r i m i -
K h i n c h i n ,
t h e
s e t
variables.
b e y o n d
i n
s u b s e t s
b e
o f
far
o f
all
a n d
c e n t u r y
E u r o p e
o f
E
a n a l o g i e s
s e r i o u s
s t a n d a r d s
o f
f r o m
r a n d o m first
s u m
set
a r e
s c h o o l
as
r o o t s
t w o
T h i s
u n i f i c a t i o n
t h e i r
n o t
t h e
r e t i r e d
C e n t r a l
A m e r i c a n
a p p l y
h a s
d e f i n e
u s e d
o n e
w h o ,
E u r o p e a n
t h e
p r o b -
E u r o p e a n
w o r k e d r e s u l t s
o n
i n
o f
o r g a n i z a t i o n a l
i n
F i s h e r
-
E u r o p e a n 1 9 5 0 ,
a n d
m e d i -
w h i c h t h e
p r o b a b i l i t y
d e p a r t m e n t s t h e o r y
o f t o
C h a r a c t e r i s t i c
w a s
c o n c e p t u a l
-
a n d
o f
h e
w a s
m a t h t h e o r y .
Mathematical
c o m p l e t e ,
u n i t s .
a n d
statistics
b o o k
in p r o b a b i l i t y
c o n c e p t ;
s m a l l e r
t r a d i t i o n
A .
F o u n d a t i o n s
i n t u i t i v e ,
1 9 3 0
w o r k
1 9 4 6
b e e n
R o n a l d
t h e
t h e
b e t w e e n
e x p e r i m e n t a l
n e v e r
a n
o f
science
in his
b y
M a t h e m a t i c a l
b u t
o f
C r a m e r ,
a n d
i n t r o d u c e d
f o r m a l l y
citizen
t r a d i t i o n s
typically
o w n
w a s
" O n
C o n t i n e n t a l
t h e
t h e o r y
d i d
a
e m p i r i c a l
t h e
m o d e l
p a p e r
H a r a l d
unify
h a v e
o f
r e a c h e d
w o r l d .
m a t h e m a t i c s ,
w a s
statisticians, w h o
f e r e n c e ,
t h e
field
t a k e n
o f
n i n e t e e n t h
C e n t r a l
h a v e
F i s h e r
a b s t r a c t
t h e
r i g o r
t h e
o v e r
statistical
S w e d e
e m a t i c a l t r i e d
a
fact,
b e t w e e n
n e w
in
t o
t h e
B e r n s t e i n ,
b e e n
early
n o
p r o b a b i l i t y
R u s s i a n
t h e o r y
S t a t e s
Statistics."
a p p r o a c h .
basis
L y a p u n o v ,
since
h a v e
s t r i k i n g
t h e
p r o b a b i l t y
f u n d a m e n t a l
i n t e r e s t e d
a r e
o b t a i n e d
t h e
sets
e x p e c t a t i o n ,
t h e
o f
t w o
1 9 8 2 ) . o f
his
w o r k
its
basic n o t i o n s .
i n d e p e n d e n c e
1 9 8 7 ) . Its i n f l u e n c e
1 9 3 0 s ,
c o n c e p t
T h e o r e t i c a l
n o t
first
this w a s
a n d
n u m b e r s
s e t s "
as a f u n c t i o n
t h e r e
o n
o f
set,
t h e
is
"field
If
basic
m o r e
a set
t h e
M a r k o v ,
U n i o n :
t h e
in
T h e
i n t r o d u c e d
( G a n i ,
1 9 2 2 ,
a n d
l a r g e
h a d
S c h n e i d e r ,
o f
t r a d i t i o n
it
o f
P r o b a b i l i t y
is e q u a l
sets in
m a t h e m a t i c a l
r e e s t a b l i s h e d
w h i c h
t h a t
a
o n e .
c e r t a i n
o f o t h e r
m e a s u r e
H a u s d o r f f .
a
a x i o m a t i c a l l y
h a v e .
i n
u n i o n
is d e f i n e d
s y s t e m a t i z e
C h e b y s h e v ,
discipline,
t e r m s
f u n c t i o n s
t h e i r
K o l m o g o r o v
a n d
w a s
K o l m o g o r o v ,
abilists
t h e
t o
set
a n d
o n e . A l l o t h e r
s h o w e d
i n t e g r a l
a n d
i n c l u d i n g
in
o f
d o w n
s h o u l d
e a c h
z e r o
o f
v a r i a b l e
p r i o r
K o l m o g o r o v o f
t o
b e t w e e n
p r o b a b i l i t y
d e f i n e d
n o t i o n
assigns
t o
laid
p r o b a b i l i t y
p r o b a b i l i t y
o f a r a n d o m
o r t h o g o n a l i t y
T h e
T h e
real n u m b e r s ;
d e f i n i t i o n s ,
t h e
t h e
e v e n t s , is e q u a l
n o t i o n
t w e e n
It
111
K o l m o g o r o v o f
n u m b e r
in c o m m o n ,
e l e m e n t a r y
this
real
p r o b a b i l i t i e s .
E . T h e
c o n c e p t
s e t - f u n c t i o n .
" p r o b a b i l i t y , " e l e m e n t s
t h e
experts
Methods o n e
still
finds
m a t h e m a t i c s , statistical
in-
o f
t h e
this
is
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112
The
split,
in
1 9 7 3 ,
Statistics
a n d
Still, 1 9 2 2
since
statistical a s a m p l e
t h e
t h e
Annals
w e
a n d b e
a n
o f a c o u n t r y ,
infinite
p o p u l a t i o n ,
( w h e r e
a n d o f
that a
it
t h e
c o i n
as
d o e s
c o m e
i m p o v e r i s h e d ) .
m a d e
are
T h e
ficiently
a b o u t
a v e r a g e
o f
t h e
,
. . . , *•„).
m e t e r s
m a y t h e s e
F i s h e r
stated,
data,
u n k n o w n t o
that
find
data
p r o v i d e
a b o u t
that
c o n t a i n s
t h e
Fisher I n
called
a
abstract
the
s a m e
X
o b s e r v a t i o n
x
values
=
x
l i h o o d is
m o r e A
o f 0
2
,
a n d
likely
statistical
applicability.
it
that
f r o m
a n d
h e
t h e n t h e
is
t h e
data,
a n d as
its
t h e
w i t h
a
a s s u m e d d o e s
a n d
t h e
trials
h a d
o f is
o f
n o t
instance,
e v e n
certain
that
t h e
n o t
b e -
actually
that
is t o
o f
as
t h e u s e d
called
the
s a m p l e
T h e
g i v e
para-
i n f o r m a t i o n
o b t a i n
r e l e v a n t
data
o r
statistical
p a r a m e t e r
o f t e n
p o p u l a t i o n ,
c a n
suf-
F i s h e r
statistics.
o f
b e e n
a s a m p l e
t h e
p o p u -
t h e y
d r a w n .
task
full
c o m -
a n d
soil
called
t h e
p o p u -
f a r m i n g
characteristics
t h e
T h e
t h e
F o r
s a m p l e
o f
is
s a m p l e
s a m p l e
for
b e t w e e n
this c o n c e p t u a l
t h e
like s
a
r e p e t i t i o n s
a v e r a g e
statistical
variable X , p(x;
0),
w h e n
0
0
2
that
=
0
g i v e s
( D a w i d ,
a b o u t
t h e
model
i n f e r e n c e , statistics
i n f o r m a t i o n
values.
a b o u t
M
a p a r a m e t e r
0
it is o b s e r v e d
that, o n
m o d e l
F o r
a n d
o f
all p o s s i b l e
t h e
as p o s s i b l e
it is said t h a t
t h a n
o f
a parametric
S u p p o s e
than/>(x; 02); t h e n
( w h e r e
his
A
t h e
o f t h e
statistic
p o p u l a t i o n
statistic.
is i n f o r m a t i v e
0 o f 0 .
o f
is
in
p e r f o r m e d
as
It
i n f o r m a t i o n
f u n c t i o n
o b s e r v a t i o n
of
b e i n g
felt.
a n d
p o p u l a t i o n
sufficient t e r m s ,
p r o b a b i l i t y
u n k n o w n
as m u c h
set
t h e
tosses
toss
characteristics
letters
s u m m a r i e s
c a t i o n o f a n o b s e r v a b l e a
t h e
p a r a m e t e r s .
c o n t a i n
o f
c o i n
F i s h e r
w h i c h
d i s t i n c t i o n
a h y p o t h e t i c a l
o f
s a m p l e
characteristics
partially
t h e
p o p u l a t i o n
f r o m
R o m a n
T h e s e
b e
a b o u t
t h e
small
Annals
c o n c e p t
is d r a w n .
actually p e r f o r m e d
indiscriminately,
for
t h e
b e
t y p e
f o l l o w e d
p r e d e c e s s o r s ,
p o p u l a t i o n
a n d
is
abstract
a s u r v e y
it m a y
o r
as a r a n d o m
letters, like a,
parameters,
as in
s a m e
o u t ) ,
tosses
t h e
clarifications
s a m p l e
all p o s s i b l e
t h e
b e t w e e n
his
a mean
small G r e e k
(x}
T h e
t h e
e x p e r i m e n t
p r o c e d u r e
b y
w h i c h
o f
t h e
e m p h a s i z e d
o n e ,
set
w e a r
i n t o
c o n c e p t u a l
i n t r o d u c i n g
generally
that
c o n s i d e r e d
h e e d e d
talked
t h e
n o t
d i s t i n c t i o n
as
f r o m
agricultural
e x p e r i m e n t a l
p u r s u e d
Fisher
m o r e
in
Statistics, Theory.
e x i s t i n g
b u t
s a m e
t h e n
Mathematical
it
his p a p e r ,
is a s s u m e d
c o m p a r a t i v e
lation.
at
actually
experts
Probability
p o p u l a t i o n
m u n i t y
c o i n
of
l o o k
I n
t h e
in
c o n s c i o u s l y
c a n
m o d e l .
m a y
Annals
Fisher
p a p e r ,
lation
o f
inference
t h e
the
=
for
p r o b a b i l i t y
when/>(.*•; that X
a n d
1 9 8 3 ) .
l i k e l i h o o d
basis o f
0 ,
consists
x
Fisher's
9)
is n o t
a n d
o f
e a c h o f
t h e
o f 0, is l a r g e r that X
specifi-
v a l u e
o f
m a k i n g
idea
t h z t p ( x \
t h e o b s e r v a t i o n
a
is
t h a n — x
t h e
that
a n
for
all
s a m e 0 ^
0
is t h e
larger like-
alone,
0,
. is
instance,
a
v e r y t h e
abstract
a n d
flexible
n i n e t e e n t h - c e n t u r y
c o n c e p t
p r o b l e m
o f
o f
w i d e
m e a s u r e -
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The
m e n t
a n d
m o d e l .
A
m i n e
a
e r r o r
in
h o w
m e a s u r i n g
m e a s u r e m e n t
p o s s i b l e t h e
close
m a y
b e
b u t i o n t h e
A s s u m i n g
w i t h
v e c t o r
since
in
2 0
u)
s a m p l e x
= p ( x ; n o
a v e r a g e
v)/p(x;
o f
t h e
will
n o t
c o m m u n i c a t i n g
t h e
h o o d
s a m p l e ) .
a s s u m i n g
a n y
o b s e r v a t i o n rect"
a s s u m e
o n l y
P e a r s o n
h a d
h e
data
p e r i m e n t a l ,
a i m
t o
as
set
v a l u e
for
m a d e . in
test.
statistical t h e
t h e
success
d i s t r i b u t e d a
w h o l e
that
e s t i m a t e s
p a r a m e t r i c
t h e
families
usually
Fisher's
o f
s i m p l e r
n e w
t h e
a w a y
t o
tra-
distri-
t o
k n o w
b e
i n d e -
A
this.
t h e
s e n s e
o f
u,
a n d
value
individual scientist
is
p r o c e d u r e s
is
v a l u e
o f
UQ) is
( t h e likeli-
m a x i m i z e d ;
probability that
his
t a k e n
m a x i m u m
t h e
is u),
t h e
t h e
his
t h e
X
. . .p(x20;
v a l u e s
M
t o
is
true
t h e o f t o
f r o m
n o r m a l w h i c h
a
the "cor-
p r o b a b i l i t y
p r o v i d e d
t h e
t o a
Grammar closely o f
d i s t r i b u t i o n s
c o n c e p t s ,
Pearson's, like
curve,
a n d
n o r m a l
o r
h e
d i d
n o t
s u m m a r i z e
t h e
t h e o r y
t o
Fisher's
e x p e r i m e n t .
fertilizer
F i s h e r a n d
sufficient
w a s
c o n s t a n t s , "
of Science.
a
t o
e x -
biological
tied
t o
n o t
Fisher,
m e r e l y
causal p o w e r
t e n d e n c y
o b s e r v a t i o n a l ,
b e f o r e
b u t
w e r e
t h a n
t h e
" f r e q u e n c y
Pearson's
o f
t h e
n o r m a l
a v e r a g e
c o n t a i n s
called
t h e r e f o r e ,
in contrast,
I n
u.
o f
smaller
c u r v e s
p o w e r s ,
in line w i t h
i s \i.
X , .
their
o f t e n
causal
a b o u t
b e
p r o c e d u r e ,
a b o u t
t i m e
c u r v e s ,
t h e s e
w e r e
b i o m e t r i c i a n s ,
w e r e
fit
o f
t o
t h e
m e a s u r e m e n t s
a
n
g u a r a n t e e
w e
t h e n />(*;
statistics
d e t e r m i n i n g
w i t h
it
v a l u e
fi)
t o
t h r o u g h o u t
a c c o r d i n g
family
g e n e r a l l y
x
assign
m o v e
t o
m o r e
o n l y
a s s u m e d
s e n s e
p a r a m e t e r s
o f
will
is
is, g i v e n
s a m e
t o
s o u g h t
I n
g a v e
m o d e l s
u
It
statistical m o d e l s ,
T h e
UQ e q u a l
q u a n t i t i e s
H e
T h e
t h e
d e t e r m i n e s
m e a s u r e m e n t s ,
different
individual
is at
a
d e t e r -
c o n s t a n t
statistic, in
p r e c i s i o n
c o l l e a g u e s o f
b e
u s e d
i n f o r m a t i o n the
n o
c o n s i d e r e d
are
k n o w
o b s e r v e d
entities
p a r a m e t e r s
u n d e r
w e
causes, c o m p l e t e l y
p a r a m e t r i c
that
t h e
identify
w i t h o u t
H i s
case. data.
o b s e r v a t i o n s .
if
are
d e f i n e d
a special
"quaesita,"
a v e r a g e
m o d e l , t h e
e n d
T h e
u:
for
that
n u m b e r
actually
statistical
K a r l
t h e
o t h e r
x
d i s t r i b u t i o n
this
o f
his
are
for
T h a t
t o
that
t o
s a m e
u.
true
p r o d u c t / > ( * , ;
is a s u f f i c i e n t
t h e
m o r e
a s s u m i n g
p l u s
e s t i m a t e
is
a b o u t
g i v e
k n o w n ,
m e a s u r e m e n t s
p)
/ n
m e a s u r e m e n t s ,
justified,
in
is t h e
is
p a r a m e t e r t o
statistical
m e a s u r e d
w i t h
t w e n t y
s a f e g u a r d s
x,
t h e
t a k e n
take
a
p r o c e d u r e
e x p e r i e n c e
m e a s u r e m e n t s
2
i n f o r m a t i o n
t h e r e f o r e
o f
u. I f w e
b e
o f
t h e r e
a r o u n d
o f t e n
=
t o
t h e
t h e n
e x p e r i m e n t a l
t h e
o f
is
ideally,
o f
c
o f
p)
t e r m s
A s s u m i n g
u n k n o w n
and/>(x;
in
o b j e c t
o n l y
m e a n
)
113
t h e
and,
m e a s u r e m e n t s
size
is a l o t
r e p e a t e d
c o n t a i n s
t h e
. . , X
x .
g r o u p e d
t h e o r y
that/>(x \ x \
o f
, .
are
u)
1 a n d
t h e
p r e c i s i o n
t h e r e
t h e o r y p(x;
( X ,
result
t h e
1), a n d
variance
a v e r a g e
t h u s
(say
a n d
error
p e n d e n t , T h e
that
experts
c o n c e p t u a l i z e d
p r o c e d u r e
m e a s u r e m e n t s
e r r o r
b e
m e a s u r e m e n t
k n o w n
ditional
c a n
m e a s u r e m e n t s ,
t h e
m e a s u r e d . a
error
inference
o n e
o r
u s e d
d r u g in
m a y
statistics,
his
a r g u e w a s
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114
The
b o u g h t
b y
b u t i o n s
l i m i t i n g
(Stigler,
r e t u r n
t o
d i s t r i b u t e d ,
o r
h o w o r
o t h e r
i n t e r e s t
Still,
h i m s e l f
sufficient
l o a d
c a r r i e d
b u t i o n ,
in
o f
t h e
f a t h e r s
h a v e
t h e
s t o c h a s t i c
b u t
o f
that
t h e
o f
d e n t
c h a n c e
n e a r
t h e
e n d
o f
d e p e n d e n t
" l a w
o f
large
d e n t
trials. I n
n e c e s s a r y
M a r k o v d i t i o n s
describes state
a
o f
t h e
studies,
o f
in
m u s t
s t u d y
a
o f
h a v e
p o w e r f u l o f
m a y
h e
s u c h
say
t h a t
p r o b a b i l i t y
analysis
a n d
m o d e l s
i n f e r e n c e ,
o n e
F i s h e r ' s
a
f r o m
1 9 6 8 ) .
k i n d
p r i o r
as t h e
distri-
o f
statistical
so-called
stochastic
-
it t h e
c o n t e x t
o f
sufficient 1 9 0 6
s y s t e m t h e
t h e
still
o f
in w h i c h o f
u n d e r l y i n g
r a n d o m
h e i g h t d i d
n o t
series
a n d
s t o c h a s t i c p h e n o m e n a ,
probability h o w e v e r ,
t h e o r y
t h e
a n
explicit
f o r
i n t e r e s t
b y
m a n y
-
is o n l y
l a w s
o f
p r o c e s s
at
t r u e t h e
l a r g e
dis-
t h e
i n d e p e n -
o f
t h e
n o t i o n
this
so-called
for
i n d e p e n -
R u s s i a n
e v e n
s c h o o l
called
transition t i m e
A .
u n d e r a
after-effects,
g i v e n
W h e n ,
n u m b e r s ,
is n o w
w i t h o u t
p r o b a b i l i t y
s y s t e m
b y
in
t h a t
h o l d s
1 9 0 6 ) . W h a t
o f
p r o b a b i l i t i e s .
i n v e s t i g a t i o n
t h e t h e
o f
f r e q u e n c i e s
c o n v e r g e n c e
a
o f
(see,
1.7),
is P o i s s o n ' s
( M a r k o v ,
t i m e
t h e o r y
m a t h e m a t i c a l
t h o u g h t
c o n d i t i o n s
state
in
(see
t o
t h e
w i t h
1 9 7 2 ) ,
t h e
i n d e p e n d e n t ,
associates
s t u d y
c e n t u r y
( L a n c a s t e r , like
t o
5.7).
a g e n e r a l
m o d e l
n o t
a c c o r d i n g
n i n e t e e n t h
m e a s u r e m e n t s
empirical
in
t e r m
t h a t
t h e
p r o b a b i l i s t i c
c e n t u r y ,
w a s
o f
t i m e
m e a s u r e m e n t s
n o w
t h e
is a
o v e r
a x i o m a t i z a t i o n
c o n v e r g e
a r o s e ,
m o d e l
o b v i o u s l y
t h e o r e m
n i n e t e e n t h
o n
o f
w h i c h
studies
p h y s i c s
d e p e n d e n c y
o n l y
t h e
m o d e l s
in
t h e
t h e o r e t i c a l
m a t h e m a t i c a l
d e p e n d s
fact
c h a n g e s
s u c c e s s i v e
K o l m o g o r o v ' s
a physical
t h a t
I n t e r e s t i n g l y ,
in
I n
b y
is
statistical
c o n -
c o n c e r n s
( B r a d l e y ,
special
n o r m a l l y
d e v i a t i o n s t o
a t h e
R e c e n t l y ,
l e d
m o d e l
t h a t
w e r e
S i m i l a r
tests
o f
statistical
o n e
n u m b e r s "
o f w e a k
o f
t h a t
trials
h a s
distri-
r e s p e c t
a s s u m e d
m i l d
1 9 8 1 ) .
t h e
p a r t
c h a r a c t e r
t h e
a n d
this
s y s t e m
B e r n o u l l i ' s
s h o w e d
is
k i n d
o u t g r o w t h
t h e
a p p r o a c h
w e r e
e v e n t s
u n d e r
o f
this
n o r m a l i t y . "
f u n c t i o n s
t o
in
o f t e n
statistical
e r r o r - t h e o r y
s t o c h a s t i c i t y t o
a r e
c o n c e p t s
s o n s
in
o f
a p p r o p r i a t e .
i n
w a s
o b s e r v a t i o n s ,
( H u b e r ,
o f
R u s s i a n
A c c o r d i n g
c h a i n
a n
c u l m i n a t e d
c u s s i o n
o f
T h e
p r o c e s s e s .
p r o c e s s e s is n o t
s o
a
h e i g h t
d y n a m i c
m e t h o d s
his
m o d e l
d e s c r i b e s
t h e
t h e
" m y t h
r e s t r i c t e d
w h i c h
c o r r e l a t i o n a l
a n d
o f
h e
families
1 9 5 1 ) .
i n d e p e n d e n c e
e v e n
n o t
i m p o r t a n t
laws.
since
p a r a m e t r i c
B a y e s i a n t h e
w o r k
d i s t r i b u t i o n - f r e e
s e e m
( H o t e l l i n g ,
p r o b a b i l i s t i c
a n d
b y
w h i c h
a s s u m e d
f o r
t h e
t h e
m e t h o d s
a
is
statistic,
particularly
p r o c e s s ,
o f
a n d
a n d
is b o r n e
i n f e r e n c e A
i d e a
r e s t r i c t e d
F i s h e r ' s
d i s t r i b u t i o n
so-called
c o n c e p t ,
s t u d i e d t h e
i n
t o
statistical
t h e s e
m o r e
f u n c t i o n
classical
o f
F i s h e r ' s
u n i f y i n g
t h e s e
ideas,
k n o w n
g o o d
experts
Ironically,
c o n t r i b u t i n g
" r o b u s t n e s s "
f u e l e d
o f
s o m e
t h u s
a b o u t
n o r m a l i t y t h e
1 9 7 6 ) .
t o
n i n e t e e n t h - c e n t u r y
o b s e r v a t i o n s ,
c e r n
h i m s e l f
inference
t o a n d
A . c o n -
M a r k o v w h i c h a n o t h e r n o t
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o n
The
t h e
p r e v i o u s
i m p o r t a n c e a
h i s t o r y o f
t h e
w h i c h
p r o c e s s e s H e r m a n o f
t h e
a n d
U d n y
scientific
w e r e
a n d
w i t h
t h e y
deliver,
in part, 1 8 6 9 ;
t r e n d s
t o
a n d
p h y s i c a l
a n d
see
m a k e
sciences
2.2),
e l u d e
r e g u l a r
s h a p e
o f
T H E
S T A T I S T I C A L
o n
A
T h e
discipline
n e t w o r k f o r m a l c l u d e t i o n s
o f
i n f o r m a l ,
i n t e r n a t i o n a l o f
T h e
N
o f inferential
specialized
a n d
t h a t
F i e n b e r g ,
1 9 8 5 ) .
It
a
1 8 8 5 w i t h
c o n t i n u a t i o n
w h i c h
w a s
Statistical
o f
t h e
o r g a n i z e d ,
( N e u m a n n - S p a l l a r t , m e t h o d s
o f
official
w o u l d
o f
statistical
Q u e t e l e t ,
u n d e r
t h a t
b r i n g
o f
b u r e a u s .
t h e
i n t o
t h e
b u t
o p e n
also
P e a r s o n
v a r i e t y
f r o m
t h e
o f
sociology,
social
sciences
"social
physics"
t o
e x p l a i n
social
1 9 6 7 ) .
l a w l i k e n e s s
a p p r o a c h e s ,
I n
o f
t h e s o m e
s u c h
as
t h e
1 9 8 5 ) .
I N S T I T U T I O N S
a
t o
a n d data. S o m e
is
c o m p l e x
t h e
c o h e r e n t
i n s t i t u t i o n s ,
w o r k i n g s .
o f
a n d
c o n g r e s s e s c o l l e c t i o n
careful
1 9 8 5
ISI
w h e n
T h e s e
a n d
in-
t h e
sec-
Q u e t e l e t , in
a i m e d
t o
scientific
l a w s
b y
a n d
f o u n d e d
i n t e n d e d t h e
t o
b e
first
o f
t h e
B r u s s e l s
C e n t r a l in
f o r m u l a t e
1 8 5 3
u n i f o r m
i n t e r n a t i o n a l
m o s t l y
m e m b e r s
c o m p a r a b l e
a n d
it w a s
p r o m o t e w e r e
Statistical
( A t k i n s o n
C o n g r e s s e s ,
t o
a n d
ISI w a s
h e l d
m e m b e r s
t h e
i n
t h e
Statistical
statistical
o f
b y a
I n t e r n a t i o n a l
jubilee
l e a d e r s h i p
o f
a n d
t h e
c o m p a r e
T h e i r
o n l y
o r g a n i z a t i o n s
its f o u n d a t i o n
t h e
n o t
w o r k .
c e n t e n a r y
A t
o f
b y
p r o f e s s i o n a l
B e l g i u m ,
a m a s s i n g
w o r k
a r c h i t e c t u r e ,
( B a r t h o l o m e w ,
its d e v e l o p m e n t
1885). T h e s e
statistical
t h e
p o s s i b l e
s h o w
o r g a n i z a t i o n its
classification
c o m p a r a b i l i t y
it
w i d e
( B a r n d o r f f - N i e l s e n ,
I n t e r n a t i o n a l
C o m m i s s i o n
e x p e c t e d
classical
statisticians
it is t o d a y .
a n d
I N F L U E N C E
is i n s t r u c t i v e
w h a t
a
p h y s i c s ,
P R O F E S S I O N :
D
i n t e r n a t i o n a l
K a r l
o c e a n o g r a p h y ,
statistics is c h a r a c t e r i z e d
w h e r e
c e l e b r a t e d
t o
m o r e
b e a c h
n a t i o n a l
w h i c h
in
w a y
f o r
1 9 8 6 ) . F o r
p r e d i c t i o n s
g u i d e
I n s t i t u t e ,
( G a n i ,
m a k i n g
k n o w l e d g e ,
a n d
u n i v e r s i t i e s c e n t r a l
b y
t h e
a
t o o l
c h e m i s t r y ,
Q u e t e l e t
a
p h e n o m e n a
r i p p l e s
s t o c h a s t i c
C r a m e r
o f
i n
statistician
m a t h e m a t i c a l
a p p r o a c h
t h e
raised
o f
H a r a l d
t h e
m e t e o r o l o g y ,
e c o l o g y ,
p r o v i d e
t h a t
t h e
t h e o r y
especially
m o d e l i n g
A d o l p h e
n a t u r a l
3 . 7
a
s h o r t - r a n g e
t h e y
f u r t h e r
a n d
a g e n e r a l
c o m b i n i n g
just a f e w
also
w e r e
a n d
1 9 5 9 ) .
a n i m a l
w h a t
d e p e n d e n c e
M a r k o v
o b s e r v a t i o n a l
n o w
t o m e n t i o n
( Q u e t e l e t ,
in
a b o u t
P e a r s o n
o f
S w e d e s ,
m o r e
a r e
K a r l
p o i n t
e c o n o m e t r i c s ,
p l a n t
Q u e s t i o n s
c e n t r a l
( B a r t l e t t ,
disciplines:
c o s m o l o g y ,
T h e
t h e
1 1 5
p r o b a b i l i s t
s t a r t i n g
a g a i n
p r o c e s s e s
e p i d e m i o l o g y ,
a
experts
a n d
t h e
1 9 8 1 ) .
Y u l e
S t o c h a s t i c
L e x i s
b e t w e e n
( O n d a r ,
R u s s i a n s
p r o c e s s .
o f
b e c a m e
W o l d ,
G .
t h e
w o r k
c o r r e s p o n d e n c e
C h u p r o v ,
o f
inference
d i r e c t o r s
o f
h o p e d ,
w i t h
statistical
d a t a
r e g u l a r i t i e s
f o r
a
f u t u r e
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The
116
"social physics." T h u s o f
statistical
congresses goal:
t o
t h e
s l o w l y
b e
b i n d i n g
data
a
nature.
T h e
o g o u s
t o
ISI
t h e
their
t o
i n t r o d u c e a n d
T h e
c o m p r e h e n s i v e styles O n e
a n d
d e b a t e
k n o w l e d g e t h e
a n d
a b o u t
t u n g t h e
d e r
o n
p o p u l a t i o n
o f
t h e
B u r e a u h e
o f
called
m e n t s
w a s
b e t t e r
if
care
b y
tive
m e t h o d "
w i t h a
t h e
p a p e r a n d
in
ISI,
n o t , for
t h e
t h e
g a t h e r i n g
h o w e v e r , a
s a m p l e
in o r
a
its in
that
o f
still
K i a e r ,
u s e
a g r e e d
battled
against
g e n e r a l
p r o -
local
u s i n g
s a m p l e s in
relied
o f
O n e
m o r e
Kiaer's
C e n t r a l o r
w h a t a r g u -
b e
m u c h
since
m o r e
"representa-
s a m p l i n g ;
t o
o n e
his
o f t e n
i m p o r t a n t
o f
w e r e
f r o m
o f
Kiaer's
(Jensen,
g e t
B e o b a c h -
t h e
i n v e s t i g a t e d ,
o f
t o
Bulgaria.
s a m p l e s ,
w o u l d
h a d
in
i n v e s t i g a t i o n
s a m p l i n g
i d e a
clash
a
traditions.
a statistician
1898).
in
for
i n v e s t i g a t i o n s "
r a n d o m
R a n d o m c e n t u r y
t o
t h e
data h a d
e x e r t e d .
o f
this
t h e
for
b e e n b e
see
d i r e c t o r
characteristics
census.
in g e t t i n g
it
w a s
a
characteristics
b e
l e a r n e d
w a s
o n l y
1 9 2 6 ) .
v e r s i o n
r a n d o m n e s s
f r o m u n d e r -
A n
early
o f
s a m p l i n g
in
s a m p l i n g
1 9 3 4 ) .
p e r i o d , a i m its
c o u l d
w e
c o m p l e t e
a s a m p l e
h a d
basis
material
" e r s c h o p f e n d e
(Kiaer, in
m a k e
at large. T h e s e
( N e y m a n ,
either
i n t e r v i e w e r s
N e y m a n
i n t e r w a r
data
anal-
t h e
a n d
c o m m u n i t y
again
p r e s s e d
p o p u l a t i o n
b e g i n n i n g
i m p o r t a n t
t h e
indi-
c o n g r e s s e s :
data
u s i n g
"Partial
A n d e r s
w h o
o f
t h e
It w a s
in
scientific
o n
as t h e
s o u r c e
c o l l e c t e d
1 8 9 5 ) .
o r
o f
as
association
different
is, o n
m e t h o d "
o f
i n v e s t i g a t i o n ,
b y J e r z y
w a s
N o r w a y ,
w h o l e
p o p u l a t i o n
a c c e p t e d I n
d i d
M a y r ,
c o u n t r i e s ,
quality
trained
search
c o m p l e t e
s t o o d
t h e t h e
b e t t e r
s y s t e m a t i c
(
that
p o w e r
t u r m o i l ,
s e l e c t e d
its p a g e s
f a r m i n g
called
d o u b l e
science.
possibility
M a y r
free
g o a l
t h e
for p r i v a t e
statistical
m a n y
as t h e
M a s s e , "
r e p r e s e n t a t i v e
that
t h a n
o f
o f
o n
f r o m
s u c h
v o n
s a m e
their
m o r a l
i n t e r e s t i n g
since
v e r y
a
w e r e
statistical
unscientific.
E u r o p e a n
" t h e
t h e
s t u d y a n d
t h e
statisticians w h o
sozialen
u n d e r
m e m b e r s
p r o v i d e
statisticians
G e o r g
Statistics
o f
o f
m e t h o d s
t h e
political
as a p u r e l y
w i t h
statistics,
century,
i m p r e c i s e
smaller
o f
ISI
a p o p u l a t i o n ,
p r i m a r e n
c o n s i d e r e d
t h e
t o
o f
w i t h
a n o p p o r t u n i t y
c o m p i l a t i o n
k n o w l e d g e
o f
w h a t
b u t
t h e
c o n c e r n e d
n i n e t e e n t h
m o r e
w h e r e
France^
h i s t o r y
interest
s u c h
de
o f
t h e m
t o
H o w e v e r ,
a v i c t i m
officials
a r g u m e n t s
p r o p o s e d
in
b e c a m e
t o p r o v i d e a n d
a t t e n t i o n
r e p r e s e n t a t i o n .
e x p o s e d
qualifications,
p r o c e e d i n g s
data
t h e r e f o r e
t h e
also g i v e n
g o v e r n m e n t
also
ideas
u n i f o r m i t y
foster
for
w a r ) , a n d
Institut
h a d
initial zeal a n d
( w h i c h
w a s
p e r s o n a l
a n d
place
e x c h a n g e
o f
m o t e
their
m e e t i n g
F r a n c o - P r u s s i a n t o
I n
lost
experts
c o n g r e s s e s
analysis
r e s o l u t i o n s
viduals
t h e
inference
t o
o r g a n i z a t i o n s collect
scientific
a p p e a r e d
statistics
goals.
a n d
A m o n g
that
c o m p e t e d
w i t h
set
s t a n d a r d s
for
t o t h e m
w e r e
t h e
t h e data
L e a g u e
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o f
The
N a t i o n s , t u t e
t h e
o f
I n t e r n a t i o n a l
A g r i c u l t u r e ,
U n i o n
for
t h e
1 9 3 4 ) .
B u t
it
t h e
h i s t o r y
t h e
o f
o r g a n i z a t i o n ,
t h e
t o o k
t h e
n a r r o w l y a n d tical
a n d
1 9 4 7 ) .
Its
c a m e
the
a n d
all
tributors
t o
h o l d
t h e
w h o s e
a d v a n c e d
s t u d e n t s ,
in
o f
Francis
m e t h o d s
o f
ideal
o f
e m a t i c a l
W a r s a w
a n d
g r o u p
K a r l a n d
o f
a
in
o f
t o s t u d y w i t h
a n d
p u b l i s h e d
o f
a n d
a
in t h e
that
w o u l d t o
w h i c h
topics.
T h i s
t h e m
W .
a n d
w a s
a
c o u l d
P e a r s o n , o n l y o n e
all
o f
t h e s e
b e g a n
m a i n l y
p r o b l e m s . f o u n d e d
t h e
in
t o
N e y m a n
1 9 0 1
o n in
t h e t e r m s
intellectual
b o d y t o
b y
statistical
b a s e d
n e w
a p p l i e d
w h e n
m e t h o d s
W e l d o n
a
in
i m p o r t a n t
u n d e r s t a n d i n g
o f
in
t o o k
f e w
journal
t h e
t h e
G a l t o n
n e w
b i o l o g y
b e
o f
t o
s p r e a d
s l o w l y
1 9 2 5 ,
A
t o
influential
b e c a m e
F. R.
t o
first
l a b o r a t o r y I n
1 9 8 6 ) .
c o n t r i b u t e d
t h e m t h e
c o n thirty-
successors
field.
training,
active
" D e c l a r a t i o n
statistical
o w n
p r o m o t e
w h i c h
a
b e -
statistics,
l a b o r a t o r y
learn
institutionalized
p o s t g r a d u a t e s . K a r l
k i n d
t h u s
1 9 8 5 ) ,
Francis
z o o l o g i s t
statistics
T h e
are
(Rice,
f o r t y - o n e
b y
Biometrika,
statis-
Its
e n d o w e d
m o r p h o l o g i c a l
l a b o r a t o r y
t h e
Institute,
o f
o f
It
t h e s e
b y
v o l u n t a r y
p r o f e s s i o n a l
o f
their
m o r e
r e p r e s e n t e d
a p p r o v e d
a p p l y i n g
statistical
their
O f
t o
N a t i o n s
a
earliest
statistics. M o s t
f o r m u l a t i o n s o f
c h e m i s t
-
t h e
w a s
activities.
t h e m
i n d u s t r y o f
ISI
in
I 9 6 0 ) .
U n i t e d
a c o m m u n i t y o n
in
( N i x o n ,
F i e n b e r g ,
P e a r s o n .
b r e a k
m a t h e m a t i c a l
a n d
( Z a h n ,
c h a n g e s
m e t h o d o l o g y .
k n o w
T h e
s h a r p
T h e
t h e y
Statistical
p r o b l e m s
o p p o s e d
P e a r s o n ' s
d o m a i n
i n t e r n a t i o n a l
as
statistics,
t o o l s
u n l i m i t e d
data
a n d
I n t e r n a t i o n a l
a c a d e m y "
r e c e n t l y
L a b o r a t o r y ,
P e a r s o n ,
ISI.
p r o f e s s o r s .
n o w
t e c h n i q u e s
p e r s p e c t i v e
types.
w e
G o s s e t ,
w a s
K a r l
variation,
s t r u c t u r e
S.
w o r k
biological a n d
o f
W .
e x i s t i n g
G a l t o n ,
t h e o r y
( A t k i n s o n
as
t h e
t h e
e x c l u s i v e l y
ISI
a
t h e
s e m i - g o v e r n m e n t a l
science
t o
o f
o f
p r o f e s s i o n a l i z e d
w a s
m a t h e m a t i c s
their
collect
s t u d y
as
the
m a s t e r i n g
S o m e
t o
a p p l i e d
s u c h
p i o n e e r s b y
b e
c o n t e x t
Insti-
P r o b l e m s
Institute
o r g a n i z a t i o n
T h e
t h e
m a r k e d
o r g a n i z a t i o n ;
laboratory."
f r o m
that
statistical
(International
G a l t o n
a n d
P o p u l a t i o n
t h e
t h e
university
d i r e c t o r
s t u d e n t s
c o u l d
w i t h
statistics
t h e
first
o f
p o s i t i o n s .
E t h i c s "
w a s
o r
Volume
"statistical
laboratories
that
a g e n c y
m o s t l y
o f
o f
j u d g e d
t o w a r d s
Centenary
D e p a r t m e n t s
b e
I n t e r n a t i o n a l
f u n d a m e n t a l
f u n c t i o n s
c o u n t r y
shifted
n o w
in
official
t o
w h a t
university
so-called
a n
association
P r o f e s s i o n a l
1 9 0 4 ,
t h a n
international
are
o f
o n
t o
"international
w e r e
activity
m e m b e r s
t h r e e
w h o
n o t
s h e d
a g e n c i e s
a n
rather
e x p e r t s
m e r i t ,
as
o f
a i m s
t h e
Society,
W a r
led
a n d
a d m i n i s t r a t i v e
d e f i n e d
scientific
W o r l d
a n d
c o n s t i t u t i o n ,
i n t e r n a t i o n a l
O r g a n i z a t i o n ,
I n v e s t i g a t i o n
ISI,
111
experts
E c o n o m e t r i c
S e c o n d
N u m e r o u s o v e r
L a b o r
t h e
Scientific
w a s
inference
o f
m a t h -
a n
a l m o s t
attract c a m e
t h e e i g h t s t u d e n t s
a n
f r o m
w a s
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a n
118
The
E n g l i s h m a n . J a p a n e s e . India, t h e
T h e
T h e
a n d
o t h e r s
n e x t
l a b o r a t o r y
i n t o
a
similar
i m p a c t
o n
S e c o n d
W o r l d
y e a r
1 9 2 9 - 3 0
G a l t o n
a n d
f r o m
cine,
a n d
W a r ,
t h e
w a s
a
( H o t e l l i n g ,
K a r l
o f
a g r i c u l t u r e ,
o f
o f
w a y
a n d
it
I n
at
m o r e
t h a n
social
t h e
s c i e n c e
-
in
i n c o r p o r a t e
p e o p l e
U S A
d u r i n g
-
t h e
w a s
( h a v i n g
t h e
w o r l d ,
b i o l o g y ,
w i t h
t h e
F i s h e r
all o v e r
w o r k
g r e a t
a c a d e m i c
L o n d o n
c h e m i s t r y ,
t o
a
b e f o r e
w h e n
in
f r o m
L o n d o n ,
e x e r t e d
t h e
C o l l e g e
c a m e
a
C h i n a ,
C o l l e g e ,
1 9 3 4 - 4 4 ,
disciplines
t o
w h o
f a r m
p e r i o d
fifty
e x p e r i m e n t a l
a n d
U n i v e r s i t y
U n i v e r s i t y
C a n a d a ,
o f
Statistics.
t a u g h t
o n
e x c e p t i o n
m a n a g e d
H o t e l l i n g ,
w a s
t h e
S p a i n ,
h a d
t h e n
t h e
w i t h
f r o m
A p p l i e d
v o l u n t e e r
E u g e n i c s
U . S . ,
P e a r s o n
H a r o l d
1 9 4 0 ) .
P e a r s o n )
a v a r i e t y
t i m e
role.
t h e
s t u d e n t s
R o t h a m s t e d ,
fertilizing
P r o f e s s o r
s u c c e e d e d
t h a t
experts
f r o m
D e p a r t m e n t
in
statistics
all
b r o u g h t
B y
a
F i s h e r ' s p r e s e n c e p l a y e d
w e r e
y e a r
Y u g o s l a v i a .
inference
h i m
m e d i -
( Y o u d e n ,
1 9 5 1 ) . T h e
i n f l u e n c e
Workers, in
w a s
t h e
t u r a l a n d
w a s
m a n y
t h e
t h e
t h e
o f
at
at
A n n
P e r h a p s statistics
in
later
t h e
a n d
a
m o s t
t h e
rest
t h e
o f
in
f o r
C a r o l i n a
at
a n d
First
h a d
w i t h
a
n e a r l y
e d i t i o n s
2 0 , 0 0 0
c o p i e s
G e r m a n ,
a p p l i c a t i o n s
in
a n d
a g r i c u l -
q u a l i t y
t h e
w i d e
c e n t e r s
a n d
n e w
1 9 3 6 .
c o n t r o l ,
N e w
U n i t e d
S n e d e c o r
a n d
o n
t h e
at
v a r i e t y
o f
h u s b a n d r y
o f
w e r e
M i c h i g a n
d e v e l o p m e n t i n
1 9 3 8 ,
B e r k e l e y ,
D e p a r t m e n t
L o n d o n .
i n
F i s h e r ' s
statistics
U n i v e r s i t y
Statistics, N e y m a n
it i n
F i s h e r
himself,
a n i m a l in
States.
f o r
m a d e
a c c e p t a n c e ,
C a l i f o r n i a t h e
t h e
a r r a n g e d
C o l l e g e ,
Y o r k .
E u r o p e
N e y m a n ' s
E u r o p e
S t a t e
Methods,
t h e
f r o m
I o w a
e n t h u s i a s m
Hill, in
f r o m
o f
i n
a g r o n o m y
C h a p e l
o f
o f
Statistical
in
w i t h i n
s e e n
o f i n f o r m a t i o n
L a b o r a t o r y ,
b o o k
w a s
D e p a r t m e n t
as h e
t h e 1 9 3 1
i n f l u e n c e
life.
Research
e l e v e n
S p a n i s h ,
f o u n d
flow
U n i v e r s i t y
S t a t e s
w i t h
L a b o r a t o r y
w o r k e r s
U n i v e r s i t y
his
fruitfully
biologists,
o f
c e n t e r s
d i r e c t
in a s e p a r a t e
c o l l a b o r a t e d
sessions
o f
for
t h r o u g h
e x p e r i m e n t a t i o n ,
statistical
D i r e c t o r
h o s t
U n i t e d at
w e n t
Italian,
t h e
Statistics
C o l u m b i a
statistical l a b o r a t o r y
o m e r s ,
t h e
O t h e r
p o s i t i o n
r e m a i n e d a n d
t h e
t h e
Methods
fields.
f o r
a c a d e m i c
o f N o r t h
A r b o r ,
F r e n c h ,
his w e l l - k n o w n
t o
1 9 5 1 ) .
U n i v e r s i t y
faculty
in
It
e x i s t e n c e ,
scientific
s u m m e r
available
( Y o u d e n , t h e
a n d
its
i n d u s t r i a l
c h a n n e l s
g r e a t
t w o
o f
Statistical
analysis o f v a r i a n c e
w a s
S n e d e c o r ,
t e a c h i n g
m e t h o d s
S t a t e s
b o o k , 1 9 5 1 ) .
i n t o
assays,
b r o a d e s t
t h e
W .
l e c t u r e
his
t h a t p e r i o d ,
U n i t e d
G e o r g e
y e a r s
t r a n s l a t e d
b i o l o g i c a l
first
( Y a t e s ,
e x p e r i m e n t a l
o f
first
t o
I n
trials,
O n e t o
t w e n t y - f i v e
a n d
J a p a n e s e .
F i s h e r ' s
t r e m e n d o u s
first
sold,
o f
F r o m
scientists,
o f
w h e r e
a h e
M a t h e m a t i c s ,
c o p i e d
this
o f
o f
P e a r s o n ' s
base,
i n c l u d i n g
N e y m a n a s t r o n -
m e t e o r o l o g i s t s .
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The
inference
Statistics
N e y m a n ' s
arrival
p h i l o s o p h y
o f
explicitness
in
c o n t r a s t
"find
t o
w o r k e r s , " m o o d " T h e t o
as
o f
in
t h e
o n l y u s e f u l
m e n t
in
m i t t e e
1 9 4 2
o f
t h e
c o u l d
also
quality
a n d
I n
it
fact
able
stitutions.
B o t h
t h e
sciences,
a u t o n o m y
t h e
w e r e 1 9 8 5 ) .
d o c t r i n e
o f
It
s e q u e n t i a l
statistical d e c i s i o n lished
after
f u n c t i o n s cision I n
t h e o r y t h e
m a j o r
o f
a n
in
t h e
a n d
t h e
Virginia.
H e
at
e x p e r t a r g u e d
t h e
e x p e r i m e n t
w a s
o b v i o u s l y
W a l l i s
a n d
at
t h e
t h e
that o n e
n e e d
twist
n o t
s u p e r i o r
o r
e c o n o m i s t
b e
in
( S a v a g e , t h e
( u n d e r
A .
N a v a l
c o u l d
o b v i o u s l y
et
b u t
areas
al.,
1 9 4 0 ) .
W a r
that
social
ina n d
d e p a r t m e n t a l
o f
A b r a h a m
t h e
in
t h e
t h e o r y
W a l d
a n d
statistical o r
a n d
N e y m a n ' s
p r u d e n t
in
as
selection,
a n d
lines
personalistic
u n d e r at
W a r ,
o f
p u b -
d e c i s i o n
B a y e s i a n
at
t h e
d e -
either
F r i e d m a n
a n d
s o
b e c a u s e
T h i s
o f
idea
several o f
( u n d e r
analysis a
N a v y in
m a n y t h e w a s
t r a n s f o r m e d
t h e
Statistical
P r i n c e t o n
G r o u n d
first
o n e
( t h e
S e q u e n t i a l
P r o v i n g
w e r e
o f
C o l u m b i a
a s u g g e s t i o n
inferior.
t h e r e
c o n t r a c t
W a l l i s ) ,
see after
c o m p l e t e d ,
M i l t o n
m o r e
N e y m a n ) .
t h r o u g h
U . S .
statis-
1 9 8 5 ; B a r n a r d
m a d e
W o r l d
n o t a b l y W .
s u c h
its
t h e
o f
less
e n g i n e e r i n g
a n d
t h e o r y
t h e
in
b y
t h e
n u m b e r s ,
disciplines -
C o m -
that
W o r l d
m a t h e m a t i c a l
S e c o n d
u n d e r
i n d e x
S e c o n d
b y
D e p a r t -
o f
stressed
-
t h e
1 9 5 4 ) .
w o r k i n g
C o l u m b i a at
o f f s p r i n g
a l o n g
w a s
W a r
P r e p a r e d n e s s
( F i e n b e r g ,
1 9 5 0 ) . T h e
forces,
B e r k e l e y
e f f o r t
t h e
( E i s e n h a r t
military
d e v e l o p e d
1 9 4 7 ,
S.R.G.,
t h e
w e l l
p e r s o n n e l
statistics
m o r e
b o t h
S a v a g e
o f
P r o g r a m
t h e
fit
t h u s
a n d
o t h e r
o f
w h i c h
a n d
a subjective
o r
m a n y
w a r
b e h a v i o r ,
a r m e d
s o
in
d e v e l o p m e n t s
statisticians
S . R . G .
o r d n a n c e
n e w
States d u r i n g
o f
D e f e n s e
research
p r e d i c t i o n s , a n d
h a d
a v e r a g e s
f e l l o w
(in
war.
W a r
f o r e c a s t i n g
a n d
t h e
analysis
L . J .
G r o u p ,
W i l k s ) ,
n a t e d
o f
g r o u p s
R e s e a r c h
t o
t h e
b e h a v i o r "
a p p r o a c h i n g
D e m i n g
A s s o c i a t i o n ,
r e c e p t i o n
b y
( W a l d ,
g i v e n
t h e
Statistics, a n
activities
i n d u s t r y
f u n c t i o n s ,
w a r
U n i t e d
b r a n c h e s
S.
t h e
w a s
their
E.
earlier
w e a t h e r
p o s i t i v e
i n d u c t i v e
b y
t o
H i s
particular
Fisher),
e x p e r i m e n t a t i o n ,
t o i n f l u e n c e
l e d
b y
t i m e d .
w i t h
" i n d u c t i v e
d i c t a t e d
W .
N a t i o n a l
surveys, a n d
b y
1 9 3 8 ,
u n d e r s t o o d
calculating
t h e
f u r t h e r e d
Plackett,
o f
in
t h r o u g h
statisticians w e r e
social
t o
s a m p l e
w a s
A n d
Statistical
just g o o d
b o m b i n g ,
w a s
w e l l
f o r w a r d
c o m m u n i c a t e
M a t h e m a t i c a l
A m e r i c a n
c o n t r o l ,
g u n n e r y
t h e o r y
o f
c o n t r i b u t e
t o
w r o t e
1 9 8 0 ) .
Institute
n o t
data
in
c h a n c e ,
o f a statistician is t o m a k e
action,"
(Wallis,
m a t h e m a t i c a l ticians w e r e
for
b y
b r o u g h t
r e q u i r e m e n t s
f u n c t i o n
basis
o f
119
w a r
w a s ,
c o i n e d
i n f e r e n c e t h e
t o
States
h e
r e d u c t i o n s
a n d
g o e s
inference,
e x p r e s s i o n
t i m e
a
U n i t e d
statistical
statistical
t h e
p r o v i d e
t h e
experts
S.
origiofficer,
D a h l g r e n , r o u n d s
n e w
m e t h o d
p i c k e d b y
that
u p
b y
A b r a h a m
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120
The
W a l d t h e
i n t o
a
t h e o r y
w o r k e d
o f
for
R e s e a r c h , t o
f u l l - b l o o d e d
flee
s h o r t
w h e r e
A u s t r i a
r e f u g e
in
t h e
F o u n d a t i o n . P e a r s o n (reject
o r
m o r e
after
in t h e
tests
o f
It
t u r n s
t h e
statistical
d e c i s i o n
p r o b l e m s
in
f o r m a l
a
M o r g e n s t e r n , w o u l d
incur
It is clear tical t h e
W a l d
w h e n that
research. w a r
e f f o r t
sources,
s u c h
research d u r i n g
large
o f t h e
g o t
as t h e
s t r e n g t h e n e d
d e c i s i o n
a n d
their O u r
m e c h a n i z e d
1 9 4 0 ,
p s y c h o l o g i s t s
zsscss
their
M u r r a y , ( 1 9 4 9 , S e c o n d
t h e
g u i d e
this
u s e d
is
1 9 8 7 ) . 1 9 5 0 )
T h r o u g h
o n
W o r l d
t h e W a r ,
t h e
social
o n
n e e d s
o f e d u c a t i o n a l
t h e m
in
( D a n z i g e r ,
o f
p s y c h o l o g y
t h e
t o
s u c h o f
a d m i n i s t r a t o r s
bureaucratic
s a m e
a n d
t h e
O s k a r o n e
first
k i n d .
o f
statis-
that
financing
fit
i n t o
f u n d i n g t h e
t h e y
h a d
is
its
that
military
d e c i s i o n s
basic f u n d e d
that
c a n
w i t h
in
b e
it
also
o f
as
that
w a s
c u r r i c u l u m
et
d u r i n g
a c c e p t / r e j e c t
t o a n d
S t o u f f e r
"objective"
o n
m e t h o d s
soldiers
a t r e n d
o n
B e f o r e
( G i g e r e n z e r
studies
t h e
m a d e
p s y c h o l o g y .
results
a n d
m e a s u r e m e n t s .
u n s t a n d a r d i z e d
for a n
decisions
a n d
statistical p r o b l e m s ,
w a r
p s y c h o l o g i s t s ,
g a m e s
projects
A m e r i c a n
t e c h n i q u e s
o f
o f
d e c i s i o n
t h e specifics
c o m b i n e d
a n d
t h e o r y
losses
h o w e v e r ,
o b s e r v a t i o n a l o f
t h e
in
p o w e r f u l
as
N e u m a n n
statistics
i n f o r m a l
i m p a c t
statistical
their h o l d
their
a n d
role
m o r e
o f
m a k e
fixed
W a l d ' s
e r r o r
t o
n o t
p r o b l e m s
w h o m
here,
r e a s o n i n g
t h e
largely
e x p e r i m e n t a l
s t r e n g t h e n e d b y
o f
that
t o
k e p t
s t u d e n t s
r e a s o n a b l e
f o r m a l ,
e x a m p l e
R e s e a r c h ,
idea
t h e
is
t h e o r y
t h e
a p p r o a c h
t h e
p r i m e
w a r
C a r n e g i e
d e c i d i n g
size
research
c l a i m
o f
lead
as a n
t h e o r e t i c
t o
A
t h e
t h e
f o u n d
d e c i s i o n s
i n f l u e n c e d
a p p l i e d
N a v y
p e o p l e
o f
o f
o f
a c c u s t o m e d basis
W a r
a n d
able
t w o
a c c o u n t
d e c i s i o n
A f t e r
1 9 6 1 ) .
v o n
o f
b e e n
b e t w e e n
statistical
i n t o
1938,
sense.
J o h n
take
W o r l d
O f f i c e
( O l d ,
t h e
t o
n u m b e r
scientists
w a r
b y
h a d
C y c l e
N e y m a n -
c a n
t h e
h a d
o f
s a m p l e
U s i n g
w h o
s e q u e n c e s
o p t i o n
t e s t i n g
nature."
f u n d e d .
t h e
t h e
i n t e r p r e t s
a w r o n g
S e c o n d
t h e
N e y m a n - P e a r s o n
able
m a k i n g
has
H e
in
t h e o r y ,
B u s i n e s s
s u p p o r t
c h o o s i n g
that
d e v e l o p e d
w a s
t h e
A
t h e
against
t h e o r y
also
director.
o f
J e w
for
G e r m a n y
t h e o r y
s e q u e n t i a l
f u n c t i o n s
" g a m e
utility
in
t h e n
t h e o f
R o m a n i a n
Institute
financial
instead
m e a n s
that
size,
w a s
a
t h e
is
statistician
o u t
s a m e
w i t h
N e y m a n - P e a r s o n
w a s
w i t h
analysis
T h i s
t h e
A u s t r i a n
Anschluss
w h i c h ,
o b s e r v a t i o n s .
a d v a n c e .
t h e
States
o f
W a l d
M o r g e n s t e r n
S e q u e n t i a l
accept),
at
t h e
U n i t e d
d e c i s i o n s
analysis.
t i m e
O s k a r
experts
m o d i f i c a t i o n
s e q u e n t i a l
a
inference
al. t h e
variety
r e i n f o r c e d
t e c h n i q u e
t o
i n n o v a t i o n
1 9 8 7 a ) .
3 . 8
T h e
agricultural
l e m
c o n c e r n i n g
C O N C L U S I O N
c h e m i s t J o h n s t o n e x p e r i m e n t a l
f o u n d
d e s i g n
h i m s e l f c o n f r o n t e d a n d
t h e
i n f e r e n c e
w i t h f r o m
a
p r o b o b s e r -
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The
v a t i o n a l
data
trying
t o
g a t i o n
-
in o f
t h e
p l i n e o f
I n
t o
d o u b t f u l
m e n t s , n e w
Statistical
t h a n
Society,
t h e
w h e n
p e r i o d t h e
t h e
p e r h a p s , n u m b e r deliver b e
a c a d e m i c equally
m o r e
p r o b l e m s
this,
c o m e
t h e s e s u c h
t h e t o
b e
tools. W e as
t h e
m e a n i n g
o f
c h o l o g y ,
w h i c h
w a s
in
that o p e r a t e
c h a p t e r T h e
a
o f
discih i s t o r y
c o n c e p t u a l
far
f r o m
b e i n g
c o m p e t e ,
a n d
scientists
(see
a c h i e v e -
h a v e
s h a p e d
a w a i t i n g
t h e r e
t o
in
this
t h e is
ideal
o f
b y
t h e
t h e m , n e w
m o s t
d e d i c a t e d
really,
o f t e n
a n d
that
e x i s t i n g
that
a c c o m -
instances
science
W e
t h e
equally
t o s e a r c h i n g
in a p o p u l a t i o n .
t o
h a v e
a n d
e x e m p l i f i e d a
o r
historian
e x p e r i m e n t
f r o m
a n d
s u d d e n l y
c o u l d ,
s t r i k i n g
d e a r l y
statistics
are
l o n g e r
e n d
c o n c e p t s
s o m e
a scientific
t o a discipline a v e r a g e
o f
n o
t h e
A .
accurate,
w h i c h
a n d
R.
m i n d s ,
a n d
w a s
applications
c h a p t e r
p e r h a p s
m e n ' s
t h e r e
R o y a l
m u c h
that, q u i t e
m e t h o d s
a d d r e s s
t h e
chapter,
for
s h a r p
p h i l o s o p h e r that
this
p r e p a r i n g s o
t o
o f
i n in
t h e p s y -
a s k i n g for
will r e t u r n
for
causal t o
this
i n f e r e n c e
are
6.
c h a n g e s
u b i q u i t o u s
entire
interests,
at w o r k
realistic,
s e e n
t h e
b e e n
sufficiently
h a v e
o n
this
institutional
t o
t h e y w o r k ,
t e r m s
l a w s
o f
a d d r e s s
sufficiently
are
T h i s
discipline
u n i f i e d is
in
i n v e s t i g a t i n g
social
a n d
b e c o m e
t r a n s f o r m e d
g e n e r a l p s y c h o l o g i c a l factors
w h i c h
in
causality.
o f
political
causes h a v e
r e c o g n i z e
in
dif-
t o
statistics
e p i g r a p h
r e d e f i n e d
c h a n g e
in a q u i t e p r o b l e m s
t h e
a n d
presidential
1 9 5 3 ) . T h e
t o o l s
late
e n -
p i e c e s
single
plants.
natural
abstract
a n d
practice
a n d
t h e
i m p a t i e n t l y
a n d
a
efflorescence,
h a d
(Fisher,
n e w
c o n c e p t u a l
1 9 5 3
t h r o u g h
fastidious,
b e c a u s e
his
i m p o r t a n t ,
o f
a c c o m p a n i e d
c a m e
t h e
p r o v i d e d
t o o l s
t h e g o o d s "
in
s t u d i e d
investi-
o f
their
typical
Bits
u n d e r
b y
e x p e r t s .
m a n i f e s t
institutions
t h e
i n t o
n e e d s
" h i d d e n
o f applications
c r e a t e d
p a n y
o f
is
inferential
i m p r e s s i v e
w h i c h
o f
o f
b e
in
a c c u s t o m e d
b y
h a v e
d o c t r i n e
i n f e r e n c e
that
n o w
statistics.
d o m i n a t e
t o n e
e x a m p l e
p u r s u e d
c h e m i s t r y
o b j e c t s t o
n o t
m a t t e r
a n d
c o m e
are
t h e y
e c o n o m i c
o f
s p e c u l a t e d
s h a p i n g
t o
w i t h
u p b e a t
h a v e
w e r e
subject
natural
c o m b i n a t i o n
6 ) . N e v e r t h e l e s s ,
p r o b l e m s
t h e
d e f i n e d
s c h o o l s
c o m p r o m i s e s
t h e
F i s h e r
this
A l t e r n a t i v e
p r o f e s s i o n
I n
there;
m e t h o d o l o g i c a l
t o g e t h e r
b y
scientists
research
121
p h y s i o l o g y
agricultural
a n d
Y e t
a n d
c o m p l e t e d .
o f
t h e
m a t h e m a t i c a l
h e r e
probability.
g o v e r n
this o n e
that
a c a n o n
e m e r g e d
c h a p t e r
like
experts
T h e s e
displayed
this
i n f e r e n c e ,
s t r u c t u r e
a
fact,
that
case,
variation
disciplines
a c c o r d i n g scientific
l a w s
q u e s t i o n s
w a y . o f
t h e
h y p o t h e s e s .
J o h n s t o n ' s
v i r o n m e n t ,
variety
causal
analyze
B e c a u s e
f e r e n t
t o
inference
a n d
b r o u g h t
b y
p r o f o u n d .
publicly d e m o n s t r a t e d , m e n t
that
t h e
e v e n t s
w e r e
n o t
r e q u i r e d
a n d
t h e
I n
early
it w a s
r e p o r t e d t o
b e
n e w
able
m e t h o d s
m o d e r n
c u s t o m a r y
h a d t o
o f
statistical
science,
k n o w l e d g e
t o h a v e w i t n e s s e s sign a
actually h a p p e n e d . replicate
h a d
t h e
B u t
t h e s e
t o
b e
d o c u -
w i t n e s s e s
d e m o n s t r a t i o n s ,
w h o s e
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122
The
p r o p e r
e x e c u t i o n
bureaucratic t o
reach
I n
a n d
Scientists,
data
g r o u p .
B u t
b e
social
m e n t a l
setups.
cial
their
this
b o o k ,
a n d
o u r
w i t h
t h e s e
o f probability.
g r e s s
o f
ideas
m e n t
o f
m e t h o d s
fields
h a v e
a b o u t
has b e e n g i v e n is
treated
in
in
d e e p
A n d
m e t h o d s
m o s t
as
o f
b e
w e
j u d g m e n t
facts
in
w i t h
e y e -
o f
their
c h a p t e r
t h e m
b y
a
a
figures.
m e c h a n i z e d
s a n c t i o n e d
o f
a n d
m e m b e r s
a r g u e
a n d
k n o w l e d g e
satisfied
t h e
m o d e r n
ideologically
m a n i p u l a t i n g
t r a n s f o r m a t i o n w i t h
yet,
it
that
studies.
especially
o f o f
w a s
all o u r
7,
e x p e r i are
n e w
role.
v i e w
o f
closely
D u r i n g
i m p o r t a n t
a t t e n t i o n
w a s
t h o s e
b r o u g h t
as is characteristic
particular
n e x t
b y
decisively
i n f e r e n c e
a n
t h e in
c o u l d
t o o l s
are
statistical
c o n s i d e r a b l e
t h e
inferential
p i i v a t e
b e c o m e
c l o t h e d
In
cru-
k i n d
o f
d e s c r i b e d
in
specialist.
d e a l i n g
a d v a n c e
has
s h a r e d
m e t h o d s
d e v e l o p m e n t s ,
o f
b e
science.
o n
places,
d e m o c r a c i e s ,
t h e
T h o s e
t h e
life
a n d
t o
intuition,
a n d
statistical
m e t h o d s
p l a y e d
o n
reliance
social
t i m e s
priests o f
accountability,
" o b j e c t i v e "
e p i t o m i z e
for
h i g h
s u c h
n e e d
m o d e r n
N u m b e r s
t h e
n o
p u b l i c
in
authority.
professional,
h a d
relying
e x p e r t s
a r m e d
P e r h a p s
elite
experts
t h e
societies,
d e m o c r a t i c
little
a n d
o n
i m p o r t a n t
less
h a v i n g
balling
t o
utilitarian
c o n c l u s i o n s
political
m u s t
still d e p e n d e d
a n d
u n a c c e p t a b l e .
inference
t h e
this
tied
last
O n e
in this chapter.
o f
o f
t h e
a b o u t story, t o
t h e
century, these,
T h e
w o r l d b y
t h e
t h e p r o -
d e v e l o p t w o
s u c h
agriculture,
o t h e r ,
g e n e t i c s ,
chapter.
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W h a t
does
chance
William
ever
Paley
d o
for
us?
(1802)
4 >
En
is
p r o b a b i l i t y radiation,
transition
—
pair
u n i t
a p p r o p r i a t e
p r o c e s s e s
e n e r g y
f r o m
t h e t h e
Ztt
t o
radiation validity
Planck's radiation
quanta,
w a s
t h e
V =
m a t t e r
o f
e m i s s i o n
P r o b a b i l i t y
w a v e s
d i r e c t e d t h e
a
(Em—
E )
o f
that
fully
c o n v i n c e d
o f
p.
o f l a w
/ h i m
n e w
. . t h e
o t h e r
o f
b u t
t o
o n l y
also
that
E
w o r d s ,
t h e
h a d
the
pic-
a d v o -
since
o f it
t h e r m o d y n a m i c s
theoretical a s s u m e d
t h e
reality
e x i s t e n c e ,
o f
is
probabilities already
a c c e p t
their
n o t
( w h e r e
transition
u n i t y
e m b r a c e d
statistical l a w
c o r r e s p o n d s
t o
that o f
a
[that radio-
1 2 3 ) . o f
g o v e r n e d
e v e r y
e x t e r n a l
classical
t h e
l a w )
E i n s t e i n
a r g u m e n t .
i m p l i e s
E/c
c o m b i n a t i o n
fully a w a r e
o f
I n
h e s i t a t e d
t h e
".
(Planck's
i n h e r e n t
light
further
radiation
light).
h a d
p r o c e s s ,
recoil
o f
their
n o t e d :
w i t h o u t o f
s p e e d
p r o b a b i l i t i e s Am>]
w a s
a n d
m o m e n t u m
radiation. T h i s
( [ 1 9 1 6 ] 1 9 1 7 ,
f o l l o w i n g
t h e n
w a s
E i n s t e i n
E i n s t e i n
o f
w i t h
c o n s e q u e n c e
e m i s s i o n
spherical b y
c o u l d
t h e
w
E„
s u r r o u n d i n g
the
e n e r g y £
is q u a n t i z e d
c the
phycisists
as well.
p r o c e s s "
theory.
p l a c e d
for
E i n s t e i n
a n d
E i n s t e i n
inevitable
M o r e o v e r ,
the
for
o f p o s s i b l e
b e t w e e n
particle
M o s t
s p o n t a n e o u s
his
t h e
E i n s t e i n
radiation
q u a n t u m
all k n o w n
active
t h e
discrete
radioactivity o f
o f
o f
o n l y
A n y
p e r
t h e
etc.
a m o u n t
f r o m —
T h e
c a n
this:
transition
the
o r
Z„,
an
probabilities
(2)
,
w
states
w a s
o u t s i d e ;
b y
B„md
idea
Z
o f
Em
q u a n t a
has a spatially w e l l - d e f i n e d
t h e
quanta, t h e
for
t h o s e
q u a n t u m
f r o m
p r o b a b i l i t y
for
e q u i l i b r i u m
e n e r g y
o f
e n e r g y
i n d u c e d
d e n s i t y
c o n d i t i o n
i m p o r t a n t
t h e r m a l
ture
n o w
a b s o r p t i o n
t h r e e
m o l e c u l e
states
a b s o r p t i o n
s p o n t a n e o u s the
a
c o u l d
a s s u m p t i o n s .
discrete
f u r t h e r
t h e m
t h e r m o d y n a m i c s .
specific
o f
o r
in
o f
b e t w e e n
b y
i n t e r f e r e n c e
t h e
m o r e
decisive
o f
i n h e r e n t validity
n u m b e r
a
b e t w e e n
m a n n e r .
T h e
o f
f e w
e m i s s i o n
for
b u t
radiation
f r e q u e n c y
t h e
transition
T h e
t h e r m o d y n a m i c s
m o r e
e n e r g y
a
A
the
a n y
(3)
a
o n
this s c h e m a t i c p i c t u r e
s i m p l e
Still
m a k e
Amtl
physics
transitions
o n
characterized
p r o c e s s
finally
t h e
case
e m i s s i o n
a s i m u l t a n e o u s
B o h r ' s
light
b e
w i t h o u t
a n d
B o l t z m a n n ' s
v e r y
c a n
p r o b a b i l i t y
t h e
F r o m
a n d
Z„
a similar
d
—
Emi
t o
in
probabilities
his
h i m
a g a s
a n d
o f
r e s t e d
s i m u l t a n e o u s
for
Em
t e r m s
e n a b l e d
p r e s u p p o s e d ) BmHd
h e
revolution
m a t t e r
c o n n e c t i o n o f
(1)
o f
in
e n e r g i e s
in
Em
stztcs
c a p t u r e d
O n c e
probabilistic
t h e p h i l o s o p h i c a l e m i s s i o n
e x c i t a t i o n h e
e l e c t r o m a g n e t i c
t h e
d i r e c t i o n
e m i t t i n g
o f
a n d
t h e
light
w a s
o f
a b s o r p t i o n .
c o n c l u d e d
e m i s s i o n
m o l e c u l e
significance
that,
h a d
since
b e e n
q u a n t u m
" o n l y
reor,
d e t e r m i n e d
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The
b y
' c h a n c e ' , "
1 2 7 ) .
at
least
A l t h o u g h
fully
a b o u t
its
t h e o r y
t i m e
t h e
a n d
a m
t h e
c o n n e c t i o n
c o n f i d e n t
( [ 1 9 1 6 ] 1 9 1 7 , " d u r a t i o n "
p p .
s u c h
a
b e c a u s e
o f
p r e d i c t i n g
in
t h e
w a s
a c c e p t a b l e .
in
a n o t h e r .
t h e
I n
p .
least,
I
w a s
g e t
o t h e r ,
t h a t
is
h a v e
r e p l a c e d
emission,
d i l e m m a
is
e v i d e n t .
d e e p - r o o t e d
a
closer
reliable
t o t h e
n o t
t o
t h e
w o r d t o
t h e
t h e
d u r a t i o n
C o h e r e n t
p h y s i c a l
p h i l o s o p h i c a l
t h e
i s o l a t e d
p r o b a b i l i s m
h a d
b e c o m e let
I
o n e . "
r e f e r r i n g
w i t h
t e r m
t h e
it l e a v e s
h e r e
a n
t h e
o f
'chance'. N e v e r t h e l e s s
o f
p u t
u s a n y
(p.
u n e a s y
w e a k n e s s
o b v i o u s l y
c o n s o l i d a t e d ,
t h e o r y "
p r o f o u n d l y
n o t
t o
7 6 ;
t h e
" T h e
t h e
c h o s e n
E i n s t e i n
b e i n g
at
o n
p r o c e s s e s
c o m p a r i s o n
f r o m
E i n s t e i n ,
it d o e s
t h e o r y ;
o f
w a s
t h a t
d i r e c t i o n ,
f o r
h e
w r o t e :
m o m e n t
o n e
e v i d e n c e
far
fact
1 9 7
s t a t e
h e
trans,
E i n s t e i n ' s
h i m
t h e o r y
a p p r o a c h
" t i m e , "
radioactivity, it
t h e
p r e s e n t
this
w a v e
w i t h
d r a g s
t h e
e l e m e n t a r y
t h a t
i n p h y s i c s
T h u s
t h e
E n g l i s h
t h i n k i n g
Y e t
w i t h
t h e
p r o c e s s . )
t h e o r i z i n g
in
1 2 7 - 8 ;
impossibility
o f
o f
b y
s t r u c t u r e . h a n d
revolution
t o
c o n v i n c e d
o n e
d i r e c t i o n
fully
o f
" a c c o r d i n g
p r o b a b i l i s t i c
lies o n
m a k i n g
probabilistic
p h e n o m e n o n m u c h
a l o n e
" c h a n c e "
h a b i t s o f
s t r o n g e r .
intellectually
b e t w e e n
i n v e r t e d
c o m m a s . P h i l o s o p h i c a l l y w i t h
t h e
p a r a d o x e s
q u a n t u m h e
t h e o r y
e x p r e s s e d
w a v e
a
H e n c e
t h e
firmation
o f
as
q u a n t a
t h e
o f
a
c o n c e p t i o n s
III.l).
H i s
d e n c y
t o
T h i s
p r o c e s s e s o f
h o l d
a n d o f
r a d i a t i o n .
r e q u i r e d
b a c k
t h e
o f
in
e m i s s i o n O n
t h e
particle
its
a n d
a
n e e d
c o m p l e t e
a p p l i e d ( 1 9 2 4 )
in
t h e
t o
a b s o r p t i o n
o n e
h a n d ,
idea o f a m a c r o s c o p i c
free
t h e
in
f r o m
g r o u n d s
I n d e e d ,
statistics
w i t h
".
o f
o f
o f
c o n -
g e n e r a l
l a w s
i n d i v i d u a l
. . i n
c o n t r a s t
in
n u m b e r
w h i c h
o f
t h e
b y
t h e
e x i s t e n c e
c o r r e l a t i o n
c o n t i n u o u s o f
b e t w e e n
w i t h
b y
t h e
u s e
a
t e n -
B o h r ,
e l e m e n t a r y
w a v e
distant
t i m e
p r o c e s s e s .
o f
i n t e r f e r e n c e
is
( 1 9 2 3 / 2 4 ,
a t t e m p t
e x i s t e n c e
it
a n d
i n d i v i d u a l
r e m a r k a b l e
t o
i n d i v i d u a l
s p a c e
c o m b i n e d
o f
a n d
as a
in
p h y s i c s
a r g u e d ,
radiation.
t a k e n
e v e n
t h e
e n e r g y
c o n t r a d i c t i o n
w a s
d e s c r i p t i o n h i g h l y
b e
t h e
t h a t
B o h r
t h e
n o t
t e r m s
o n
( 1 9 1 8 - 2 4 ) ,
e l e c t r o d y n a m i c s "
r e c o n c i l e
a n d
t h e
s t r u g g l e d
p a p e r s
a t o m
r e t e n t i o n
classical
classical for
t h e
c o n c l u s i o n :
p r o c e s s e s
a m a n n e r
his
m o m e n t u m ,
in
also
c o n c e p t i o n
c o u l d
strict
a d i f f e r e n t
f r o m
t h e
f r o m
Slater
o n
as well.
h y p o t h e s i s
a t o m i c
I n
c h a r a c t e r i z i n g
t h e
w i t h
B o h r ,
o f
o f statistical results o f a g r e a t
o n
w a s
results.
s t r u c t u r e
V
p h e n o m e n a
t h r o u g h
e m p h a s i s
N i e l s
q u a n t u m
b y
e n e r g y
b o r r o w e d
s t r a t e g y
K r a m e r s ,
p i c t u r e
d e s c r i p t i o n
c a r r i e d
t h e
q u a n t u m
n a t u r a l
o n l y
t h e
f r e q u e n c y
o f
like
i n d i s p e n s a b l e
it s u g g e s t e d
o f
a l w a y s a q u e s t i o n
b e
t h e
a n d
e x c l u d e d
particle
h i m
d e s c r i p t i o n
c a n n o t
o f
w a s
m i n d s ,
E i n s t e i n ' s
w i t h
t h e
c o n s e r v a t i o n
T o
p r o c e s s e s ,
s p e c t r a
r e m a i n e d o f
success
t h e
b y
u n e a s i n e s s
o f l i g h t
o f
p r o c e s s e s . t h e
line
d e f i n i t i o n
m o m e n t u m
s u c h
e n t a i l e d
o f
his
t h e o r y
e v e n
less c o n s e r v a t i v e
s t r u c t u r e
p h e n o m e n a e m i s s i o n
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a n d
198
The
a b s o r p t i o n g e s t e d o r
processes.
t h a t
l i g h t
b e a m s
7 8 5 ,
788,
p r o c e s s ,
a n d
f o r
S l a t e r
d e c l a r e d
is
t h e
e n t r o p y
l a w "
W h e n
h a d
X - r a y s
m a t t e r
o f
t h e
t u m
o f
a n d
t h e s e
p .
in
1 5 6 ) .
I n
specific
f r o m
this
h e
t h e
t h e
w a v e
m e c h a n i c s
strict
a n a l o g y
t o
w a s
t h e
o n l y
r o o m
f o r
in
r e j e c t i o n
o f
a l t e r n a t i v e
m i c r o p r o c e s s e s ,
t h e
in
a n d
individual
p r i n c i p l e s
o f
e n e r g y ,
and*
Slater
t h a t
a
t h a t
a n g l e
t h e
t h e
h o l d
l a w
t h a t
it
o f
o f
t h e
e n c o u n t e r t h e
o f
is
" a
t h e
in
S i m o n ,
o f
o f
t h e
a g r e e s
o f fre-
fully
c o n s e r -
o f a l i g h t
w h i c h
t h e
directly I n
c o r r e c t
s p a t i o - t e m p o r a l
r e p r e s e n t a t i o n
s c a t t e r i n g
strict
1 9 2 5 ) .
still u n k n o w n
" o r d i n a r y
w r i t t e n ,
q u a n -
B o h r - K r a m e r s - S l a t e r
e x p e r i m e n t s
a n d
t h e
d e f l e c t i o n
i n c l u d i n g
single
w a s
v a r i a t i o n
recoil e l e c t r o n w a s
a n d
t h e
w a v e
a classical p h y s i c s
its o b j e c t s
a n
K r a m e r s ,
m e a s u r e d
r e a c t i o n
t h e o r y
p i c t u r e s "
o p t i c a l
coinci-
o f
t o
w o u l d particle
p h e n o m e n a
( 1 9 2 5 ,
right.
p a r t i c l e
o f
b y
C o m p t o n
f r o m
B o t h
m i n a t i o n
t h e
e a c h
p r o v i d e d
s u r m i s e d
w a s
p r o v e d
r e f u t a t i o n
1 9 2 5 ;
as
s e e m e d
a t o m s ,
a b o u t
c o n c e r n i n g
r a d i a t i o n ,
in
G e i g e r ,
far
h e
o f
e n e r g y
o n l y
results
w i t h
X - r a y s w i t h
equally
m e c h a n i c s
w a s
B o h r
l a w
-
d i s t a n t
said
t h e o r y "
B o h r ,
m o m e n t u m
K r a m e r s ,
his
s c a t t e r e d
results,
t h e
strictly
s p a t i o - t e m p o r a l
H e n c e
b e e n
s u g -
i n t e n s i t i e s
" f o r m a l
c o n s e r v a t i o n
h a d
f o r
B o h r ,
p i c t u r e
A
a n d
deviate
p a r t i c l e
e l e c t r o n .
t h e
b y
X - r a y s
a n
o f
W h a t
( 1 9 2 3 ) , in w h i c h
a n d
d e n c e
basic
c l a i m e d
p u b l i s h e d
m o m e n t u m
h o w e v e r ,
( B o t h e
p a p e r
s c a t t e r e d
v i e w ,
t h a t
a
t h e
b e t w e e n a n d
l o w
p r o b a b i l i t y
a b s o r p t i o n s .
e n e r g y
a v e r a g e .
o n l y
o f
l i g h t
e x p e r i m e n t s
d e s c r i b e
o f
for
o f
7 9 3 ) .
a l r e a d y
E i n s t e i n ' s
v a t i o n
a r g u e d
n o w
n o t
c o n n e c t i o n
c o n s e r v a t i o n
w a s
b o l d
C o m p t o n
a n d
all
h a n d ,
c o n s i d e r a t i o n s
causal
T h e y
(p.
this
b y
t h e
t h e
a g o
t o
o t h e r
d o e s
p i c t u r e
d i s a p p e a r
d i r e c t i o n s ,
t h e
t h a t
e m i s s i o n s
m a c r o s c o p i c
l o n g
statistical
w i t h
t h e o r y
i n d i v i d u a l
p r o c e s s e s .
o n
a
r e s t r i c t e d
u n t e n a b l e
q u e n c y
-
O n
physics
q u a n t u m
s h o u l d
d i f f e r e n t
t h e o r y .
a b a n d o n e d
r a d i a t i o n o n l y
7 9 0 )
b u t
p o s s i b l e
w a v e
i n
in
Einstein's
p h e n o m e n a
t r a v e l l i n g
t h e
revolution
A l t h o u g h
i n t e r f e r e n c e
r e c o n f i r m e d ( p p .
probabilistic
t e r m s b o t h
o f
c h a r a c t e r i z e d
m a n i f e s t
p i c t u r e s ,
d e s c r i p t i o n
d e s c r i p t i o n
r e p r e s e n t a t i o n
t h a t
a n d
b y
t h a t
i n d i v i d u a l
essentially
c o n c e i v e d
c o m p l e t e
visualizable
t h e r e f o r e ,
o f
t h e
w e r e
d e t e r -
p r o p e r t i e s .
finally
p r o v i d e d
m i c r o - o b j e c t s
i n v o l v e s
It
a n d
p r o b a b i l i s t i c
p r o p e r t i e s .
Q u a n t u m
D u r i n g
t h e
first
t w e n t y - f i v e
a n d
t h e o r e t i c a l
e v i d e n c e
t h e
i m p o s s i b i l i t y
o f
a n
years
o f
a c c u m u l a t e d o r d i n a r y
m e c h a n i c s
this
c e n t u r y
t h a t
t o
a
s o m e
m a s s
o f
e x p e r i m e n t a l
physicists
s p a t i o - t e m p o r a l - c a u s a l
s u g g e s t e d
p i c t u r e
o f
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t h e
The
m i c r o w o r l d , until
t h e
b e
a
radical
p a n y i n g
it in t e r m s
s u m m e r
H e i s e n b e r g
probabilistic
o f
m a d e
belief in
last
h e
w r o t e
w a s
a
o f his
first
a n i n t e r p r e t a t i o n
d e s c r i b i n g
t h e
line
o f
classical
a n d
all
m y
that
c a n n o t
p o o r
(see
v a n
b e
d e r
p e r h a p s
o f
spectra
g e o m e t r y efforts
p o i n t
n o t
w a s
c o n c e p t s
a l t o g e t h e r
1928, p p . s i m p l e t i m e A s s u c h
1 8 7 - 8 ) .
a
a c o n s e q u e n c e
o f
i m p o s s i b l e
t o
b u t
o f
b y
b e
e x h i b i t i n g
a
w i t h
o f
d i s t r i b u t i o n
T h e s e I n s t e a d erty
o f
value
probabilities t h e y b e i n g
c o n t e n t t o
r e s e m b l e
o f
a
o r d i n a r y
a reliable p e r s o n ,
o f b y
s u c h
o f
t h e
t u r n e d
b u t
are
n e w
J o r d a n ,
a
o f
certain o n e .
their
m u t u a l
p r o v e d ,
it
p o s i t i o n
is
a n d
scientific
articu-
t w o
so-called
c o n j u -
n u m e r i c a l
value,
T h i s
T h e y
is
t h e
w e r e
c o n t e n t
e x t r e m e l y
classical
physics
A
direct
m o r e is
c o u l d w a y
i n d i c a t e d
o f b y
o b s e r v a b l e
m a g n i t u d e s
u p
the
a n d
t o
characterize
different
m a g n i t u d e t h e y
o u r
t h e
t h e o r y
b u t
t o
m a g n i t u d e s ,
o f
say,
a precise
o u t
b e t w e e n
to,
w a v e
infinite
( 1 9 2 7 )
t h e
h o w
m a k i n g
a n
at
physical
values.
n o n e
dispositional that
e v e n
for
m e c h a n i c s .
classical
o b s e r v a b l e ,
o b j e c t
-
k i n e m a t i c
2 8 - 9 ;
a n
a
r e p l a c e m e n t
character
relations."
n u m b e r s
o f a transition
are
o f
include
m a g n i t u d e ,
either
o n e
r e n d e r e d
q u a n t u m
i n t e n t i o n
probabilities, t h e
b e
least
p p . t h e
o f
essential
u n d e r s t a n d i n g
i n d i v i d u a l
classical
A t
f a v o r
b y
H e i s e n b e r g
b e e n
t o
o b j e c t s
s i m u l t a n e o u s l y
" u n c e r t a i n t y
probabilistic
T h e
h a d
A s
t h e
p r i n c i p l e s
physical
p o s s i b l y
velocity,
indicates,
n e w
o f
o r b i t s
r e p l a c e m e n t "
establish
e x p r e s s e d
elliptic
o f
p a p e r
o r
1 9 6 7 ,
p o s i t i o n
d i s t r i b u t i o n
at
t o
f o r m u l a
significance,
d y n a m i c a l -
really
a n d
c o n c e p t
this
k i n d
m e c h a n i c s
[i.e. t h e
suitable
n e w
r e p r e s e n t a t i o n
o r
5.1).
a t t e m p t
original
a
t h e
w a s
a c c o m -
"I a m
circular
o f
relating
n u m b e r s ,
v a l u e s
l o n g e r
f a m o u s
t h e
t h e
theory.
r e p l a c i n g
n o
c o m p a t i b l e
H e i s e n b e r g ' s his
(see
title
b u t
1 9 2 5 :
physical
a
W a e r d e n ,
say,
m a t r i x
precise
a p r o b a b i l i t y
for
o f
d e r
o f
possibility
c o u l d
H e i s e n b e r g ' s
p o s s i b l y
t h e
t h e
is f o r m a l l y
array
finding
d e t e r m i n i s t i c
w a y
v a n
least
W e r n e r
a letter
m a t r i x
9,
t h e
killing
i n t r o d u c e
f u n d a m e n t a l l y .
d e t e r m i n i s m
i m p o r t a n t
in
w h i c h
p r o p e r t i e s o n l y
o f
ascribe
-
n e w
A s
I n
o n
m i s s i n g
his m o t i v e s
f o r m u l a
o f
t h e
at
picture,
m o m e n t u m
c h a n g e d
m o m e n t u m lation
a n d
t o
represent, o r
relationships
g a t e
that
a n d
t h a n
T h i s is w h a t
"matrix,"
as p o s i t i o n
o n l y
(cf.
h a v e
2 7 ) .
particle
f r a m e w o r k
n u m b e r s
b y
t h e
t e r m s
c o m p l e t e l y
p.
rather
o v e r
an
at
R y d b e r g
in
o f
a b o v e .
Pauli o n J u l y
t h e
n o t
a n y h o w ,
r e p r e s e n t a t i o n
s p a c e - t i m e
d o e s
1 9 6 7 ,
t o
still
a c c o u n t .
it. O n e
revolutionary p a p e r
a t o m s ]
a i m
o b s e r v e d
a statistical
-
o f
W a e r d e n ,
H e i s e n b e r g ' s
r e f e r r e d
o f
w a s
alternative
t o w a r d
t o his friend W o l f g a n g
that
199
o f particles. W h a t
s t e p
c o n j e c t u r e
c o n v i n c e d
o r b i t s
o r
in physics
c o h e r e n t
decisive
B o h r ' s
the m a n u s c r i p t
( 1 9 2 5 ) ,
o f w a v e s
1 9 2 5
t h e
revolution
are
m a t r i x ,
states o f in
n o t
o n e
p r o p e r t i e s ,
ascertained
b y
s u c h
set
a s y s t e m
o f
m a n i f e s t
a
h e n c e
t h e
o f o r
states.
p r o p e r t i e s . as t h e
o b s e r v i n g
an
p r o p entire
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200
The
s p e c t r u m m a t r i c e s o f
o f d o
e v e n t s ,
o u t
classical
( 1 9 2 6 a )
n a m e d
h i m .
w i t h
f r o m
S c h r o d i n g e r p r o p e r t i e s o l d e r
t h e n
o f
q u a n t u m
m u c h
h o p e
o f
t r o n s
abstract
(e.g.
i n d e e d
d e f l e c t e d
b y
n u m b e r , s e n t e d
t h e had
s u c h
o n
as
t h e
cases
the
r e g i o n s
his
b e e n t h e
as
e n c o u n t e r e d
that
b e
o f
w a v e s
that,
w i t h o u t
a
o f
n e w
c o n t i n u i t y
ideas
a n d
n o
less
t o
b e
w a s
s o o n w i d e l y
o u t
Sig-
t h r o u g h
e n c l o s e d
in
a
u n d i s t u r b e d
a
finite
r e g i o n .
m i c r o - s t r u c t u r e .
m o r e
t o
d e r i v e o f
t h e
w a s
than
b e c a u s e
f r o m
t h e y
optics.
T h e
r e i n f o r c e d
s h o w e d
light
t h e
attractive
h o w e v e r ,
familiar
t h a n
L o u i s E r w i n
a s s u m p t i o n
w h i c h
t h e
p r o b l e m s .
u s e d
physics
o f
m o s t
t h o u g h
a p p e a r e d
1 9 2 7 )
o f
w i t h -
o f
that
n o t
a d - h o c
classical
G e r m e r ,
w a v e s ,
i n d e e d
p i c t u r e s
typical
m a t t e r ,
stable
kinematics,
o f
are
c o n f i n e d
t h e
w a v e s
traditional
a n d
that
c o u l d
o r
q u a n t u m
o b t a i n e d
that s p r e a d
a
chain
stable
are
e q u a t i o n
w a v e s
f o r e v e r
a
character
c o n v e n i e n t
r e p r e s e n t
t h o u g h t
p o s s i b l y
t o
H e
entails
w i t h
In
that
t o
t o
w h e n
electric
o r
that
b y
elec-
X - r a y s ,
s u c h
as
r e c o g n i z e d d e a l i n g w i t h
b y
t h e
w h e n
M a x
dissipate
stage
B o r n ,
that
packets.
o f
o f
t h e
o f t h e
r e p r e c o n v e n particle,
a p p e a r a n c e s in
a l m o s t
theoretical
e l e c t r o n s
w a v e s ,
b y
i n t e r a c t i o n
w a v e s
all
e v e r - e x p a n d i n g
p r o b l e m s
light arise for m a t t e r
the
c o m p l e x
m o r e
B u t
o v e r
t h e
o f
m e a n i n g )
particle-like
scattering
final
a
a well-localizable
t h e
b e h a v i o r
s q u a r e
b e i n g
physical c h a r g e
w a v e
packets
a b s o l u t e itself,
o n
e x p l a i n
this
particles again in t h e w a s
i m m e d i a t e
the
w a v e
t h e
a m p l i t u d e
so-called
the
that
concentrated
tried
contrast
particles,
a n
o f
b e
c o n s t r u c t i n g
first
( t h e
h a v e
d i s t r i b u t i o n
s u p p o s e d
b y
at
f u n c t i o n
electron.
a l w a y s p r o d u c e M o r e o v e r ,
also
again
like
w a v e
space.
e x p e r i m e n t s
-
w i t h
t h e
n o t
theory o f
b u t
w e l l
D a v i s s o n
d e n s i t y
w a v e s
m o s t
a
w a y
p i o n e e r i n g
w a v e
o r
t h e
structures.
p r o p e r t i e s
w a t e r
his e q u a t i o n
t h e r e f o r e
c o u l d
tionally
o f
o f
this
result m i g h t
the
rate,
crystal.
S c h r o d i n g e r a m p l i t u d e
o r
-
n o t i o n
b e h a v e d a
I n
o n l y w a v e s
S c h r o d i n g e r ' s
k e e p i n g
p r e s e r v i n g
n o t
r e m a i n
a t o m
theory.
in
e x p e r i m e n t s
walls
that
B o h r ' s
H e i s e n b e r g ' s
light
m i g h t
s h o w e d
t h e
characterize
stable
f a m o u s
b e c o m e
n e v e r t h e l e s s
w a v e s
o f
a n y
e v e n t
n o n p r o b a b i l i s t i c
w a v e l i k e t h e
a n
a s s u m p t i o n s
P u r s u i n g
d e s c r i b e d
like
reflecting
o u t s i d e ,
S u c h
-
t h e
o f
a t o m .
s a m e
a n d
A t
f o r d o i n g all s o r t s o f m i c r o p h y s i c a l
this e q u a t i o n
indefinitely
vessel
w e r e
t o o l
T h e y
a d - h o c
as if t h e
o n
t o
d e s c r i p t i o n
a c c o u n t s
d i s c o v e r e d
It w a s
m a t h e m a t i c a l
space
a n d
physics
c i r c u m s t a n c e s .
process.
pictures.
1 9 2 4 )
in
h y d r o g e n
theoretical
S c h r o d i n g e r
nificantly,
a
c o m p l e t e n e s s
(e.g.
after
as
arbitrary
s p a t i o - t e m p o r a l
B r o g l i e
u s e d
s u c h
it s e e m e d
t h e
v a r y i n g
c o n t i n u o u s
t h e
a brief t i m e
u n d e r
a
q u a n t u m
revolution
a s p a t i o - t e m p o r a l
a l o n e
sacrificing
d e
g i v e
a v o i d s
earlier F o r
n o t
structure,
m e c h a n i c s t h e
reactions
let
l o n g - l i v e d
probabilistic
m a t t e r , p r o c e s s .
E i n s t e i n as well.
h a d
I n
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t h e
The
case o f that
t h e
t h e
w a v e ,
w h e r e a s
e l e c t r o n s
e a c h
It r e m a i n s
Einstein's
light
t w o
b e
h i m s e l f
d i f f e r e n t o f
t h e
p r e t a t i o n a n s w e r e d ( m o r e
o f
m a t r i c e s
his
" o n l y
S c h r o d i n g e r ' s p r o b a b i l i t y
e q u a t i o n
( C a r t w r i g h t ,
T h e s e
1 9 8 7 ) .
s h o w n
probabilistic
m a g n i t u d e
g i v e n
physical
w a v e s
at a g i v e n
urable
physical
m o m e n t u m ,
is
at
o f
a n c e
t h o s e
( 1 9 2 6 b ) ,
this that
his
e q u i v a l e n t ,
H e n c e ,
as
B o t h i n g
far
as
a p p r o a c h e s
dispositional
c o n c e p t u a l
t o o l s
it w a s
n o t as
alike
s o l v e
p r o p e r t i e s ,
full
t h e o r y t h e
as
b e
m e a s u r e d
this
b y
that
directly
real
t h e
in
a
special
n e w
m e c h a n i c s
f u n c t i o n
m e a n s
in
a n
illusion.
first t o
b y
t h e
o f
o f
the
m e a s a n g u l a r
T h e
full
classical
pic-
a p p e a r a n c e physical
Q u i t e
o f
reality,
in
a c c o r d -
S c h r o d i n g e r
h i m s e l f
q u a n t u m in
that
t h e
a n d
o f
deter-
state
states.
T h e
r a n g e
exactly
m o m e n t u m ,
t h e
generally
T h i s
o f
n o
o f
(or
a n y
h a d
w a s
v a l u e
initial
if
w a y
B o r n
is n o w
a n d
t h e
particles,
realism,
o r
[the
o n l y
this
t h e
the
i n t o
i n t e r p r e t a t i o n
differ
o f
f u n c t i o n
i n t e r p r e t a t i o n
o f
r e q u i r e d
correct,
w a v e
p r o j e c t e d
d e t e r m i n a t i o n
p r o b l e m s
B o r n
r e p r e s e n t
a p p r o a c h e s
is
probabilities,
b e
d e s c r i p t i o n .
t h e y
inter-
t h e
p r o c e s s e s
r e c o g n i z e d ,
m u c h
b e
c o n t i n u o u s
directly
t o
c o u l d
h e
r e c o g n i z e
p r o b a b i l i t y
a n d
c o u l d
Instead, t o
particle.
p o s i t i o n ,
p r o v e d
H e i s e n b e r g ' s
h o w e v e r
a
w a v e s
o u g h t
a g i v e n
forces
material
a n d
s o o n
q u a n t u m
o f
t h e
S c h r o d i n g e r ' s
a p p r o a c h ,
a n d
strictly
d o
s u c h
c o m p l e t e n e s s
result,
finding
characterizations,
w i t h
S c h r o d i n g e r ' s
w i t h
t h e y
characterize
variance
s p a t i o - t e m p o r a l u n d e r
B u t
the
T h i s
i n d e e d
c o n d i t i o n s ,
p r o p e r t i e s ,
w h i c h
d e t e r m i n a t i o n tures,
time.
are
o f
B o r n ' s
o f
t h a n
H e i s e n b e r g ' s
m o t i o n
a c c e p t s
at o n c e .
less
m e a n -
t o
w e r e
v e r s i o n
t h e
d e t e r m i n e
t h e
o n e
n o
t h e
o f
t h e
will
forces
characterizing
t h e m s e l v e s
w e
possible":
"defines
n o t
p r o b a b i l i t y
a
b y
is
probabilities o r
w e l l - d e f i n e d
m a t t e r .
transition
reflect
the
values)
m i n e d
t u r n
a c c e p t e d
d e f i n e
w a v e s
o f
t h e
o f
t h e n
A c c o r d i n g
w a s
t o
S c h r o d i n g e r ' s
that
in
that
that
i n f l u e n c e
H e i s e n b e r g ' s .
u n d e r s t o o d o f
s t r u c t u r e
direction]
S c h r o d i n g e r ' s
f u n c t i o n
t h e
the
spherical
a b s o r p t i o n .
c o n c l u d e d
8 6 5 ) .
B o r n ,
t h a n
for
p r e d i c t s
e x p a n d i n g
scattering p r o c e s s e s
b)
square)
W h e t h e r
that
travel in a
i n t e r p r e t a t i o n
s h o w s
F o r
t o
arrays
p.
t h e o r y
is f o u n d
w a v e s . W h a t
a particular
t h e
a n
c o n c l u s i o n
u n d e r
as
( 1 9 2 6 a ,
w a v e s .
S c h r o d i n g e r
t h e
a b s o l u t e
[ f r o m
statistically.
less
o n e
its
c o m i n g
certainly
t o w a r d s
P r e s u m a b l y
d i r e c t i o n "
o n l y
d e s c r i b e
w a v e s ?
precisely,
n e w ]
t o
m a t t e r in
available
( 1 9 2 6 a ,
b y
201
o u t w a r d
f u r t h e r
r e a l i t i e s : p a r t i c l e s and
that
e l e c t r o n
B o r n
t a k e n
d r i v e n
for
r e m a i n
situation
t h e m s e l v e s
f o u n d
i n g
this
q u a n t a
f l o w
e l e c t r o n
available
in physics
o f e l e c t r o n s
will
particular
direction.
n o t
revolution
s c a t t e r i n g o f a b e a m
e m e r g i n g
F r o m
probabilistic
d y n a m i c s
m a t h e m a t i c a l
are
f o r m .
p r o b a b i l i t y
is
irreducible.
m i c r o p h y s i c s
b y
i n c o r p o r a t -
probabilities,
a m o n g
t h e
basic
physics.
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202
The In particular,
ing,
the
probabilistic
as t o
h o w
can exist. Maxwell's puzzle a t o m s o f different It
s u p e r t h e o r y
is
stable
significant
o f change
a n d
a n d
transitions
structures
a n d
m o t i o n s ,
that
this
m o t i o n ,
such
b e t w e e n h o w e v e r ,
c o n q u e r e d
o f this w o r k
became,
as it w e r e ,
intricate
historical a n d
these
o f
t w o
the
a
central
a
bridgehead
reason
will
to stay w i t h
only
h u m a n
the
answerkinds
the existence
d o n e
in
t e r m s
o f
T h e
o f
to
a n o t h e r
o f the p r o d u c t i o n
position and
very c o m b i n a t i o n b e in
the
d e e p e r
physics
radiation, a n d
o f
stable
reason
since
e m p i r e
o f
o f
possible
w h y
Bohr's
and
certainly since
mechanics. Statistical physics
the
is
s o o n
o f
b u t
change.
lose
us. T h e
mind,
different
its
in
It
chance.
W e
o f chance
the
a n d
is h a r d
impact.
e m p i r e
also
from,
o f was
In
spite
the thus
o f
systematic relations b e t w e e n t h e r m o d y n a m i c s
probability in
matter
irreversibility
reasons
n o t
appears
by q u a n t u m
p r o b l e m
for
well-distinguished
as a t h e o r y
t h e m .
consolidation
this
o f
finally resolved;
was
o n
theory
a perspective
exemplars exactly resemble each o t h e r
Einstein's pioneering w o r k
q u a n t u m
physics
(as M a x w e l l h a d envisaged), b u t in t e r m s o f
structures
has
structures
(cp. 5.3) w a s
sorts w h o s e
a t o m s a n d molecules
probability
in
they answer, o r at least p r o v i d e
question
explained.
revolution
just to
m a y seems
constitution
as
see
d e e p that
o f
be the
a n d the
either
therefore to
as,
all
o f
expect
r o o t e d
n o t
universe.
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[Statisticians] conquest
have
rivalled
already
only
by
o v e r r u n Attila,
every
branch
M o h a m m e d ,
o f
and
science
the
w i t h
a
C o l o r a d o
rapidity
o f
beetle.
M a u r i c e
Kendall
(1942)
6 =
s t u d y .
m e t h o d ,
itself
as
a n
O n c e it
w a s
i n t u i t i v e
statistician. A r o u n d c e p t i o n m i n d
a n d
as
b e t w e e n a n
e v e n t ,
v i e w .
I 9 6 0 ,
statistician. t w o
t h e
p u t e r .
T h e s e
a n d
p s y c h o l o g y
radically
Q u e s t i o n s
a
p r o b l e m , a r e
likelihood
e s t i m a t i n g t i m e
t w o A n d in
t h e
r e v o l u t i o n a r y
t h e y 1 9 6 0 s
as
m e t a p h o r s
b y
d o e s
t h e
t h e
t h e n
s t e m
rise
t o o l s :
o f
t h e
t h e
s c h o o l statistics
t h e
c a u s e
t o
p o i n t
o f
c a l c u l a t i n g
m e t a p h o r
o f
a
n e w
setting
its n o v e l t y
d o m i n a n t
f r o m
203
m i n d
this
o n e :
p e r -
d i s c r i m i n a t e
a t t r i b u t e
samples,
as
m e t a p h o r :
t e r m s
T h i s
s u c h
m i n d
f r o m
similarly p o w e r f u l o f
n e w
t h e
in
r a n d o m
p r o b a b i l i t i e s .
science
a
as a p e r s o n ,
d e s c r i b e d
'accelerated o v e r
p r o c e s s e s
a p p r o a c h e d
ratios, t a k i n g
n e w
h o w
o b j e c t
t o d a y
p r i o r
t h e
a n
c o g n i t i v e
t r a n s f o r m e d
w e r e
as a n o t h e r ,
g a v e
o f
s u c h
r e c o g n i z e
f u n c t i o n s
s a m e
v o c a b u l a r y .
B o t h
s o l v e
a n d
a b o u t
w a s
s o u n d s ,
o r
probabilities
u n d e r s t a n d i n g
t h i n k i n g
B r a i n
c r i t e r i o n
o u r
a
decision
e m e r g e d
m i n d
as
at
c o m -
a n d
c o n c e p t u a l
n e w
c o g n i t i v e
o f
b e h a v i o r i s m .
a n d
c o m p u t e r s
Statistics
204
w e r e
originally
m i n d ,
t o o l s
t h a t
t h e m s e l v e s W h a t c a r e e r
t o o l s
t o
a r e
c h o l o g y
a
a
t o o l
f o r
t h e
a n
w h i c h o f
i n s p i r e d
cast
t h e s e
m a k e s a b l e
n e w
c e r n i n g
o f
classical
t h e
I n
t h e
a g a i n
First,
t a u g h t a n d
a n d
h a n d s
o f
n e w
h o w
p e o p l e
results,
o f
a n d
in
s h o u l d
a n d
a
o f
w a s
h o s t o f
o f
o f
S e c o n d , t h e o r i e s ,
T h i r d ,
o n e
t h i n k i n g
t h a t
t h e
r e a s o n -
p r o b l e m s
p r o b a b i l i t y
thinking,
as w e l l
p s y -
r a p i d l y
it.
r e v i v e d
rationality,
t h i n k
l e n d
e n t e r e d
r e a s o n i n g .
psychologists w i t h
o f
c h e c k e r e d
c o g n i t i v e
effect
h i m ,
t h e
r e q u i r e d
i m p l i c a t i o n s
s y n o n y m o u s
o f
p s y c h o l o g y
its f o c u s , w i t h
p r e s t i g i o u s
statistics
r a n g e
t h e
science
m i n d .
a c c o u n t
m e m o r y ,
a n d
t h e
o f
r e c e n t
a n d
j o u r n a l s
v a r i e d
n o r m a t i v e
b e c a m e
itself w i t h
a n d
d e v e l o p m e n t s ,
p r o b a b i l i t y ,
t h e
i n f e r e n t i a l
it,
u n c e r t a i n t y
d e s c r i p t i v e
o n c e
c o n c e r n e d
u n d e r
m e t a p h o r s
p e r c e p t i o n ,
t h e o r e t i c a l
statistics.
t h e o r y
o n
I n
e x p e r i m e n t a l
i m p r e s s i v e
l i g h t
j u d g m e n t
m a n
a n d
n e w
scientist.
a b b r e v i a t e d
a n a l y z i n g
t e x t b o o k s
mind
as i n d i s p e n s a b l e
i n t o
p s y c h o l o g y .
i n s t i t u t i o n a l i z e d : t o o l
b o t h
necessarily
i n
the
b e h a v i o r a l
c o n s i d e r e d
is
statistics as
t h e
t r a n s f o r m a t i o n
f o l l o w s
o f
o f
of
c o n t h e o r y
probability
a n d
p s y c h o l o g y
as h o w
t h e y
i n
fact
d o .
6 . 2
T H E
B e f o r e
1 9 4 0 ,
m e n t a l
p s y c h o l o g i s t s ,
t h e o r y tics.
statistical
c o n s t r u c t i o n .
T h e
" f a t h e r
v o l u m e
o n
1 8 9 7 ) ,
w e r e
f r o m
m e n t s
o f
ideas a n d
o f
a n d
u s e d ,
c o n s i d e r e d
t h e
f o r e m o s t
p e n s a b l e T h e
N e w t o n i a n like
t o p i c
e l e m e n t
ideal
a n d
h a d
t h e o f
p r o t o t y p e
as
o f
o f
t h e
o f
i g n o r a n t
t o
it
statis-
w r o t e
o f
a
v a r i a t i o n
m e a s u r e W h a t
ideas
a n d
o f
i n
Kollektivmasslehre
t h r e s h o l d s .
m e t h o d ,
r o l e
F e c h n e r ,
coefficients
i m p o r t a n c e .
e x p e r i -
n o
as
discipline
e x p e r i m e n t a l
w e r e
w a s
n o t
t h e
w e
ele-
call
k n o w n
Statistics
L e w i n
a r g u e d h e
t h e
( L e w i n ,
t h e
w a s y e t
d e t e r m i n i s t i c is n o
a n d
C l a r k
H u l l ,
G a l i l e o ' s o f
H u l l ,
as a
a n d
n o t
a n
t h e
y e t
indis-
d e t e r m i n i s t i c
e x p e r i m e n t a l
t h e r e
l a w
1 9 3 5 ;
o f
t h a t
c o n s i d e r e d a n d
p s y c h o l o g y
P i o n e e r s
a b o u t
discipline, a n d
l a w s
n o t
o f
c o n s t r u c t i o n .
d o u b t s
r e s e a r c h
a n d
t o o l s
a l m o s t
T h e o d o r
statistical
first
as
p l a y e d
p u b l i s h e d
n e w
w h e r e
r o l e
h o w e v e r ,
as s e n s o r y
w i d e s p r e a d .
b e h a v i o r i s m ,
p s y c h o l o g i c a l
t i m e
t h e y
G u s t a v
t h e
P E R I O D
m i n o r
m e a n s ,
p s y c h o l o g i c a l
w a s n o
o f
s u c h
t h e o r y
K u r t
a strictly s y s t e m a t i c A m e r i c a n
a
s e l f - i m a g e
logical p r o c e s s e s .
o f
is
i n
in
s c i e n c e
H e l m h o l t z
start
e x p e r i e n c e ,
p e r i o d
n o t
w e r e ,
p e r c e n t a g e s , v e r y
a
1 9 5 0 ,
p o s t h u m o u s l y
pre-statistical b u t
b e f o r e
o n l y
p s y c h o p h y s i c s , "
t h e
m e n t a l
p l a y e d
P s y c h o l o g i s t s
statistics,
( F e c h n e r , u s e d
P R E - S T A T I S T I C A L
s t u d y
falling 1 9 4 3 ) .
n a t u r e
p l a c e
f o r
o f
o f
late
t h e as
i n
t h e o r e t i c i a n
falling as
p s y c h o -
statistics
a m a j o r
b o d i e s A s
p s y c h o l o g y
b o d i e s
as
p r o t o t y p e
1 9 5 5 ,
D a v i d
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Statistics
K r e c h , faith:
a
l e a d i n g
t h e
b e l i e f
e x p e r i m e n t a l i s t , t h a t
w e
c o r r e l a t i o n s
r e s p o n s e .
c o u l d
n o t
E x a m p l e s
t h e
tistical
m o d e l
w e r e
for
qualities, d e c a d e
f o u n d
S.
a l m o s t
p a r t
o f
w h i c h
N o n e
o f
m e t h o d
T h e
d r e a m
peculiar
o f
b e h a v i o r
t h e
n o t
a n d
p s y c h e
h i s t o r y
a r o u n d
t h e
c u l a b l e
G r e a t
-
o f
u s e
M a n
(e.g.
m e t h o d s
d e s c r i p t i o n , o g i s t s
u s e d
t w e e n
1 9 4 0
h y p o t h e s i s . non
o f
H o w
u s e d ,
a n d T h e
A
d i d
t h r e e
t h r e e
m e t h o d
E
a n d
issue F o r
t h e
1 9 2 0 s
o f
t h a t
c o n t a i n
W
m o d e l
m e t h o d s
i n d i s p e n s a b l e
w a s
o f
c o u r s e
t h e
t o n g u e ,
all
B o r i n g , o f
o p p o s e d
n o t
S h e r l o c k d e v i a n t
d e t e r m i n e d , G .
o f
( G i g e r e n z e r ,
a n
h i s t o r y
as
B r u n s w i k
if
t h e
n o t d e a n
p s y c h o l o g y t o
t h e
incal-
T O O L S
T h e
o f
as t o o l s : 1 9 4 0 ,
g r e a t
t o o l s
for
i n f e r e n t i a l h a s
e x p e r i m e n t a l
i n f e r e n c e statistics called
c a m e
f r o m as
t h e
t h e
d a t a
p s y c h o l -
b r e a k t h r o u g h
b e e n
f r o m
i n f o r m a l
a n d
r a t h e r
v o l u m e s articles
m e a s u r e m e n t ,
b e -
d a t a
t o
sine
qua
" i n f e r e n c e
1 9 8 7 ) .
i n f e r e n c e s
i n c i d e n t a l t h e
t h e
Z e i t g e i s t ,
t i m e
M u r r a y ,
s p e c t r u m
i n s t a n c e ,
s c a l i n g
t h e
A
c o n s e q u e n c e ,
F r e u d ,
o f
s e n s o r y
m e a s u r e m e n t
c h a n c e
a
f u n c t i o n a l i s m ,
as a
as
sta-
p r o c e s s e s .
statistician.
E d w i n
b e f o r e
statistical
d r a w
w a s
a n d ,
psychically
f u n c t i o n s
w a y s .
d u r i n g
p s y c h o l o g i s t s
t h e
in
N
A l r e a d y
w i t h
( G i g e r e n z e r
e x p e r i m e n t e r . Psychology
all
o t h e r
s e n s o r y
S i g m u n d slip
p h y s i c s
p r o p o s e d
a s s u m p t i o n s
w i t h o u t
t e r m .
a n d
1 9 6 3 ) .
i n s t i t u t i o n a l i z a t i o n
h e t e r o g e n e o u s b u t
s e r v e
1 9 5 5 ,
t h e
a n d
s i m p l e r
o r g a n i z e d
o f
T H E
i n f e r e n c e . i n
e v e n
o f
p r o b a b i l i t y
as
s t i m u l u s
T h u r s t o n e
i n t u i t i v e
e v e r y
t e c h n i c a l
forces
L.
p r o b a b i l i s t i c
d e -
m e c h a n i c s .
p r o b a b i l i s t i c
t h e
laws,
statistical
q u a n t u m
u n c e r t a i n
b y
o r
o f
n i n e t e e n t h - c e n t u r y
T h u r s t o n e ' s
d r e a m
B o r i n g ,
m a y
statistics
scientific
r e v o l u t i o n "
t i m e ?
a n d
a
L.
his
e s t a b l i s h e d
o f
6 . 3
Statistical
t i m e ;
c o n s i d e r e d
effect
b r i g h t n e s s ,
like a n
r e p l a c e d
p s y c h o l o g y ,
d e t e r m i n i s t i c
a l w a y s
t h e
t h e
o f
d i s t r i b u t i o n
p s y c h o l o g y .
detail
t o
1 9 2 7 ,
as a u n i v e r s e
u n c o n s c i o u s , e v e r y
a r e
v o i c e s
t h e
a n d
C o n t e m p o r a r y
l o u d n e s s ,
n e e d
e x p e r i m e n t a l t h e
I n
o p e r a t e s
t h e o r y .
o v e r d e t e r m i n e d o f
c u e s
o r
o f
t o
H o l m e s
t h e s e
c a u s e
c o n f e s s i o n
d e t e r m i n i s t i c
t w e n t i e t h - c e n t u r y
s o o n
d i d
d e t e r m i n i s t ' s
d i s c o v e r
p r o c l a i m e d
at
203
i n d e t e r m i n i s m
n o r m a l
f o l l o w e r s b u t
will
d e s e r t .
a
t h e
b e t w e e n
p e r c e i v e d
s y s t e m
successful,
S t e v e n s ,
t h e
p e r c e p t u a l
n o
o f
B r u n s w i k
p e r c e p t u a l
1 9 8 7 b ) .
in
mind
m u l t i p l i e d .
t h e
t h a t
a s s u m e d
E g o n
t h a t
m o r e
S.
n o r
m e a s u r i n g
later,
t h e
n e i t h e r
v o i c e s
w h i c h
a s s u m i n g
w a s
-
m e c h a n i c s
T h e r e
t h a t
ideal
b e
the
v o i c e d
e v e n t u a l l y
s c r i b i n g o n e - t o - o n e
w a s
of
in
o f
t h e i r
d a t a
f o r m a l t h a n
a p p r o a c h e s
essential
t h e Journal
w h i c h
b e f o r e
results
t h a t w a s
t o
t h e
of
Experimental
are
s u m m a r i z e d
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206
Statistics
a n d
d e s c r i b e d
f e r e n c e s
o n
j u d g m e n t , e n c e s
b y
d a t a
p i c t u r e
e x p e r i m e n t a l issue
o f
s o m e tial
criteria.
statistics. o f
W o l f g a n g
b u t
c o u n t e d
t h e
o n l y
t h e m
i n
o f
in
l e a d i n g
tests
t o
figure
M e l t o n ' s
c a n t
o n l y
c a n t
at
lish
at
t h e n o
0 . 0 1
l o n g e r
c o u l d
W h a t
t h e
f r o m
a n d
n o k i n d
P s y c h o l o g i s t s F i s h e r
h a d
d u r i n g
t h e
level a v o i d
l o n g e r o f first
o f
1 9 2 0 s ,
t o
T h e o f
t o w a r d
t h e
e y e b a l l i n g
y e t
n e e d
t o
i n f e r e n -
P i a g e t
his
o f
o p e r a n t
m e m o r y ,
all
w i t h o u t
f r o m
h a d
areas
t h e I n
level
1962,
d e s e r v e d
a
a p l a c e
h a d
o n his
in
o f
m e s s a g e
m a j o r
8 0 %
t h e
t h e
o f
t h e
u s e d
( T o d a y , his
t h e
last
d i d
n o t
reject signifi-
t h o s e
signifi-
P s y c h o l o g y w h o
t w e l v e
results
w h e r e a s
e x p e r i m e n t e r
t h e
Experimental
t h a t t h a t
in
criteria
of
a n d
j o u r n a l .
articles
significance
s t a t e d
for
m a d e
m a n u s c r i p t s .
o f
Journal
m a n u s c r i p t s
a n
u n i v e r s i t y
journals
1 9 5 9 ) .
M e l t o n
o n ,
h o p e d
s t u d e n t s t o
p u b -
significance. m a d e
F i s h e r ' s
analysis
t h a n
a c c e p t a b l e ,
t h e
o f
b e e n
W .
1 9 4 0
h a l f
u n p r e c e d e n t e d
acceptability
p u b l i s h e d ,
b a r e l y
test
t h e
A .
( 1 9 8 0 )
a b o u t
p u b l i s h e d ,
his e d i t o r i a l p o l i c y
statistics, a n d a v o i d
w a s
(Sterling,
A .
t h a t
1 9 3 9 ,
p s y c h o l o g y
in
n e v e r
w e r e
o f
d a t a
in s h o r t ,
a l m o s t
t h e
1 9 5 5 , m o r e
g u i d e d
w a s ,
o f
R .
p s y c h o l o g i c a l
f r o m
t h a t w a s
1 9 3 4 ,
T w e n e y
a n d
H o w e v e r ,
I n
in
a n d
1 9 3 4
e d i t o r s for
t i m e
R u c c i
statistics
a n d
different
e n c o u n t e r e d
a n d
t h e
principles
o f
o c c u r r e d
m a n u s c r i p t s
statistics
p u b l i s h e d
K a r l
details
laws, J e a n
first
b e t w e e n
o n
B y
1 0 0 % . )
w e r e
0 . 0 5
o r
a n d
c o u n t r i e s .
t h e
small.
criterion
b e g i n n i n g .
m e s s a g e
h y p o t h e s i s
for
still
statistics,
c o n c l u s i o n s 9 0
s p e a k i n g
p a r a p s y c h o l o g y .
m a i n
criteria w h i c h
null
c o u l d
a
a c c e p t a n c e
Psychology,
w a s
t e x t b o o k s
t e a c h
journals
justify
t h e
years.
o f
t h e
is b e t w e e n
for
t h e
o n l y
E n g l i s h
statistical m e t h o d s
significance
this w a s
f o u r
t o
M o r e
d i s t i n g u i s h e d .
n o t
his
differ-
articles
a p p r o a c h
G e s t a l t
t h e o r y
ratio,
results
d i d
p e r s o n a l
m e a n
o t h e r
e v e n
S k i n n e r
his
a p p e a r e d
a n d
flood
s t a r t e d
statistical B u t
A
his
F.
a p p l i c a t i o n s
e d u c a t i o n o f
B.
B a r t l e t t
t h e
v a r i a n c e
s e v e n t e e n
p s y c h o l o g y .
curricula
in
i n t e r e s t
institutionalization
in
i g n o r a n c e
p s y c h o l o g y
d e r i v e d
b y
in-
i n f e r e n c e .
o c c u r r e d
analysis
j o u r n a l s ,
K o h l e r
o f
b u t
w h i c h
c o m p a r i s o n .
critical
n o t
f r o m
c u r v e s ,
o f
d e s c r i p t i v e
e v e r y t h i n g
F r e d e r i c
r u l e t h e
w e r e
in
c o m p a r i n g
u s e d ,
o f
t h e
b y a
articles
n o n - s t a n d a r d i z e d
d e v e l o p m e n t ,
Sir
m e t h o d
c h a n g e
F i s h e r ' s
o f
a n d
a
E x p e r i m e n t a l
intellectual
statistical T h e
i n c l u d i n g
o r
e r r o r ,
also
r e p o r t
a n d
d r a w n ,
s p e c i f y i n g
i n f e r e n c e
p i e c e m e a l
i n f e r e n c e ,
c o n d i t i o n i n g , a
a
p r o c e d u r e s ,
f o r m a l
t h e o r y
is
is
r e a d e r ,
w e r e
a n d
mind
e y e b a l l i n g
p r o b a b l e
m e t h o d
d e s c r i p t i o n
b y
t h e
w i t h o u t t h e
the
i n f e r e n c e
d r a w n
w i t h
as
c h i - s q u a r e
o f
o v e r a l l
s u c h
n o
a r e
v a r i a n c e s
criteria
issues
b u t
b a r g a i n i n g
t h e
P e a r s o n ' s
detail,
h y p o t h e s e s
w i t h
f o r m a l
i n
of
t h e
t h e o r y
v a r i a n c e c a m e
i n d i s p e n s a b l e
t o
o f
n u l l
u s i n g
i n s t r u m e n t ?
h y p o t h e s i s
a g r i c u l t u r a l
p s y c h o l o g y
f r o m
testing. e x a m p l e s
a g r i c u l t u r e .
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Statistics
B y
t h e
m i d - 1 9 5 0 s ,
c l e a n s e d soil
o f
t h e
fertility,
special
t h e
in
all
gists, a n d
a
a g e n e r a l
f r o m
( f o r
S t a t e
at A l l
visited
F i s h e r
t w o
o f
b o o k s
I o w a
r e s e a r c h e r s . o f
F i s h e r ' s
l a t t e r
t h e
A l l e n
G r a d u a t e a n c e a
g r a d u a t e
c o u r s e s
o n
plicated, k n o w n ,
t h e
N e y m a n
h a d
r e j e c t e d
m e t h o d
o f
t w e e n m e n t a l H o w
t w o
1 9 5 1
t h e o r y
a n d
o f
o f
P e a r s o n
w h i c h
u n i f y
a n d
h a d
e n g a g e d
h y p o t h e s i s a n d
a n d
t e s t i n g
w h e r e
year.
t h e y as
a
a n d
U n i v e r s i t y e d u c a t i o n a l
d e v e l o p m e n t at
S t a n f o r d H o t e l l i n g ,
L. G .
T h r o u g h H u m p h r e y s ,
B y
a n d
w h e r e
1 9 5 0 ,
T w e n e y ,
statisticians a n d
E g o n
o f
it
W a r .
A s
h a l f h a d
f o r t h
w a s
u n d e r s t o o d w a s
his
o f
t h e
o f f e r e d p r o g r a m
b e c a m e
s h o w n
c o n t r o v e r s y
set
b e c a m e
P e a r s o n
n u l l
vari-
1 9 8 0 ) .
s o o n S.
d i s p r o v i n g
p o w e r
analysis
u n i v e r s i t i e s
a h e a t e d
o f
in
statistics a g r a d u a t e
W o r l d
p r o g r a m
t h e
f r o m
at S t a n f o r d ,
( R u c c i
in
for
U n i t e d
S t a t e
S t a n f o r d .
t r a i n i n g
s a m e
m a d e
S e c o n d
P a l m e r
S n e d e c o r
M c N e m a r ,
at
later
I o w a
w h e n
f o r
t r a i n i n g
at
t h e
I o w a
f r o m
it
statistical
a n d
statistical
research
N e y m a n
i n f e r e n c e
t h e
A m e r i c a n
h a d
a n d
statistician
Q u i n n
1 9 3 5
F i s h e r i a n
J e r z y t h e
in
m a k e
p s y c h o l o -
t w o
at
p s y -
statistical
S n e d e c o r
w a s
O f
o t h e r s .
t h e
1 9 5 4
t h e
F i s h e r ' s
h y p o t h e s e s ,
in
o f
W .
l a t t e r
pigs,
p s y c h o l o -
F i s h e r ' s
t e x t b o o k
r e c e i v e d in
t o
o n
L i n d q u i s t
o f
m a n y
l e a d i n g
a n d
after
i n d u c t i v e
in
a n d
s t r e a m
t h e
p r o f e s s o r field
t o o k
Fisher's ideas in
F i s h e r
F.
It
U n i v e r s i t y ,
statistical
C o l l e g e , a n d
t r i u m p h
p a r t i c u l a r
his
t h e
r e q u i r e m e n t
G .
himself,
H o t e l l i n g .
a n d
m e t h o d s ,
p u s h e d
E.
associate
in
1 9 8 0 ) .
i n v o l v e d
p s y c h o l o g y
State
3.4, N e y m a n
b e h a v i o r ,
in
articles
o f
p o t a t o e s .
u n s o p h i s t i c a t e d
statistical
r e c e i v e d
G r a n t ,
b e t w e e n
as in
t h r o u g h
b e c a m e
D a v i d
t h e
o f
c o u l d
s t e a d y
a g r i c u l t u r a l
1 9 3 7 ) ,
ideas
F i s h e r i a n
H o w e v e r ,
a
w h e n
t h e
b e c a m e
d e p a r t m e n t s
r e q u i r e m e n t
t h a t
t h e o r y
w e i g h t
m e s s a g e
C o l u m b i a
F i s h e r
b y
a n
p r o g r a m
at
i n f l u e n t i a l
s t u d e n t s
p s y c h o l o g y
o n ,
p u b l i s h
S n e d e c o r
w a s
in 1 9 3 4 at I o w a
d o c t r i n e
T w e n e y ,
1 9 3 4 ,
i n s t a n c e ,
E d w a r d s ,
t o
b y
I n f l u e n c e d
Fisher's
g r o w t h
F i s h e r i a n
M i n n e s o t a
t a u g h t
m a i n l y
w h e n
t h e
t h e
t h e
( 1 9 3 5 ) .
m a t h e m a t i c a l l y
a n d
o f
P s y c h o l o g i s t s
f o r
t h e
as
Experiments
1 9 3 0 s
H o t e l l i n g
his
U n i v e r s i t y ,
M c N e m a r ,
R u c c i
( S n e d e c o r ,
i d e a s
g r a s p
b e g a n
E n g l a n d ,
w r o t e
of
s u c h
v a r i o u s e d u c a t i o n a l j o u r n a l s , Psychometrika,
w e r e
v i s i t i n g p r o f e s s o r .
Design
o n
p r e s e n t e d
o n ,
U n i v e r s i t y
in
w h i c h
largely
see
t h r e e
m a n u r e
late
207
t h e
H a r o l d
t h e
States.
his
t h e
Bulletin,
details
o f
t o
mind
e x a m p l e s
m e t h o d o l o g i c a l
F r o m
1 9 4 0
C o l l e g e ,
J o h n s o n
y e a r s
the
available
a g r i c u l t u r a l
F i s h e r ' s
f e w
d e l u g e d
w e r e
effect
w a s
Psychological
ideas
o f
t h e
fields.
t e x t b o o k s
t h e
a n d
o n l y
basis f o r
gists
s m e l l
i n f l u e n c e
c h o l o g i s t s
b o o k s
of
c o m -
b e c a m e
i n
s e c t i o n
w i t h
Fisher.
h y p o t h e s e s
i d e a as
i n t r o d u c e d
o f a
as
i n d u c t i v e
d e c i s i o n as
a
t h e
b e -
f u n d a -
c o n c e p t . c o u l d
t h e
t e x t b o o k
w r i t e r s
a n d
t h e
t e a c h e r s
o f
t h e
n e w
c u r r i c u l a
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208
Statistics
cope
w i t h
the
agreement, w h o
in
chology
a n d
plicated
to a n d
teach
sampling,
vals
a n d
N e y m a n
c o m p e t i n g into
b u y
Pearson's
theory. T h e s o m e
hybrid
w o u l d
hypothesis N e y m a n as
the
with
a n d
Fisher's,
ideas
a n d the
s t e m m e d
hybrid
statistics
as if t h e r e
to
sell
neither
a b o u t
(although
T h e
o f
type-I
so
on.
t e x t b o o k s
errors
taught,
Fisher,
the
f r o m
one
type
the in
be
texts sure,
r u n
alter-
eager
n o w
to
taught
a d d e d this
a n d
to
null
context),
o f
significance
b e c a m e
m i s h m a s h e d
that
a n d
as if it w e r e T h e r e
for
a
O f
N e y m a n
in
level
as
3.4.
w e r e
b e c a m e
N e y m a n
of statistics.
the existence o f a d e e p controversy, m u c h
section
the time
indicated
anonymously,
p r e s e n t e d
controversial
the
not
inter-
fuse
to
l o n g
it w a s
others
was presented only
in
text
ran-
to
d e t e r m i n e d
o f
o f
still less
n o t
interpretation
significance
Fisher's,
error
be
h o w e v e r ,
to
type-II
it c o u l d
c o m -
particular
n o
statistical
nor,
t o o
p o w e r ,
psychologists
T h e
Fisher
1956)
Psy-
declared
textbooks,
described
a n d
in
simply
desired
dis-
Guilford,
Statistics
almost
tried
as
inference.
approved.
existed
the
alternative
P.
specifying
statements
theory,
eager
w h i c h
f r o m
tone? J.
t h e impossible. B u t it w a s n o t
Pearson's
p r o p o r t i o n
as a n
o f
achieve
mass o f texts
inductive
have
ideas
H o w e v e r ,
statistical
w e r e
o f
testing
W h a t e v e r
a n d
o f
statistics,
Pearson
to
on.
theory
d o i n g
f u n d a m e n t a l
third edition in
Pearson's
so
great
hybrid
m e t h o d
polemical
sophisticated
o f avoiding probability
statisticians
the
m o r e
advance
a n d
the
the m o s t widely read text)
a n d
sizes in
issues,
e d i t i o n o f h i s Fundamental
(p. 217). T h e
course, this m e a n t natives:
a n d
( e v e n as late as t h e
o u t c o m e s , a n d
first
N e y m a n
sample
mind
controversial
personal
the
o f p o w e r
d o m
the
(probably
to discuss
started
o f
bitter
Education
the concept
ideas
the
1942 published and
levels
subtlety
of the
w a s
s o m e
o f
Pearson. the
only
n o
the T h e
truth,
m e n t i o n
less o f t h e c o n t r o v e r s i a l
o f
issues,
n o r o f the existence o f alternative statistical theories. If the originators
o f
the ideas w e r e m e n t i o n e d
o f
Hays
(1963),
t h e n
Fisher's theory J.
N e y m a n
the
a t all i n a t e x t b o o k , as in t h e e x c e p t i o n a l case
reader
"was carried
a n d
E.
was
told
o n t o
the
S. P e a r s o n "
earlier
Fisher has linked the "inference
(p.
thing w h o
o f
cumulative
287).
But,
a n d
the
"high
state"
f r o m
is c r e d i t e d w i t h
o f
a n d
is
merely
skeleton.
so successful
to
imagine
w h a t
Fisher
f o u n d i n g
w a s
Pearson's concepts w e r e
testing to experimental
has b e e n
progress:
in the w o r k
design
revolution" was consequently a revolution in
e x p e r i m e n t e r s
different
Fisherian
significance
design. This revolution today's
story
to a high state o f d e v e l o p m e n t
n o t practiced in psychology; N e y m a n tacked
a
the
that had first
t h a t it is o f t e n
" e x p e r i m e n t " taught
(see
could
(3.3),
and
experimental difficult m e a n
3.2). W i l h e l m
experimental psychological
for
s o m e W u n d t , labor-
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Statistics
a t o r y
i n
1 8 7 9
s p e c t i o n
w i t h
1 9 8 7 b ) . h a d
in
r e c e n t
W u n d t ' s
n o t h i n g
a m o n g
t h e m
c h o l o g i s t s ;
d o
a n d
t h e
t h e
d i f f e r e n c e s
d e s i g n m e s h
w e l l
m e n t
d i d
w a s o f
h a v e
w i t h n o t
m o n o p o l y .
s u r v i v e
I n T h e
statistical
p r o g r a m
scientific b e e n
o f
d e d i c a t i n g
m e t h o d o l o g i s t s
c o u l d
h a p p e n ? w e r e
A s
t h e
this
o f
p r a c t i c e d in
r e p e t i t i o n , e x p e r i m e n t ,
b y
G e s t a l t
w h i c h
p s y -
i n d i v i d u a l d e s i g n ,
in
t h e
e n v i r o n m e n t ;
a n d
F.
n a t u r a l
c o n d i t i o n i n g .
his
T h u s ,
statistics,
m a n y
n o
o n e
o f
his
a n d
c o u l d
h e l p
in
S k i n n e r
b o o k s
" t o
this
ideas
d i d
o f
n o t
e x p e r i -
m o d e l
w o n
a
e x c l u d e
d e v i a n t
i g n o r i n g
F i s h e r ' s
h i m s e l f
t h e
b o o k
B .
F i s h e r ' s
statistics
F i s h e r ' s
s u c c e e d e d
analysis,
w h o s e
his
a n d
m o n o p o l y
e x a m p l e ,
A l t h o u g h
a l t e r n a t i v e
r e v o l u t i o n ,
w e
i n s t i t u t i o n a l i z a t i o n
h a v e
n e g l e c t
o f
a r g u e d
p r e s e n t a t i o n
t e c h n i q u e s .
T h i s
t r o v e r s i e s
a n d
e x c e p t i o n ,
b e e n
c o m m o n
in
b y
p r o b a b i l i t y t h a t
t h e
fidence
( 1 9 8 4 ,
statisticians
w o u l d
t h a t
d i d
all t h e s e t a t e d
b y
p . a n d
n e v e r
h a v e
H o g b e n ,
q u e s t i o n s . similar
K a h n e m a n ,
is t r u e r e s u l t
1 9 5 7 ;
i n m a k i n g
A n d ,
a n d
l a y m e n
false,
M o r r i s o n t h e
level
a n d
m o r e
a n d
o f
a n d
(4)
(see
i n
1 9 8 2 ;
r a t h e r
t h a n
t h e
in
o f
j o u r sig-
(2)
t h e
p r o b a b i l i t y
d e g r e e
1 9 7 0 ) . a n
s e e m s
o f t h e
level o f
t h e
s e e m
h a d
n o t i o n
o f
B r e d e n k a m p ,
t h i n k i n g
O a k e s ,
c o n -
effect,
t h e
H e n k e l ,
i n d u c t i v e
w h e r e
a u t h o r s ,
t h e
(3)
t h e
statistical
e d i t o r s
t h e
false,
a n d
f u n c t i o n
as t h a t
o f significance
w i s h f u l
e r r o r s
( E d d y ,
o r
is r e p e a t a b l e
i n t e r e s t i n g l y ,
c o m m o n s e n s e
o r
t r u e
o f
r u l e
w h i c h
a u t h o r s
m a g n i t u d e
is
t h e
i m p o r t a n t
beliefs, s u c h
t h e
h y p o t h e s e s
e x p e r i m e n t a l
a n
b o d y
a n d
w i t h
statistics
t h e o r i e s ,
p s y c h o l o g y ,
b e e n
illusions
t e x t b o o k
(1)
in
h y b r i d
i n s t i t u t i o n a l i z a t i o n
m o n o l i t h i c
a u t h o r s ,
p l a y e d
o f
a l t e r n a t i v e
a l w a y s o f
e r r o n e o u s
h y p o t h e s i s
its p a r t
e x p e r i m e n t e r s
f r a u g h t
d e t e r m i n e s n u l l
h a d
c i t a t i o n
W e l l - k n o w n
t h e
t h e
t h i n k i n g
w a s
a n d
e v e n t
a t t r a c t i v e
n u m e r o u s
itself
1 9 7 8 ;
T h e
a n o n y m o u s
t e c h n i q u e s
s t r a n g e
t h e
w h e r e
r e s u l t "
C a r v e r ,
a
a n d
a l t e r n a t i v e t h a t
is
t h e
t h e
a p p a r e n t l y
t h e o r i e s
f o r w a r d
nificance
a n
o f
issues
a l t e r n a t i v e
i n s t i t u t i o n a l i z a t i o n . nals p u t
o f
itself
p r a c t i c e .
"significant
a b o v e ,
c o n t r o v e r s i a l
a n o n y m o u s
a
i n t r o s p e c t i o n
r e p r e s e n t a t i v e
a n d
w i t h
( D a n z i g e r ,
Fisher's: i d e a s
i n t r o -
B r u n s w i k ' s
c o u r s e ,
d e s i g n
o f
still o t h e r
o p e r a n t
for
s y s t e m a t i c
as
o f
p h y s i o l o g y
e x p e r i m e n t ,
w i t h o u t
o f
m e t h o d
c o m p l e t e d . "
H o w
t h e
w e r e
i n f e r e n c e
S k i n n e r i a n s ,
o f
in
d e s i g n s .
t h e
as
e x p e r i m e n t ,
E g o n
u s e d
in
e l e m e n t s
c o m p a r a t i v e
p s y c h o l o g y ,
t h o u g h t
k e y
single-case
d i f f e r e n t
p h i l o s o p h i c a l
p r a c t i c e
T h e r e
s t u d i e d
b e e n
b e h a v i o r .
I l l )
b l o c k i n g .
209
e x p e r i m e n t
t h e
a n a l y z e d ;
m e t h o d
c o u l d
w i t h
G a l t o n i a n
j u d g m e n t
S k i n n e r ' s
o f
mind
t h e
e x p e r i m e n t a l
d e m o n s t r a t i v e
w e r e
the
c o m b i n e d
c o n c e p t i o n
t o
r a n d o m i z a t i o n ,
w h i c h
Leipzig,
of
c o n 1 9 7 2 ;
W i s h f u l a n s w e r
t o
t o
b e
facili-
r e a s o n i n g
o f
b o t h
1 9 8 6 ;
T v e r s k y
1 9 7 1 ) .
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a n d
210
Statistics
T h i s
d o e s
n o t
u n c o n t r o v e r s i a l w e n t
w i t h o u t
m e a n
h y b r i d
p r o t e s t .
h y p o t h e s i s
t e s t i n g
P e a r s o n i a h
e l e m e n t s ,
o f
belief)
a n d
w a r d s ,
L i n d m a n ,
1 9 7 0 ) .
O n e
s a m p l e t h e
o f
is
e n c e s
in
in
( I 9 6 0 ,
p .
t h e
t h e
n o
s u b j e c t s
p u t
[ s a m p l e
will
real
g e n e r a l l y
i n t e n t i o n
t o
g a t h e r
f a c t o r s
s e e m
statistics
in
c h o l o g y ' s
p r a c t i c a l
o f
tions, t h e
a n d
t a r g e t t h a t
c a t i o n
a n d for
t h e
( 1 9 8 7 a )
p s y c h o l o g i s t s fresh
f r o m
E m p h a s i s for
o f
o n
t h e
T h e
t h e
(e.g.
t h e
n o t
o f
t h e
n u l l
a
l a r g e
w e s t
States,
a c t u a l A s
r e j e c t e d , d a t a
E d -
H e n k e l ,
v e r s u s
U n i t e d
n u l l
d e g r e e s
a n d
m i n i m a l ) .
e n o u g h
its
differ-
N u n n a l l y
it
n u l l
t h e r e
o f a n d
u s u a l l y
is g a t h e r e d ,
t h e
o f
is t h e
h y p o t h e s i s
usually
w o u l d
in
itself
I n
statistics
o b s e r v a t i o n
o f
a p p l i e d
t o
t h e
t h a t
w a s
t o
i n t o
t h e
p r i m e Psychology
t h r o u g h
m a i n
fit
a r e a
t h e f o r
t h e i r
a p p l i -
a n d
g r o u p
n e e d s
e n t e r
s t r o n g e s t
t h e
e d u -
u s e d
k n o w l e d g e ,
this
for
t h e
v i e w .
A m e r i c a n p s y c h o l o g y
p r o b l e m s , r a t h e r
l a b o r a t o r y
r e s i s t a n c e
b y a n d
c o n q u e r e d
e x p e r i m e n t a l
a u t h o r i t y
o f
d e c i s i o n s .
w e r e
s u p p o r t
p r a c t i c a l
1 9 4 2
o f
t h e i r
m e t h o d s
w h e r e
t o
q u e s -
fields
n o t
c h a r a c t e r i s t i c
o r i e n t e d t h e n
a p p l i e d
A m e r i c a ,
o b s e r v a t i o n s
m o r e
p s y -
e d u c a t i o n a l
m e t h o d s
o f
n e w
t h a n
t h e
in
n e w
r a t h e r
n o t
t h e
o f
m e c h a n i z a t i o n
t e c h n i q u e s
r e l e v a n c e t h e
t h e
w e r e
c r i t e r i o n
t h e
d e m o n s t r a t e
ofEducational
s e e m e d
T w o
w a s
t h a t
f r o m
m e t h o d s
G e r m a n y ,
c o u l d is
d r e a m
o b j e c t i v e
p h i l o s o p h i c a l s y s t e m
t h e
p r o v i d e d
c l a s s r o o m ,
r e l e v a n c e
t o
w a y
a n d
practical
t h e
d r i v e
F i s h e r i a n
e v i d e n c e
t h e in
a n
i n s t i t u t i o n a l i z a t i o n
t h e
t h e Journal
v a r i a n c e
exactly:
t h e
E x p e r i m e n t e r s
r a t h e r
k n o w l e d g e
for
early
E d u c a t i o n
p s y c h o l o g y .
e d u c a t i o n a l
s e c o n d
m a d e
e x p e r i m e n t e r s .
practical
e x p e r i m e n t a t i o n ,
is
o f
d i v i d e d
east
e x p e r i m e n t s ,
s e c o n d ,
i n c r e a s e
p r o v i d e s
success
set
o f
r e j e c t i o n
first,
w e r e
it w a s
analysis
t h e
a n d tests
1 9 8 0 ) .
p r o v e
G e r m a n
t r a d i t i o n a l l y w h e r e
t o
t h a t
l a b o r a t o r i e s
t h a n
a n d
a d m i n i s t r a t o r s
D a n z i g e r
If
I f
crucial
e x p e r i m e n t e r .
p s y c h o l o g i c a l u s i n g
b e e n
statistics
l a r g e s t
T w e n e y ,
c o m p a r i s o n s c a t i o n a l
h a v e
p s y c h o l o g y :
t h e
1 9 7 9 ) ,
e v i d e n c e d
( R u c c i
t o
i n f e r e n t i a l
( L o v i e ,
rejected.
r e l e v a n c e ,
o f
small.
as
as
N e y m a n -
criticism
( 1 9 6 6 )
w e r e
h y p o t h e s i s
t o o
( i n s t e a d
( a l t h o u g h
sizes,
p s y c h o l o g i c a l
S i g n i f i c a n c e
l a b o r a t o r y
rest
a n d
a p p l i c a t i o n s
criteria
t h e
s u c h
M o r r i s o n
B a k a n
i n f e r e n c e
d a t a . "
A m e r i c a n
k n o w l e d g e .
in
n u l l is
b e
effect
h y b r i d ,
o f s h a r p
typical
d i f f e r e n c e s
t h e
t h e
in
a p p a r e n t l y
scientific
t h e
1 9 7 8 ;
a r b i t r a r y
v e r s u s
o f
a n
calculations,
t a r g e t s
t h a t
o f
o f
d e c i s i o n s
i n s t a n c e ,
M a i n e
non
p o w e r
M e e h l ,
w a s
s u c h
size]
qua
e l e m e n t s
w e r e
F o r
b y
" I f
sine
o f
1 9 6 3 ;
significant
it:
mind
r e j e c t / a c c e p t
criticism
w r o n g .
cases
N
n e e d
T w o
as
a n d
t h e
n e g l e c t
m e a s u r e m e n t s ,
6 4 3 )
h y p o t h e s i s w e r e
t h e
S a v a g e ,
R i v e r ,
all
t h e
b e c a u s e
b e
a l w a y s
M i s s i s s i p p i
as
F i s h e r i a n
s u c h
a n d
the
i n s t i t u t i o n a l i z a t i o n
c o n s i d e r a t i o n s ,
6 0 , 0 0 0
o b t a i n e d
B o t h
d a m a g i n g
h y p o t h e s i s
t h e
statistics
a n d
c o s t
t h a t
of
t h a n as
a n d t o
easily.
a g a i n s t
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t h e
Statistics
i n s t i t u t i o n a l i z a t i o n fields,
b u t
F r e d e r i c i n g
f r o m
t h e i r
tics
b e
c o u l d
c h o l o g i s t s T h e
tics o n e o l d
in
a
a p p l i e d .
c o u l d
o f
n o t
M a n y
fact
t h e y
a s s i g n
t o
b y
s t r o n g l y
d e c i d i n g " e v e r y c h a n c e
o f
u n d e r s t o o d
as
i n f e r e n t i a l s o l u t i o n
t o
t h e
a t
least,
1 9 5 5 ,
p .
7 4 ) . T h e
a c o m p l e t e l y m e r e
t o o l ,
s e r v i c e t o
f o r
t h r e a t e n i n g least,
o l o g i c a l
t h e
level
6 . 4
u n s e a t e d
d e c a d e s '
a r o u n d
gists
r e v e r t e d
n o t
t o
t h e
n o w
o f
b e
t o o l d
t h e
b y
t o p i c
s e e m e d in
in
o v e r t h e o f
v o c a b u l a r y
a
A m e r i c a n
earlier
w i t h
t h e
T H E O R I E S
c o g n i t i v e t h e
o n
G e r m a n
v a g u e
t e r m s
f o r t h a t
easily
a b e
t h r o u g h
g i v e s
a
f o r m a l
a n d
c o m -
(Fisher,
k n o w l e d g e
b y
a reality. A s
t e s t i n g
in
a
t h e
s e e m e d
e l i m i n a t e d
p e r s o n a l
i n f e r e n c e s
w i t h o u t
1 9 8 7 a ) . at
level
t h e
o f
O F
p s y c h o l o g y ,
r e v o l u t i o n .
t h e
facts
p s y c h o l o g y
p s y c h o l o g y
c o n s e n s u s
is
s e e m e d
o n l y
n e w
( G i g e r e n z e r ,
u n i f i e d
T O
c o u l d
b e c o m e
i n d u c t i v e
light
b e l i e v e d
p r o c e s s e s "
t h a t
a
t h e
satisfying
at
as
c l a i m e d
S i g n i f i c a n c e t h e o r y
t o o k
d i s c o v e r
g i v e
is
failed
i n d i s p e n s a b l e
c o m e s
"as
h a v e
t h e m
c o n t r a s t ,
t o
e x p e r i m e n t a l
objectivity.
o r
s c i e n c e
a r r i v e s t o
o f
w h o
d e d u c t i v e
w h o
d e t e r m i n i s m
T O O L S
I 9 6 0
o f
p r o b a b i l i t y
o f
is
statis-
W h e t h e r
16),
statistical
i n f e r e n c e
u s e d
all
o r d e r (p.
o f
t h e
a h y p o t h e s i s
t h e o r i e s
k n o w l e d g e
t h a t
o b j e c t i v i t y
a b s e n c e
in
p s y -
w a s
s e r i o u s l y
( 1 9 3 5 ) ,
o f
statis-
t h o s e
scientists
statistics
o n l y
scientist
a n d
scientists, i n
t h a t
t r a d i t i o n a l l y
ideal, n a m e l y
r e i g n
Social
o f
m e a n s
for
n e v e r
s u c h
h y p o t h e s i s "
i n s t i t u t i o n a l i z a t i o n t h e
t o
b y
t e s t i n g .
p h y s i c i s t s
scientific
t h a t
social
a n d
statistics.
c e r t a i n t y
F i s h e r
c l a i m e d
p r e v a i l i n g
in
-
scientific
t h e
o f
h y p o t h e s i s
exist
p r o c e d u r e
c o u l d
F R O M
f o u r
o f
i n f l u e n c e ,
Sir
t e a c h -
3 2 8 )
m e t h o d s
i n f e r e n t i a l
m a n y
i d e a
n u l l t h a t
p r o m i s e d
t h e
t h e
said
a p p l i c a t i o n
a n d
n u l l
testing.
o f
m e c h a n i z e d
a n
w h i c h
w a v e s
t o
g i v e n
d r e a m
statistics
j u d g m e n t
A f t e r
t h a t
g r e a t
p r o p o s e d ,
p r o b a b i l i t i e s
t h e
o f a t r a d i t i o n a l
a l l o w
n o t
as
b e e n
t o
p r o b l e m
p l e t e ,
a d e g r e e
h a s
u s e s
F i s h e r
1 9 6 3 , p .
t h e
a n d
o n l y
i d e a
m a y
statistics.
o f
o f
T h e
o f
said
w h i c h
a p p l i e d
S k i n n e r
k n o w l e d g e .
A n d
h a v i n g
t o
o t h e r w i s e
h y p o t h e s e s .
d i s p r o v i n g
F.
t h e
i n s t i t u t i o n a l i z a t i o n
if e v e r
b e
B .
f r o m
t h e
significance
e x p e r i m e n t
n o t
s u p p o r t e d
n u m e r i c a l
b e t w e e n
c a m e
( S k i n n e r ,
d a t a
o n s l a u g h t
d e r i v e
s u s c e p t i b l e
211
c o n t e m p o r a r i e s
m e t h o d "
Physics,
o r
f a m o u s
yield
s o l u t i o n
p a r t i c l e s
t h e o r y
b e
a
r a r e l y
o f
c o u l d
o f
mind
l a b o r a t o r y .
t h e i r
t h e
t h a t
c o n t e x t .
c o m p o s e d
" t r u e "
s t o p
m e c h a n i c a l l y
scientific in
t o
D e s p i t e
m e c h a n i z a t i o n
d r e a m .
less
scientific
f a c t o r
c o u l d
m o d e l ,
o f
e x p e r i m e n t s
s e c o n d
d r e a m
a n
lieu
t h e i r
the
statistics
e x p e r i m e n t a l
a c c u s e d
in
d e s i g n i n g
i n f e r e n t i a l
t h e
B a r tie tt
"statistics
o f
of
m e t h o d -
M I N D
b e h a v i o r i s m
p r o g r a m s , as
b u t
t h e o r y .
A m e r i c a n
s u c h
Last,
t h e
w a s
p s y c h o l o m i n d ,
b u t
a p p e r c e p t i o n ,
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Statistics
212
restructuring, o u t l o o k
for
insight.
a n e w
p r o c e s s e s . scientists
a n d
T h e
c o n c e p t u a l
the m a i n
t h e
c o g n i t i v e
r e v o l u t i o n .
t h e
m i n d
s t a n d i n g s o r y
a n
o f
a
T h e
m i n d
f r o m
t h e
t h u s
i n c o m i n g
criteria, a n d v i e w ) a n
o r
t o
b e
p r e s e n t
as
e x p e r i m e n t a l
w h e n
w e
e x p l a n a t i o n . t w o
d e t e c t
a n
d i f f e r e n c e ) since t w o
t h e
a n d
object,
are
w h e t h e r
n e r v o u s
s y s t e m
a m o u n t A r o u n d
w a s
a
"signal")
W a l d
1 9 5 5 ,
G r e e n i n g
a n d
t h e o n l y
if
S w e t s ,
i.e.
type-I
a n d
b e e n
the o u r
o f
u n d e r s e n -
1 9 8 7 ) . s a m p l e s
t o
set
d e c i s i o n
t o
t h e
m o d e r n
object,
f r o m
m a d e
v i e w
r a n d o m
intuitive
theories,
that
M u r r a y ,
( a c c o r d i n g
is a n
a n d
e l e m e n t a r y
probabilities,
an
m e n t a l
C o m p u t e r s
a n d
p e r c e i v e
t h e
b e h a v i o r a l
c h a n g e d
f r o m
o f
t h e
w i t h
t o d r a w
this
m i n d
m e m o r i z e
statistician.
different
W e
fields
o f
false
t h e
m i n d
d i f f e r e n t
e x c i t a t i o n
f r o m
type-II
p o i n t
just
set
after a n d
error,
effect
o n e
b e e n
b e e n
the
w h e t h e r
a d d e d S u c h
t o
w i n e ,
d e t e c t i o n
d e r i v e d
o b j e c t
has
d i s c r i m i n a t i o n
e x c e e d s
that
a
s t u d i e d
d e t e c t i n g
m e t a p h o r
a n d
v i e w
a n d
o f
f r o m o n
o u r
b e t w e e n
a n o t h e r
m i n d
b y
w e i g h t i n g o f
r e s p e c t i v e l y
t h e
c o s t s
w e l l
as
t h e o r y
( n o w
a n d
called
S w e t s ,
t h e
t w o
respectively. o f
w h i c h
signal
N e y m a n - P e a r
calculates
"noise,"
o f
this
o b j e c t
( T a n n e r
signals, (as
essence,
t h e
t h r e s h o l d s
t h e o r y
is a n
o f
first
a n d
I n
t h e r e
h y p o t h e s e s
n o i s e "
m i s s e s
"the
t h e o r y " ) .
a statistician
is, t h e
differential
called
w h e t h e r
t w o
"signal p l u s
t h e
o f a b s o l u t e
o f
like
T h a t
has
a
( d e t e c t i n g
threshold.
d e t e c t i o n
b e t w e e n
alarms
if
threshold,
are
b r i g h t n e s s e s .
u s i n g
o n l y
" d e c i d e s "
noise,
s u g a r
o b j e c t s
that h a v e
E x a m p l e s
absolute
a
t w o
p r o c e s s e s
w h e t h e r
o c c u r s
"signal
is
b e t w e e n
a differential
b y
f o r
d i s c r i m i n a t i o n
e x p l a i n e d
a n
1 9 6 6 ) .
criterion
errors,
h a v e
t h a n
d e c i d e s
d i s t r i b u t i o n s
d e c i s i o n
alia,
w e
c o g n i t i v e
t h e p s y c h o p h y s i c s
(or
that
s c h o o l
that
a n d
w e i g h t ,
e x c e e d s
g r e a t e r
o r
-
d i s c r i m i n a t e
d e t e c t i o n
r e v o l u t i o n i z e d
p o s t u l a t e s
o n l y
f u n c t i o n s
inter
p s y c h o p h y s i c s .
stars
o c c u r s
detectability"
t o
s a m e
l o n g
( 1 8 1 6 ) :
a n
o f
t w o
h a v e
o b j e c t s
h e r e
that
influential
e l e m e n t a r y
t h e
H e r b a r t
t w o
a n d
t w o
h a v e
p r o c e s s e s
o f
m i n d .
a n a l o g y
testing:
T h e
t h e
nature
o n
p s y c h o l o g y .
b e g i n n i n g
coins
o f
calculate
say
t o o l s
( G i g e r e n z e r
u n d e r s t o o d , t o
the
w a s
theoretical vocabulary
j u d g m e n t
D e t e c t i o n
T o
n e w
a n
r e v o l u t i o n
u n d e r s t a n d
c o n c e r n e d
h y p o t h e s i s
e x a m p l e s
t o
p r o c e s s e s
the
i n f o r m a t i o n ,
a n
c o g n i t i v e
c o g n i t i v e
social
h a p p e n s find
t h e
are
o f
mind
p r e s t i g i o u s
statistician,
t o p e r f o r m
is w h a t
e v e n t ,
will
t o
c a m e
as
W e
r a n g e
d i s c r i m i n a t i o n
a n d
sources o f
intuitive
b r o a d
rising
l a n g u a g e
r e c o n s i d e r e d
statistics w e r e
as
T h e
i n d i s p e n s a b l e
w e r e
of the
t h e
t w o
c o r r e s p o n d
o t h e r
s o n 1 9 5 4 ;
s a m p l T h e n
a
p o s s i b l e t o
t h e
c o n s i d e r a t i o n s ,
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Statistics
s u c h
as
the
prior
r e p r e s e n t a t i o n t h e
a n s w e r
p r o b a b i l i t y
o f
a
"yes,
signal
t h e r e
of the
o f
signals).
(noise)
is
a
mind
is
signal"
Finally,
g r e a t e r is
213
if
t h e
t h a n
g i v e n ;
v a l u e
t h e
o f
the
d e c i s i o n
o t h e r w i s e
" n o ,
i n n e r
criterion,
there
is
n o
signal." T h e
m i n d
w a s
called
" N e y m a n - P e a r s o n t h e
hit
rate
rate
(i.e.
(i.e.
t h e
p r o c e s s i n g
w a s
(false
T h e
in
r e v i s i o n
in
the p o w e r
criterion)
f r o m
n o n - s e n s o r y
m i n d ' s T o tivity
a n d
criterion
type-I
o f
signal).
a n d
n e w a n d
o f
error.
in
a n e w
single, a n d
t h e
w e r e
t o
a n
b e
s c i o u s
s a m p l i n g
a
n e w
o f
t h e
o f
as
o f
a n
in
t h e
the
influence
spatial
o f
o f
" o p t i m a l
o f
type-I
w a s
r e v i s e d
a n d a n d
c o n s c i o u s
c o n n o t a t i o n s ,
causal
Gestalt
relationships
b y
a
T h e
d e c i s i o n
the
differ-
T h e
s u b -
subjective, o n
attitudes
n e w
q u e s t i o n
H o w
c o n c e r n i n g
t w o
t y p e s
o f
c a n
the
the
Finally, b y
a n d
theory.
In
c o n c e p t
statistical
s e e n
as
c o n -
p s y c h o -
o n l y o n e
t h e
w e r e
c o r r e s p o n d
k i n d o f
a
c o n c e p t s ,
" h y p o t h e s i s
a n d
sensi-
error
T h e s e
g e n e r a t e d
r e p l a c e d
their
o f
t h e
o f average error in
"decision,"
t h e
data,
d e t e c t i o n
t h e
a
m e r e
m i n d .
a n d
P e a r s o n ' s
"inference,"
o f
T h u s ,
misses.
e m e r g e d . a n d
o f
t h e
o f
a
m a n i p u l a t e d ?
research, h a d
data
o f
e x p e r i m e n t s :
individual),
N e y m a n
k i n d
d e p e n d i n g
q u e s t i o n
alarms
n e w
b e c a m e
o b s e r v e r .
o f
m e c h a n i s m s
p e r c e p t i o n
p e r c e p t u a l
distributions).
theory,
a v a l a n c h e
false
errors
k i n d
t h r e s h o l d
f r o m
a
m e a s u r e d
t h e o r y
d e t e c t i o n
testing"
the
u n c o n -
brain.
C a u s a l
T h e
o f
far b e y o n d
s e t t i n g
t w o
(as w e l l
s e t t i n g
type-II
( t h e
e x p e r i m e n t a l l y
e x p e r i m e n t s ,
p r o c e s s e s
f r e e d
o r
a l a r m
for a g i v e n
t h e o r y
sensitivity,
in recall tasks in m e m o r y
fixed
false
c o n c e p t
c o n c e p t i o n
( t h e
Pearson's
signal
q u e s t i o n
a n d
T h u s ,
v i e w
1 9 6 5 ) ,
m a x i m i z i n g
a g i v e n
T h i s
q u e s t i o n s ,
trast, t h e traditional m e t h o d s , s u c h as t h e m e t h o d physics o r
for
P e a r s o n ' s
p r o c e s s e s
t h e
a n d
criterion
the
signal)
N e y m a n - P e a r s o n - W a l d
rise
this
in
a
d e c i s i o n g o a l o f
as a statistician w e n t
c o n c e p t ,
c o n s i d e r a t i o n s
a n s w e r the
m i n d
g e n e r a t e d
m e a n s
g a v e
d e c i s i o n
o f
a
( T a n n e r ,
o f a test is m a x i m i z e d
n o n - s e n s o r y
p r o c e s s e s
that
g e n e r a t e d t h e
it
t h e
N e y m a n
c o s t - b e n e f i t
e m e r g e d
t o
t h e in
t h e
o f
N e y m a n
s e n s o r y p r o c e s s e s
b e t w e e n
a n d
o f
t h e
s e p a r a t e d
part
t o
(hit rate)
t h r e s h o l d
b e t w e e n
jective
d e t e c t i o n
d e t e c t o r "
rate).
l a n g u a g e , t h e
if it a d o p t s
" d e t e c t i o n "
a n a l o g y
p r o c e s s e s
e n c e
c o r r e c t
m e t a p h o r
o f
a n a l o g y
t h e
a l a r m
n e w
c h a n g e
o b s e r v e r , "
e r r o n e o u s
tests," w h e r e error
a " N e y m a n - P e a r s o n
relations
psychology.
b e t w e e n
e v e n t s
r e a s o n i n g
h a d
b e e n
s t u d i e d
Psychologists that
p r o d u c e d
b e f o r e
analyzed
I 9 6 0
the
p h e n o m e n a l
u n d e r
temporalcausality
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Statistics
214
( M i c h o t t e , r o c k e t e d
[ 1 9 4 6 ]
w h e n
a c c o u n t
o f
1 9 6 3 ,
a c a u s e
n a m e l y
p e r f o r m i n g
F o r
illustration,
jects t h e
in
a
a r t
P a u l h a s
a l m o s t
i n g ) :
t h e
( t i m e ) ?
F i s h e r i a n
m i n d
variables,
b e h a v i o r .
K e l l e y
p o s s i b l e
" p e r s o n " c u l a t e
a
b e c a m e c h o l o g y ,
a n d
t h e
A N O V A - m i n d D a n i e l ,
for
o f
fastest
t h e
a n d
v a r i a n c e
e x p a n d i n g
t h e
1 9 7 0 s
A
C A S E
e x p e r i m e n t a l
W u r z b u r g
s c h o o l
t h e o r y .
T h e
c e s s o r s
o f
s a m e
t h e
e.g.
t o
m o d e l
a r e a
1 9 8 0 s
i n
o f
a r e
at
b y
it.
p r o v i d e t h e
w i t h
t h e
o f
o r
t h e
t h e
t h e
i n t u i i n d e -
o b s e r v e d
for
is
e a c h
h i g h
t o
o f f o r
s h o u l d
cal-
P a u l .
causal
e m p i r i c a l
p a i n t -
t h r e e
m i n d
c a u s e
w h a t
t h e
( e n t i t y ) ,
o f
P a u l
a s k e d
a t t r i b u t i o n
e x p e r i m e n t a l
w e l l
sees
( M c A r t h u r ,
variability
t h e
s u b -
past,
b y
p a i n t i n g
a t t r i b u t e
t h e
h e
t h e
tests a n u l l h y p o t h e s i s
r e s e a r c h
S T U D Y : U
T h e
t o
s t u d y in
o f
b e
o r
said
p e r c e i v e
t o
D
E
p e r c e i v e
t h e
stick
R
social
r e s e a r c h
d o c u m e n t e d
p s y -
o n
t h e
( F i s c h
a n d
in
t h e
t h e
a r e
n e w l y i n g
t h a t
u s e d
1 9 2 0 s . o f
i n
s a w
t h e
r e l a t i o n s
i m m e d i a t e as
r e l a t i o n s
a r o u n d
a n
t o
w i t h
s o l v e
i n s t r u m e n t
t h e
p r o b a b i l i t y
e x p e r i m e n t s ,
f u n c t i o n a l as
1 9 0 0
t h i n k i n g
f u n c t i o n a l
K o h l e r ' s
in
m e n t i o n e d
s c h o o l ,
T h e y
t h e
s t a r t e d
n o r
G e s t a l t
f o u n d
T O
p r o b a b i l i t i e s
n e i t h e r o f
T H I N K I N G
U N C E R T A I N T Y
t h i n k i n g
r e o r g a n i z a t i o n
classical e x a m p l e s h a d
F R O M
w i t h o u t
G e r m a n y
m u s t
N
h u m a n
W i i r z b u r g e r s
r e s t r u c t u r i n g
a c h i m p a n z e e -
t o
w e r e
c o v a r i a t i o n
p r o p o r t i o n s
T h i n k i n g
p a r t s .
I n
d o ,
h y p o t h e s e s .
is e n t h r a l l e d
e n t h r a l l e d
t h e r e f o r e
m i n d
scientists
p a i n t i n g . "
t h e
( A N O V A )
a n d
J U D G M E N T S
sive
( b e i n g
t h e
p a i n t i n g
s u b j e c t s
e x a m p l e ,
a n d
n e w
1 9 8 2 ) .
6 . 5
T h e
T h e
" t i m e " ;
p e r s o n ,
a
c i r c u m s t a n c e s ,
m i n d
c o m p l e t e l y
n u l l
p a i n t i n g .
c o n s t r u c t e d
a n d
s k y -
p r e s e n t e d
b y
s a m e
t h e
a b o v e
d i n o s a u r i a n
i n
is
issue
t h a t
t e s t i n g
p a i n t i n g
( p e r s o n ) ,
a b o u t
t h e
" e n t i t y "
F - v a l u e
t h e
a
t h e
b e h a v i o r a l
a n d
t h e
1 1 0 ) .
P a u l
t h a t
I n
for
analysis
t h e
p .
entity,
as
o t h e r
b y
p r o b l e m
p e r s o n ,
w a y
sees
e v e r y
i n f o r m a t i o n
a s s u m e d
l o w
h i g h
K e l l e y ' s
T h e
causes.
a n d
w h o
in
p o s t u l a t e d
i n f o r m a t i o n
b e h a v i o r
w i t h
h e
is e n t h r a l l e d
e n t h r a l l e d
d o
I n t e r e s t
p r o p o s e d
v a r i a n c e
" P a u l
o b s e r v e d
t o
1 9 6 7
f o l l o w i n g
1 9 7 3 ,
1 9 5 8 ) .
s a m e
o f
a l m o s t
K e l l e y ,
c a u s e
c i r c u m s t a n c e s
t h e
b e e n
t h e
t h e
a n y o n e b y
mind
e s s e n c e ,
analysis t h e
H a r d l y
in
c a u s e d
p e n d e n t
a n
in
I n in
e x p e r i m e n t :
a l w a y s
p r o b a b l y
K e l l e y
effect
e n t h r a l l e d
q u o t e d
H a s
a n
c o n s i d e r
typical
also
1 9 7 2 ,
tive
t o
m u s e u m .
is
H .
the
H e i d e r ,
a t t r i b u t i o n .
a t t r i b u t e s b y
1 9 5 2 ;
H a r o l d
causal
of
t o
a
a
s u c -
s u c c e s b e t w e e n
in
w h i c h
p r o b l e m r e a c h
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t h e
Statistics
fruit
h a n g i n g
c l i m b ,
stick
K a r l
h i g h
in
t o
t h e
w h o
t h i n k i n g ,
p h e n o m e n o n n e x t
o f
is
e q u i l i b r i u m .
T h e
h u m a n
b e i n g
o n e
free
s t r o y i n g p p .
1, T o
o f
s o l v e
t h e
b y
at
a n d
J u s t
" w h o l e "
t h e
t w o
p l a t f o r m
u p o n
w h i c h
b y
in
o n e
application
t h i n k i n g
t o
o f
c o n t i n u e
rays
a n d
s u r r o u n d s
at
b y
w h a t
t h e
it?"
t h e i n t o "the
i n t o
a n
e x a m p l e s :
n u m b e r s . "
t u m o r ,
t o
until
settles
typical
p r i m e
s t o m a c h
t h e s e
are
Gestalt
"tips o v e r "
s y s t e m - u n d e r - s t r e s s
p r o b l e m s
o f
in a n a l o g y
s t r u c t u r i n g
r e s t r u c t u r i n g s
n u m b e r
w h i c h
w e
a
tences.
t h e
tissue?"
-
( B )
( A )
" G i v e n
p r o c e d u r e
s a m e
t i m e
( D u n c k e r ,
in
A
active
a n d
p r o b l e m
t o
a
c a n
a v o i d
[ 1 9 3 5 ]
b e
o f
s u c h
t h e r e
s u c h
m u s t
until
d e -
1 9 4 5 ,
successively
a
exists
a p r i m e
t h e r e f o r e
p r o d u c t
t o
s o l u t i o n
r e f o r m u l a t i o n s
r e p r e s e n t e d
t h e
D u n c k e r ,
p r o b l e m
n u m b e r / *
" O n e
" T a k e
a n
in
u s
o r
t h e
as
o f
a
a
is
m i g h t
greater
n u m b e r ,
be:
o n e , "
I m u s t
c o n s t r u c t
a
p r o d u c t , "
all p r i m e
o n e
try
n u m b e r
a n d
finally
n u m b e r s
read:
f r o m
p o i n t
different
t h e
t h e
t h e
rays
1
t h e t o
t h e
t h r e e
intensity b e
tissue
g r o u p s
that
o f
m a d e
it
t h e
is
its
differed t w o
the
b e i n g
passive
h a d as
t h e
D u n c k e r
w o u l d
f r o m
t i m e s t h e
last
injuring
w h i c h
for
c o n t e x t u a l
d e s t r o y
rays, t h e
w h i c h
p r e s e r v e d
w h i c h
t o o ,
in
e x p e r i m e n t s
instance,
t h u s
tissue,
for
o t h e r
in
f r o m
h e a l t h y
t w o
case
w o u l d
e m p h a s i z e s
his
versions,
passive rays
a n d F o r
objects
is d e c i s i v e
( a l t h o u g h
t h o u g h t .
o f
decisive
f r o m
g i v e n ,
" H e a l t h y
s h o w e d
w i t h
o f
" T h e
is
c o n c l u d e d
t h e
p r e v e n t
b e t w e e n
historical
t o
-
l a y o u t
t h e p r o b l e m
p r o b l e m
t w o
p r o t e c t
v e r s i o n s
o f
e x a m p l e
in
p h r a s i n g
dealt
t h e
f l o w
w a s :
o n e
active
o n e
t h e
v e r s i o n
c o u l d
passive
o f
particular
relations
c o n t e x t
active
v e r s i o n
c o u l d
their
specific
o n
t h e
D u n c k e r
P r o b l e m
f r o m
that
w o r d s ,
t h e
i m p a c t
passive
active
tell
p h r a s i n g
T u m o r
H o w
m a j o r
l a w s
"layout"
c o m p a r i s o n
t h e
original
e x i s t e n c e b y
o t h e r
t h e
rays?" T h e
tissue.
a c c o r d i n g
p r i m e
restructurings.
H o w
T h e
d e s t r o y e d .
in
active
t o o .
t h e
c a n n o t
s o l u t i o n
c h a n g e
T h e
tissue,
t h e
c h a n g e
all h a d
in
p r o v e
f o l l o w e d
t h e
a
p r e s e n t e d
a n y
see, t h e
o f
m e a n s ,
n u m b e r
for
G e s t a l t
c h a n g e
factors
p r i m e
w h i c h
field
m e a n i n g ) ,
T h e
a
1."
t h e
d i r e c t i o n
g i v e n
p
a d d
as
a
it,"
t h e
visual
t h e
t u m o r
that
" T o
t h a n
arriving
b y
i.e.
r e s t r u c t u r e
p r o v e
g r e a t e r
o n l y
elaborate
w h e r e
i n o p e r a b l e
a p r o b l e m
o r
c o n s t r u c t
that
m o s t
successive
infinite
tissue
s u c h
F o r
f o l l o w e d
t h e
as
9).
m u s t
t o p
a n
t h e
h e a l t h y
attained.
t o
215
table
r e s t r u c t u r i n g
f o l l o w i n g
w i t h
r e f o r m u l a t e
"I
T h e s e
is a n
the
figures,
c o m p l e t e d , "
t h e r e
h i m
d e v e l o p e d
reversible
o r g a n i z a t i o n
that
the
c o n s i d e r e d
structuring.
" P r o v e
a n d
mind
h a n d .
D u n c k e r ,
t h e o r y
a b o v e ,
of the
s e n -
h e a l t h y h e a l t h y t h u s
b e
injured o n e
r e c e i v e d
the t h e
m a n y
subjects
n o n e
o f
rays. that
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t h e
216
Statistics
e x p e r i m e n t e r s s h o u l d t h e
b e
by
E v e n
t h e s e
in
o f
w a s
t h o u g h t
m e r e
w h e n
o b t a i n
s o l u t i o n .
d o n e d
o f
t h e
s p e e c h "
o f
several
s t u d y
o r
m e n t a l
h a d
already
national
p r e e m i n e n c e
t h e
figures
N a z i
r e g i m e ,
reasons.
S o m e
Selz)
until
t h e
u t i o n ,
c h o l o g y .
m e r ,
t h e
t h e B u t
t h e y
f o r c e d
w h e n
it
o f
h u m a n
r e a p p e a r e d
statistics
a n d
i g n o r i n g
v a r i o u s
o t h e r
s o r y
o r
that at
o t h e r
T h e t o
m o r e t y p e tics
s u c h
inter-
m o s t
a f o u l for
in
o f
o f
t h e
political ( M a x
A u s c h w i t z
D u n c k e r ) . c o g n i t i v e
m a j o r
h e r e
in
psy-
that
w i t h
d e d u c t i v e
N o t r e v o l -
t o p i c
v o c a b u l a r y ,
deal
as
w h e r e
e m i g r a t e
t h e
n e w
a b a n -
as its
o r
( K a r l
as a
shall
t h e
b o t h
t h e
p r o p o s e d
arose
after
o f
t h e
for-
r e a s o n i n g
o r
l i n g o
t h o u g h t
m i g h t
t h e
t i m e
s a m e
p e r c e p t i o n , m i g h t
statistics
t o
E d w a r d s s t u d y
" h u m a n
p r o b l e m s .
w i t h
statistics
t h e s e h a d
b e
t h e
v i e w
r e c o g n i t i o n
f r o m
i n v o l v e
as
statistical
statistical
that
s e n -
m e m o r y , calculation
statistical p e r s p e c t i v e s b e e n
calcu-
institutionalized
e m e r g e d as
t h e
in-
e x p e r i m e n t e r .
W a r d
first
at
1 9 8 7 ) . A l l
I n
e x p e r i m e n t e r ' s
T o g e t h e r
i n t u i t i v e
h u m a n
p r o c e s s e s
t h e
a r o u n d
u r n - a n d - b a l l s
o b v i o u s . h e
b e e n
o f
o f
a s
d i s c r i m i n a t i o n ,
s h o r t l y
f a s h i o n a b l e
as
c o m p l e t e l y
c o n -
" s u b v o c a l
1 9 3 0 s ,
lives
b y
r e a p p e a r
a p p r o a c h e s ,
be,
M u r r a y ,
t o o l
g r o u p
h a v e
s h o u l d
a n d
a n d
I 9 6 0 ,
d i s p e n s a b l e
n a t u r e
c o g n i t i v e
( G i g e r e n z e r a r o u n d
t h e
least,
d e t e c t i o n
a n d
e r o d e d
W e
just
t o
solving.
v i e w
lation,
w a s
a
their
t o
ran
t o
e m i g r a t i o n
c o m p u t e r s .
T h i n k i n g
T h e
lost
as a
G e r m a n y ,
a n d
o r
P r i m e
sufficient
1 9 5 0 s
w e r e J e w s ,
o t h e r s after
I n
b e
theory.
b e h a v i o r i s m
s c h o o l s
early
c o u l d
the
t h i n k i n g
1 9 2 0 s
G e s t a l t
t h i n k i n g
w i t h
t h e
retire
b e h a v i o r i s m
a n d
m o v e m e n t s
their w i v e s
t o
suicide
f o r e i g n
as
n o r
W a t s o n ' s
r e d u c e d
that
probability
necessary
1 9 4 0 s
t h i n k i n g
C o n s e q u e n t l y ,
s u c h
t e n d e n c i e s . "
a n d
o r
o f
p o s e d ,
B.
h u m a n
p r o b l e m s
laws
t h e
d u r i n g
K o h l e r ) ,
n a m e l y
p r o b l e m
o f
W u r z b u r g
c o m m i t t e d
in
a n d
r e s p o n s e
w a n i n g
b e c a u s e
s t u d y
d e c l i n e d
track
the
n e i t h e r
A m e r i c a , J.
o f
w a s
W o l f g a n g o r
w a s
o f
that
calculation.
w i t h
w e r e
c o n c e p t s ,
lost
w e r e
1 9 6 0 s ,
d i d
tools,
of
either
W e r t h e i m e r , ( O t t o
I n
" c o m p e t i t i o n
p s y c h o l o g y
k e y
p r o b l e m s
forces.
o f
s t u d i e d
application
t h i n k i n g
t h o u g h t
statistical
yet
calculation
p s y c h o l o g y
s e q u e n c e
o r
mind
s c h o o l s
o f
n o t
m a t h e m a t i c a l
P r o b l e m ,
T h i s
m a j o r
t e r m s
calculation
N u m b e r a
t w o
u n d e r s t o o d
n a t u r e
s o l v e d
in
of the
H a r o l d
that e x p e r i m e n t e r s
at
t h e
t h o u g h t
U n i v e r s i t y
p r o c e s s e s ,
i n f o r m a t i o n E d w a r d s ' t o o l
a n d
L i n d m a n
a n d
u s e B a y e s i a n
M i c h i g a n
w h i c h
p r o c e s s i n g , "
w o r k , t h e
o f
t h e
u s i n g
d o u b l e
subject's
t h e y
role
m e n t a l
L e o n a r d J.
h e
called
in
B a y e s i a n o f
statis-
p r o g r a m
S a v a g e ,
statistics, a n d
s e e m s
in
at t h e
is
1 9 6 3 , s a m e
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Statistics time investigated w h e t h e r as probabilities are
of the
mind
217
subjects learn f r o m
revised
by
Bayes'
experience in the s a m e
t h e r o e m .
T h e
first
part
g r a m , Bayesian statistics for e x p e r i m e n t e r s , w a s a c o m p l e t e e x p e r i m e n t e r s very
interested
F o r
the
mass
m e t a p h o r b e c a m e the
already h a d in
the
a m o s t
analogy
Bayesian-type
in
o f
following
Slovic,
analysis the
E d w a r d s '
day
and o n
that
they
find
the
a n d
believed limits o f
Phillips,
attack" terns
and o n
Bayesian
the
by a simpler
u p d a t e d
the
w o u l d
m i n d
o f
w e
h o w
a n d
by
n e w
a n d
s e e m e d
type o f p r o b l e m ,
central
the
n e w
in
their
o n
the
Lawrence
situation
Phillips
o f
to
be
w h i c h
than
t o o
a
1; f o r
c o m p l e x
was
b e c a m e
estimates
was
b o o k b a g - a n d - p o k e r - c h i p
their
p r o b l e m s .
H e r e
prior
the
a
than
"conser-
for
w e r e is
pat-
e x t e n t
s o o n
for
urns-and-balls p r o b l e m s . T h e s e
" e n e m y
(dot
the
this and o t h e r
a standard
a
observations.
lesser
a n d
to
L i n d m a n ,
w h i c h was d u b b e d
the probability
to m o r e
revise n e w
and
in o r d e r
situation
o f
to
his
like a Bayesian,
to
basis
probability
kind
o n
D .
1968; E d w a r d s ,
h a d
the
the
m e t a p h o r
R e p o r t i n g
c o m p l e x
subjects
(e.g.
focus
twelve possible observations
T h e
s u m s u p
shall
the
p h e n o m e n a
L. H a y s ,
fairly
still a
uncertainty
is a B a y e s i a n .
(Edwards,
at
generated.
a fairly c o m p l e x
hypotheses
the
are
constructed,
data
dictate, a p h e n o m e n o n
situation
the
statistician
f o u r possible h y p o t h e s e s , s u c h as
revised
tried-and-true as
a n d
p r o b l e m s
kind
original
in general added
c o m p l e x
years, the
four
F u r t h e r m o r e ,
hypotheses
the
n e e d
screen).
generally
Bayes' t h e o r e m
the
behavior
T h e
T h e
schools.
p r o m i n e n t
u n d e r
o u t
that William
shower,"
the
been
that stimulated
w e r e
thinking
j u d g m e n t
p r o b l e m s ,
they w o u l d
for
have never
the
statistics. B u t
to
that the m i n d processes information
probabilities
vatism."
n e w
declared
radar
p r o -
since
Bayesian
similar
shall w o r k
a n d
was w h e t h e r
" m e t e o r
subjects
o n
questions,
radar system w i t h
the
a
1982). T h e r e f o r e ,
W e
for,
1965).
c o m p u t e r i z e d
like
revision
statistical
research
questions,
a n d h e suggested
o f
these.
original hypothesis, he
w o r k s
flop,
statistical
statistics w a s
o f probability
Tversky,
l o o k e d
question
m i n d
various
o f that
thinking.
research
explanations
N e w
o f
psychology
present
transformed o f
b e t w e e n
research p r o g r a m ,
p r o b l e m s
the
the
K a h n e m a n ,
debates
reasoning
influential
c o m p u t e r
issue
raging
o f researchers, statistics w a s
that
beginning
the
their statistics. E x p e r i m e n t e r s
way
four
reasons, replaced following
n o w
often
prototypical
e x a m p l e : " T w o contains chips a n d
urns are 7 0 % 3 0 %
red
filled
w i t h
chips
red. T h e
a n d
a large n u m b e r 3 0 %
blue.
e x p e r i m e n t e r
flips
o f p o k e r
T h e
second
a fair c o i n
chips. T h e contains
first 7 0 %
u r n blue
to select o n e o f
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the
2 1 8
Statistics
t w o
u r n s ,
s o
s u c c e s s i o n e i g h t
r e d
s e l e c t e d p.
t h e
o f
c h i p s
a n d u r n
p r i o r
is
p r o b a b i l i t y
f r o m
f o u r
b l u e
t h e
of
the
f o r
t h e
s e l e c t e d
chips.
W h a t
p r e d o m i n a n t l y
mind
e a c h
u r n
u r n . is
r e d
is
.50.
S u p p o s e
y o u r
t h e
r e v i s e d
o n e ? "
H e
t h e n
d r a w s
s a m p l e
c o n t a i n s
p r o b a b i l i t y
( P e t e r s o n
a n d
a
t h a t
B e a c h ,
t h e
1 9 6 7 ,
32) T h i s
t y p e
c a u s e
(a)
b l u e )
a r e
o f
o n l y
p r o b l e m
t w o
as
p(HR)
is
p r e d o m i n a n t l y
r e d
o n e , p(HR
d a t a
D
( e i g h t
t h e
p r o b a b i l i t y
r e d
t h a t
t h e
a n d
D
a r e
d a t a ,
If
t h e
s i m p l e r
h y p o t h e s e s
c o n s i d e r e d
s y m m e t r i c a l .
is
(c)
p r i o r
b e
r a d a r - s c r e e n
t h e
( b )
is
t h e
b l u e )
o n l y
t h a t
t h e
p o s t e r i o r
h a s
o b s e r v e d
b e e n
i f HR
p r o b l e m s
t w o
c o m p o s i t i o n s
p r o b a b i l i t y
| D )
will
t h e
c o n s i d e r e d ,
a n d
f o u r
t h a n
e v e n t s
o f
t h e
o b s e r v e d ,
is t r u e ,
( r e d
u r n s
s e l e c t e d
p r o b a b i l i t y
u r n o f
B a y e s '
o r a r e
is
HR
a n d p ( D
t h e n
b e -
t h e after
| HR)
is
t h e o r e m
states
( H
P
T h e
\ D ) = p ( H
K
u n c o n d i t i o n a l
p ( D )
If y o u
=
t h i n k
p ( D
| Hs)p(H,)
t h a t
t h e
r e d
m a j o r i t y
s u b j e c t s
ability
f r o m
i n g
E d w a r d s
o f
I n t e r e s t 1 9 7 0
0 . 5 0
in
D a n i e l
r e v i s i o n
K a h n e m a n ,
cab
was
G r e e n
and
(i)
8 5 %
identified
n e w
as
k i n d
involved
in
a hit
A m o s
a n d
operate
in
t h e o r e m ,
m e n t a l
e x a m p l e
6 2 ) :
cabs
the
in
city.
are
G r e e n
court
Question: rather
T h e
in
W h a t than
8 0 %
the
o f
w h i c h
cases
is t h e p r o b a b i l i t y
is t h e
a g r e e
revises
w a s
t h e
p r e -
w i t h t h e
t h e
p r o b -
m a j o r
find-
a n d
that
p o s e d , r a t h e r
t h e
as
P r o b l e m
T w o
given
1 5 %
presented
w e r e erred
G r e e n ) in
2 0 %
a r o u n d
p r o b a b i l i t y
u r n s - a n d - b a l l s ( T v e r s k y
cab
the
are
w h e n
s a m e
t h a n
night.
are
and
q u i c k e n e d
companies,
following
Blue,
(ii)
o f
the cab involved
witness the
the
data:
A
witness
cabs
u n d e r
with a sample o f cabs the
a n d
m a d e
(half
correct
cases.
in the accident was
Blue
G r e e n ?
s t r u c t u r e
p o k e r - c h i p
o f
u r n
tested his ability t o identify
Blue
half
at
Y o u
of
identifications
t h e
y o u
r e v i s i o n
C a b
accident
the
city
t h e
visibility conditions. W h e n a n d
t h e n
t e s t i n g
p r o b l e m s is
run
t h e c a b as a B l u e cab. T h e
w e r e
t h a t
h o w e v e r ,
T v e r s k y
the appropriate w h i c h
f o l l o w s :
(6.2)
0 . 7 5 ,
c o n s e r v a t i v e
o f
a n d
p .
the
as
c o l l e a g u e s .
1 9 8 0 ,
Blue,
c a l c u l a t e d
p r o b a b i l i t y
a b o u t
B a y e s '
T h i s
b e
| HB)p(H*)
t h e
t o
" r e a l - w o r l d "
f a m o u s
the
of
his
K a h n e m a n
A
0 . 5 0
(6.1)
c a n
p ( D
raises
t e s t e d .
a n d
this
d a t a
0.97.
p ( D )
+
f r o m
t o
p r o b l e m s
p r o b l e m s .
A
o n e
) / p ( D )
R
p r o b a b i l i t y
d o m i n a n t l y o f
) p ( D \ H
R
o f
t h e
p r o b l e m s .
C a b
T w o
P r o b l e m k i n d s
o f
is
t h e
s a m e
i n f o r m a t i o n
as a r e
in
t h e
b o o k b a g - a n d -
p r e s e n t e d ,
t h e
p r i o r
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Statistics
probabilities/>(H), also
called
p o s t e r i o r v o l v e d w a s
t o
in
t h e
hit
c o n c l u d e d •prior
that
In
f r o m t h e
a n d
w a s
for
t h e
o t h e r
if
t h e
has
that
m e a n s
S i n c e
rate
T h e a n d
w a s
the
a s k e d
(that
e s t i m a t e d
their
0 . 4 1
as
identifications),
o t h e r
k i n d
cabs).
T h e
o f
t h e
c a b
in-
subjects
t h e
is n u m e r i c a l l y
H ) ,
for
t h e
b y
|
"cor-
e q u i v a l e n t the
a u t h o r s
i n f o r m a t i o n ,
s a m e
t h e
c o n c l u s i o n
w a s
p o s e d .
w i t h
w a s
c o n s i d e r e d
o t h e r
"biases"
r e a s o n i n g . as
t h e
base o f
w e l l - e s t a b l i s h e d
a n d
that
"errors"
d u r i n g
largely
1 9 7 0
a n
has
It
a b o u t
t o
n o t
face.
B u t o f
i g n o r e d
e v i d e n c e
1 9 6 0 s
the
c o n -
diagnostic
c o n s e r v a t i v e b e e n
b e
v e r y
t h e
n e w
t o o
o l d
d u r -
a n s w e r e d , d i s t u r b i n g facts
u n d e r l y i n g
as
fact,
C o n s e r v a t i s m ,
yet
s h o u l d
r e v e l a t o r y
largely
fact.
b e
as
t h e
i g n o r i n g
s e e m e d
p o s e d .
as
facts
a n d
after
n e v e r d o
a
w e l l - e s t a b l i s h e d
p e o p l e
r e c e i v e d
o p p o s i t e
Recall
rates
w h y
s u d d e n l y
enthusiastically
t h e n
calculate
correct
B l u e
is
p r o b a b i l i t y
a n s w e r
the
p r o b a b i l i t i e s p ( D
subject
B l u e )
m e d i a n
( 1 5 %
a l m o s t
facts
t h e
h o w e v e r ,
a n t i - c o n s e r v a t i v e
it
a n d
w a s
i g n o r e
c o n s i d e r e d
q u e s t i o n
219
p o s t e r i o r
n e g l e c t
h u m a n
T h e
( 8 0 %
rate
t o g e t h e r
o f
established
heuristics,
t h e
overweighting
b e c a u s e
instead
T v e r s k y ,
p r o b l e m s
b e e n
1 9 6 0 s
o n l y
a n d
base
base
fallibility
i n f o r m a t i o n .
a c c i d e n t
subjects
o r
p r e s e n t e d
h o w e v e r ,
i n g
their
1 9 7 0 s ,
s e r v a t i s m
r u n
i n f o r m a t i o n
p r o b a b i l i t y
d r a w n
m e d i a n
mind
rates," a n d
i n f o r m a t i o n . "
a n s w e r .
d i a g n o s t i c
"base
T h e
a n d
K a h n e m a n
B a y e s i a n
t h e
called
" d i a g n o s t i c
probability.
0.80.
rect"
also
of the
t o
w e r e
m e n t a l b e
true.
D i s c o n t i n u i t y
T h e
m e t a p h o r
t h e
research
l a n g u a g e p e c t e d w i t h m a j o r
t o
t h e
talk
t h e
t h e
s t a t e m e n t s
o f
least
s h o w n
this h o n e s t p o s e d
in
f o u n d
that
l e m s .
T h e
t h o u g h t o r
k i n d
s t a t e m e n t , fifty
a w a i t first
flow.
association
is F o r is
a
o f
in
n o t
H u m p h r e y a b o u t
G e s t a l t
m o t o r
o f
a n
b y
the
c a n
us
f o u n d
a n s w e r ,
starts
w i t h
t h i n k i n g ,
the b u t
a n d
1 9 5 0 , T h e
G e o r g e a n d
A .
p s y c h o l o g y t h e y
(p.
t h e
a n d
o f
rejected
e x -
( 1 9 8 2 ) .
o f
o r
in
Slovic,
o n
t h r e e
" m o t o r "
theorists
S.
far,
t h e
m e t a p h o r .
t r a v e r s e d "
s u m m a r y
fashionable
a r o u n d
Biases
v e r y
c h a n g e d
c o m p a r e
n e w
b e
and
b e
t h e
n e w
shall
e x p e r i m e n t
m u s t
a w a i t
a
K a h n e m a n ,
b r o u g h t
his precise
that
q u e s t i o n
instance,
years'
w h i c h
h e g i v e s
D .
radically
as it a p p e a r e d
Heuristics
"Fifty
r o a d
t h e o r y .
t h e
t h i n k i n g ,
p o s i t i o n s
a n d
h a v e
this, w e
i n f l u e n c e d
t w o
that
years
t h e
o f
statistician p r o d u c i n g
s h o w
Uncertainty:
r e a s o n i n g
t h e s e
m e r e l y
( 1 9 5 1 )
c o n c l u d e s
t h e
t h a n
m o s t
t h e s e
Under
o r
intuitive
things. T o
field
Thinking
T v e r s k y ' s Judgment
t h i n k i n g
o l d
a n
p s y c h o l o g y
o f
H u m p h r e y
as
rather
a b o u t
o f
part
H u m p h r e y ' s
o f
m i n d
q u e s t i o n s
f u t u r e
that
o f
h a v e
3 0 8 ) .
m a i n t h e
m a i n
m o t i v a t i o n
p r o p o s e d
idea
A f t e r
q u e s t i o n s
persistent
t h e
at
facts p r o b o f
t h e
that
habit
instead
their
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220
Statistics
h y p o t h e s i s is
h o w
o f
t w e e n
a p r o b l e m N o n e
Bayesian,
g o o d
o f
o r
t o
art
in
the
1 9 5 1 .
n e w
p o i n t s
a n d
w i t h
o f
t h i n k i n g
in
h e r e
w h e t h e r
w h a t
s o l v e s
t h i n k i n g
t h e
irrelevant
l a n g u a g e
t h o u g h t
is
free
issues,
w h i c h
p u t e s ,
are
tician.
I n
f r o m
t h e
m a i n l y
T h i s
w i t h
l e m s
p o s e d
P r o b l e m ,
a n
c o n t e n t ,
b o t h
t h e
t h e
n e w
in
a
c h a n g e c o u l d
s o l v e d l e m s
b y
single
research
in
t h e
a n s w e r . c o r r e c t
that
T h e
a n s w e r .
t h e
b y
A s
as
t h e
n o w
i.e.
m e e t s ,
a n d
t h e
a n
if
d e v i a d u r i n g
facts
s u c h
e v e n
as
if
t h e
d i s t i n c t i o n
b e -
w h e t h e r o f
f o u n d a t i o n
as
as
a n a l y z e d
m a j o r i t y
t h e s e o f
intuitive
c o n c e p t s
dis-
statis-
a n d
a n d
t h e
this
w e
p e r i o d
o f
in
shall s o o n this
a u t h o r s
t h o s e
h a d
is
in
t h e
T h e
s h o w ,
as
f e w
a p -
i m p o r t a n t
w e r e
m o r e
n e w in
a n
o f
C a b
principles s c h o o l n o t
c h a n g e . t h a n
a n
o n e t o
o n e .
ideas
b e
P r o b reas-
h a v e
illusion
incidental
association
p r o b -
t h e
c o u l d
d e s i g n e d
this is o f t e n
is n o t
h a n d - i n -
W u r z b u r g
a b o v e ,
typically
contrast,
t h e
w e n t
f u n d a m e n t a l
p r o b l e m
a n o t h e r
illusion
t h o u g h t
o f
c o n s t r u c t e d
is
c o u r s e ,
calculation,
a p p l i c a t i o n
" T u m o r "
t o
o f
c o n s t r u c t e d .
statistical
p r o b l e m s ,
H o w e v e r ,
n a t u r e
is
f e w
t h i n k i n g
q u e s t i o n
far b e t w e e n ,
p r o b l e m
p r o b l e m s
L i n k e d
n e w
a n d
t o
A
animal,
t h e
t h e
m i n d
r e f e r e n c e s
for
t o n e
T h e
a n d
p e r s p e c t i v e ,
o f b y
pre-statistical
T h e
1 9 8 1 ) .
t y p e
s o l v e d
s u c h
t h e
o r
i n c l u d e
t h e
o n .
incidental
e x p e r i e n c e s
t h i n k i n g ,
s o
t h e
calculations,
m u s c u l a r
basis
o n
f e w
theoretical t h e
calculation.
C o h e n ,
h o l d s
theory.
p o i n t s
t h i n k i n g ,
o f
state
m e t a p h o r .
biases,
subject
o f t o
t h e
p e r f o r m s t h e
t h e
o r
t h i n k i n g
is
i n t r o d u c t i o n s .
generally,
s c h o o l ,
p o s e d
o n a b l e
in b e
or, m o r e
G e s t a l t
in
h u m a n
m i n d
in
d e f i n e d
"correct"
the
t h e
b y
neglect.
o f
statistical
e x p l a i n
a n d
literature
historical
t h e
factual
are
base-rate
deal
o u t "
a d d r e s s e d
irrelevant
as b e -
a n i m a l s
m i n d
has b e e n
contrast,
o b s t a c l e
s e n s o r y
p r e s e n t - d a y
p r o b a b i l i t y
also
as
that
" t h i n k i n g
s t a t e m e n t
the
e x i s t e n c e
p r o d u c t i v e
d i s c o n t i n u i t y
h a n d
o r
in
t h e
t o
( s u c h
r e l a t i o n s h i p
t h e
O t h e r
a n d
p r o v i d e d
a b s e n t
incidental.
idea
H u m p h r e y
p e r f o r m s
t h e pre-statistical p e r i o d
p e a r
o f
o f
I n
t h e
w h e t h e r
a n d
q u e s t i o n
p r o c e s s e s
w h e t h e r
o r g a n i s m ,
W h a t
o r
r e p r o d u c t i v e
a n
theory.
t h i n k e r t w e e n
w h e n
m i g h t
b e h a v i o r ,
still,
o n
strategy"
trial-and-error is
b a s e d
m a i n
q u e s t i o n
either
illustration.
m i n d
p r o b a b i l i t y
is
are
a p r o b l e m . "
" s h o r t - h a n d
f r o m
q u e s t i o n
p o i n t s
e x p e r i e n c e
in
o f
for
t h e
a s i x t e e n - p o i n t
p s y c h o l o g y g i v e n
t h e
o p p o s e d
c o n s e r v a t i s m
t h e s e
a n d
t i o n s
so-called
e.g.
statistics. N o n e
all
r e c o g n i z e s ,
n o t ,
g e n e r a l
as
for
s e c o n d
is a b o u t
p r o c e s s e s , o u t , "
T h e
u n c o n s c i o u s
q u e s t i o n
i m p o r t a n t
inferential
c o n t i n u e s
o c c u r s
t e r m s
i n n e r
A l m o s t
are
" w h a t
is
w i t h
third
"acting
m o r e
e x p l a i n
H u m p h r e y
T h e
b y
t h e s e
t h e
interact
a n d
m a i n l y
d e s c r i p t i v e
a t t e m p t s
p r o c e s s e s
p r o c e s s e s
mind
s y s t e m - u n d e r - s t r e s s .
t e n d e n c i e s ) .
m o t o r
h u m a n s . a
unitary
c o n s c i o u s
d e t e r m i n i n g
w i t h
t h e
of the
a
(see
If o r
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o n e the
Statistics
r e s t r u c t u r i n g a n s w e r t h e
w o u l d
b e s t
o f
i n t u i t i v e
t h e
O f
m u s t
c o u r s e ,
statistician.
statisticians S e c o n d ,
w h o
it
is
-
s i d e r a t i o n s
t h e
T h e t w o
f o r
it
v i e w
is
a n d
t h e o r y
q u e s t i o n s .
a n d
t h e s e
s e c o n d ,
v i o l a t i o n s ?
statistical t h e
h o w
L i k e
t h i n k i n g G e s t a l t
t h i n k i n g
-
as
K a h n e m a n ,
w a s
a
b e t w e e n single
t w o
k e y
n e w
a n d
t h e
t h e o r y
1 9 7 4 ,
n e w a n d
see
illusions h u m a n
a r e
s e c t i o n
r e s e a r c h
s h o w s
as
is.
p h y s i c a l
a n d
p r o b a b i l i t y
h a d
p r o c e s s e s
w e r e
r e s t r u c t u r i n g s
l e m . " l o n g t h e
it
t o o k ,
p r o b l e m
D u n c k e r f e r e n t
w a s
w a y s
m e d i a t e l y
a n d
a
o n e
o f
c h a n g e s
as
n o
rival
p r o b l e m s . o p p o s e d
w i t h o u t
l a w s o f
h u m a n
t o c o n -
t h e s e
e i t h e r
a n d
p r o b a b i l i t y
in
f a m o u s
p e r c e p t i o n
l a w s
(e.g. t h e
for
p e r c e i v e d
r e p l a c e d t h e
o r
e x a m p l e ,
m o t i o n
o f
i n
illusion
o f
B u t
physical
r e s u l t s
a n d
T v e r s k y
p h i - p h e n o m e n o n .
h a s
o f
r e s e a r c h ,
p e r c e p t i o n ;
t h e
f r o m
p s y c h o l o g i s t s
p s y c h o l o g i s t s ,
a n d
a r o u n d
t h i n k i n g
p e r c e p t u a l
b e t w e e n
l a y o u t
o r
o r
as
a n
c o n t e x t
k i n d
o f
a
o n
t h e
o f
t o
d e p e n d i n g
o n
w h i c h
t h a t
also
g i v e n t h a t
t h e
a in
reality,
p r o b a b i l i t y
e.g. t o
in
o r
k i n d
b e t w e e n
initiated t h e
n o t , o f
it.
p r o b l e m s
b y
p r o b -
a n d
h o w
p h r a s i n g
F o r
o f
i n s t a n c e ,
is a p p r o a c h e d s u b j e c t
a n
p r o c e s s e s
" i n s p e c t i n g
a p r o b l e m
o f
I n n e r
t u r n
illustrate
t h e
t h e o r i s t s
i n t e r a c t i o n
t h e
t h e
o n l y
i d e a o f w h a t
p r o b l e m .
a n d
n o t
G e s t a l t
s o l u t i o n
p r o b l e m s
l a y o u t
a n
w e r e
a r o u n d "
c o n t e x t ,
s h o w
t e m p o r a l
t h e
r e a s o n a b l e
e x a m p l e
first
b u t
e x p l a n a t i o n
" l o o k i n g
f o u n d
also
t r a n s f o r m e d
i n t e r d e p e n d e n t .
r e f o r m u l a t i o n s
s u c h
T h e
m e t a p h o r
are
t h e
b e f o r e .
-
c o n s t r u c t e d ,
as
s u b j e c t
t h e
n e w
o f f e r e d
d e p e n d e d o r
are
b e s t
p i c t u r e
is c e n t e r e d
t h e
o f
t o
t h e o r y
o n e
s a m e -
least,
e x p l a n a t i o n s
p r o b l e m s
t h e
m e t h o d s , "
W h e t h e r
t h e
p s y c h o l o g i c a l
s e q u e n t i a l l y
t h e
t h r e e
i n n e r
" h e u r i s t i c
l a w s
reality
at
in
p r o b l e m .
G e s t a l t
d i s c r e p a n c i e s
h o w
A l l
D u n c k e r
t h e
o r
o n l y
statistics
p s y c h o l o g i s t s ,
F o r
b e l i e v e s
t h e r e
p r o g r a m
illusions
single
t h i n k i n g .
q u e s t i o n s
e x p l a n a t i o n
t o
v i o l a t e
t h e
as in W e r t h e i m e r ' s
p r o g r a m ,
t h e
o n e
a
G o d - l i k e
p r o b l e m s
r e s e a r c h
u n d e r l y i n g
flashed
t h a t
b y
o f
c o r r e c t ,
a c e r t a i n
a n s w e r e d
p e o p l e
if
calculates
a n s w e r s
o f
e x i s t e n c e
o n e
belief
i n v e s t i g a t i o n s
p . 1 1 2 4 ) .
b e t w e e n
p o i n t ,
r e s e a r c h
t h e
o n
t h e
d e r i v e
N e w
s u c h
b e
G e s t a l t
t h e i r
t o
p o i n t s
m o v i n g
t h e
t h e
l i k e n
d i s c r e p a n c y
T h i s
o n
d o
w e
p s y c h o l o g i s t s ,
t h e
a n d
c a n
t h e n
statistician
c o n t e x t
First, w h e r e
t h e
H o w e v e r ,
r e a l - w o r l d
u n a m b i g o u s l y
c o n t e n t
t h e n
issue.
d i f f e r e n t
e v e n
221
is b a s e d
b a s e d
o f f e r t h a t
t h e
j u d g m e n t - u n d e r - u n c e r t a i n t y
m a i n
like
c a n
mind
statistician,
this latter
m i g h t
u r n s - a n d - b a l l s
i n c i d e n t a l
exist,
b e l i e v e d
o f
a n
First,
the
r e l a t i o n s h i p s ,
b e
a n s w e r
e s t i m a t e . t h e
f u n c t i o n a l
i n d e e d
m e t a p h o r
o n e
o f
o f
of
in
dif-
w o r k e d
i n d u c e s
a
" s e t "
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i m o f
222
Statistics
p r o b l e m - s o l v i n g
s t r a t e g i e s
s u b s e q u e n t
S u c h
i n g
o n e .
e x c l u s i v e l y
g e n e r a l
r u l e s
o f
n a t i o n s
t h a t
a n
o f
t h e
m i n d
C .
u r n
t h a t t h e
t h a t
t h e
m i n d
t h a t
is t h e
e i g h t
r e s e a r c h
s t e m s
a n y
s u c h
t h e
s o l u t i o n
e x p l a n a t i o n
as
o f
o f
a
t h i n k -
c o n t e x t - i n d e p e n d e n t
m a j o r
B e a c h
f o u r
c h i p s
t h e
t h e o r e m
m e t a p h o r
subjects'
t h e
e x p l a n a t i o n
o f
in
a
p r o b l e m s t h e i r
o f
t o
as
o f
Statis-
| H),
e.g.
d r a w n
T h e y
c o r r e c t
w a y ,
f r o m
a s s u m e d b u t
p r o p o s e d
w i t h
t h a t
t h e
s y s t e m a t i c a l l y
t h e
b a s e
p r o b a b i l i t y
n e w
t h e o r y ,
p h e n o m e n o n ,
as
m i s c a l c u l a t i o n
T h i s
d o e s
m i s -
rates. J u s t
t h i n k i n g ,
H o w
t h e
e x p l a n a t i o n
chips.
b u t
e x p l a -
I n t u i t i v e
a r e
r e a s o n i n g .
d o .
discrepancy
illustrate
as a n
c o n t r a s t ,
for
a c t u a l
v o c a b u l a r y
a n d
b l u e
o v e r w e i g h t i n g
g e n e r a l
t h e
r a n g e
p o k e r c h i p s
in
d i f f e r e n t
p r o b a b i l i t i e s p ( D
p r o b a b i l i t i e s , b y
is
s e r v e
" M a n
3 0 %
E d w a r d s ,
t h e
t h e
b l u e
q u i t e
t h e
p r o p o s e d
t h e
a n d
B a y e s '
o n e s
a
n o w
F r o m
e n t i t l e d
L. R.
a n d
e.g.
for
e x p l a i n i n g
t h e o r e m .
article
i n s e r t e d .
f r o m
q u e s t i o n s
T v e r s k y ' s
n e e d s
t w o
a n d
u s e s
is t h e
e x p l a n a t i o n
e x p l a n a t i o n
h i n d e r
c o n s e r v a t i s m ,
m i s c a l c u l a t e s
calculates
c a l c u l a t i o n
n e w
a n
r e d
t h e o r e m ,
o n
B a y e s '
r e d
7 0 %
p r o b a b i l i t i e s
B a y e s '
statistical
I n
i n t u i t i v e l y
c o r r e c t l y
calculates
a n d
P e t e r s o n
c o n t a i n s
m i n d
w r o n g
W h a t
s y s t e m a t i c a l l y
p r o b a b i l i t y
o r
t h a t
p r o c e s s e s
c o n s e r v a t i s m ,
R.
clear
r e s e a r c h
e m e r g e s .
e x p l a n a t i o n .
( 1 9 6 7 ) ,
i n n e r
mind
facilitate
m a d e
E d w a r d s '
f o r
m a y
the
insufficient.
j u d g m e n t
o f f e r e d
t y p e
tician"
t h e
h u m a n
o f
b e
e x p l a n a t i o n
b e t w e e n
n e w
w i t h
t h a t
findings
t e r m s
w o u l d
B e g i n n i n g t y p e
i n
of
t y p e
just
o f
as
t h e
K a h n e m a n
b a s e - r a t e
a n d
n e g l e c t ,
c o m p a r e ?
T h e
K a h n e m a n f e r e n t
s e c o n d ,
T h e
latter
t h e a n
T v e r s k y
o f f e r
o f
p r o b l e m :
first
t h e
d i s t i n c t i o n
is p r o p o s e d
r e p r e s e n t a t i v e n e s s e x p l a n a t i o n
b e i n g
o n e
l o w i n g
A
a n d
t y p e
a n d
r e p r e s e n t a t i v e n e s s
o f
f o r
t h e
c o v e r
a
m o s t
s t o r y
for
t w o a
o f
C a b
P r o b l e m .
and
p r o m i n e n t .
A
b e e n f r o m
written. the
probability
100
t h u m b n a i l
Y o u
will
available
that
the
find
y o u r
descriptions.
p e r s o n
" i n c i d e n t a l " shall d e a l
described
f o r m s F o r
h a s
o f
s t u d e n t s 1 9 7 3 ,
five
each
is a n
h e r e
rates.
o n l y
w i t h
o f f e r e d
as
P r o b l e m
g i v e n
t h e
fol-
2 4 1 ) :
fields.
30 engineers a n d descriptions, description, o n
dif-
personality tests to
respective
engineer,
a
b a s e
b e e n
w a s
p .
a n d administered
in their
f o r
E n g i n e e r - L a w y e r
T v e r s k y ,
descriptions o f the o n
W e
t h e
g r o u p
a n d
7 0 l a w y e r s , all s u c c e s s f u l
this information,
a n d
e a c h
" r e p r e s e n t a t i v e n e s s , "
R e p r e s e n t a t i v e n e s s
panel o f psychologists has interviewed
engineers
called
" c a u s a l "
p r o b l e m s ,
( K a h n e m a n
e x p l a n a t i o n s ,
" h e u r i s t i c "
heuristic. class
m a j o r
b e t w e e n t h e
h e u r i s t i c
a
O n
the
7 0 lawyers
chosen
please scale
basis
at
o f
have
r a n d o m
indicate
f r o m
30
1 t o
y o u r 100.
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Statistics
T h e
same
task
has
b e e n
p e r f o r m e d
accurate in assigning probabilities b o n u s
to the e x t e n t
A
s e c o n d
i n v e r t e d
s u c h
A l l
as
J a c k
o f
rates,
i.e.
b a s e
l a w y e r s .
that y o u r
g r o u p
s u b j e c t s
t h e
is a 4 5 - y e a r - o l d careful,
carpentry,
sailing, a n d
engineers
K a h n e m a n
w e r e
w e r e
o f
a n
f o r
a
223
panel
of
experts,
w h o
the various descriptions. Y o u
r e c e i v e d
g i v e n
t h e
w e r e
highly
will b e
paid
close to those o f the expert
t h e
p r o b a b i l i t i e s ,
o n l y
s a m e
n a m e l y
s a m e
s t e r e o t y p e :
ambitious.
sample
m o s t
five
7 0
e n g i n e e r s
a
panel.
i n s t r u c t i o n s
p e r s o n a l i t y
t h e
t h e
n o
w i t h
a n d
3 0
d e s c r i p t i o n s
t o
H e
is
in political
hobbies w h i c h
probability
generally a n d
social
include
h o m e
that J a c k
is o n e
of
%.
t h a t
t h e
s a m e ,
a n d
w a s
children.
interest
his m a n y
is
t h a t
b e t w e e n
d e g r e e
four
puzzles. T h e
f o u n d
p a r t
has
s h o w s
o n
100
e x p l a n a t i o n
i.e. t h e
heuristics,
time
o f
and
H e
mathematical
similarity
h e n c e
is m a r r i e d
T v e r s k y
t h e
t h e
H e
of his free
the
T h e
e n g i n e e r ,
o t h e r
in
a n d
i g n o r e d .
j u d g i n g
w e r e
mind
estimates c o m e
p r i o r
and
spends m o s t
g r o u p s
by
s t u d e n t s
m a n .
issues a n d
30
to
the
f o l l o w i n g :
conservative,
the
of
t h e
t h e
w h i c h
r e s p o n s e s
c o n c l u d e d s u b j e c t s
d e s c r i p t i o n
a d e s c r i p t i o n
" r e p r e s e n t a t i v e n e s s
r e p r e s e n t a t i v e n e s s
m e a n
t h e
s o l v e
t h e
a n d
t h e i r
t h e
t w o
b a s e
r a t e s
p r o b l e m
T o g e t h e r
w i t h
as
o f
p r o p o s e d
a
b y
s t e r e o t y p e
i s representative
h e u r i s t i c . "
w a s
t h a t
in
l a w
o f
t h e
a
f e w
h u m a n
t h i n k i n g . L e t is
u s
e x a m i n e
p r e s e n t e d
K a h n e m a n its o w n , n o t
t h e
k i n d
o f
t h e
w h i c h
t h e
o n
q u e s t i o n s
p o i n t ,
w e
t o
t e r m
i n f o r m a l
a n d
t h e
first
a n d
t h e
a
a n d
t h e
o f
i n c o m e
is c l o s e
t r i b u t i o n
v a r i o u s
h e u r i s t i c "
t o
D
a
c o l l e g e m e a n is
s p e a k
b u t
a n d
t h e
d e t e r m i n e d
a n d
K a h n e m a n ' s w h i c h
precisely. falls
is d e f i n e d d e f i n e d ( m o r e A
v a l u e
f r e q u e n c y b y
w h a t
in
h a v e
o n e
this
o r
less)
D
will
s u b j e c t
m o s t o f
k n o w s
t o t h e
w h i c h
t o
o w n
m a k e r e c e n t g i v e n
c o n c e p t t h a t
o f
a
b e t w e e n F o r
a
I n
class
H
illustration, v a l u e s
o f
r e p r e s e n t a t i v e i n c o m e s ; o r
a
j u d g -
c a t e g o r i e s .
r e p r e s e n t a t i v e b e
in
o r d e r
is
w a y
p r e v i o u s l y
f o u r
class.
d i s t r i b u t i o n a
I n
e x p l a i n
o f
o f
a n d
A n o t h e r
e x p l a n a t o r y
T h e y
a n d
a logic
v o c a b u l a r y
as a r e l a t i o n in
" h a s
( 1 9 8 2 a )
t h e y
t h e
T v e r s k y
It
o n l y p r o v i d e d
e x p l a n a t i o n .
d e f i n e
r e l a t i o n
n o t
t h e
t h e
m o r e
o f
h a s
closely.
p r o b a b i l i t y "
f r e q u e n c y . "
also
t o
a n d
l o g i c o f
i n c l u d i n g
m e a n i n g s
p r o f e s s o r s . o f
t h e o r
m o r e
this h e u r i s t i c
t h e o r e m
p o s e d ,
v a r i a b l e
T v e r s k y
t h e
itself
o f
f r o m
B a y e s '
c o n c e p t
s t r a t e g y ,
t h a t
p r o b a b i l i t y
case, r e p r e s e n t a t i v e n e s s v a l u e
c l a i m
T v e r s k y
r e p r e s e n t a t i v e n e s s
K a h n e m a n
it
o f
" r e p r e s e n t a t i v e n e s s "
b y
s h o r t h a n d
p r o b l e m s
t o
t h e
e x p l a n a t o r y
s y s t e m a t i c a l l y
is d e s c r i b e d ,
" r e p r e s e n t a t i v e n e s s m e n t
this
is as f o l l o w s :
refer
clarify
o f
explicitly
i m p r e s s i o n s
s i t u a t i o n
a t t e m p t
a n
d e p a r t s
p h e n o m e n o n
t h e
n a t u r e
( 1 9 8 2 a , p . 88)
" b a s e d
v i e w
as
t h e
t h e
a s s u m e s
if
dis-
a b o u t
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224
Statistics
t h e s e
i n c o m e s .
It
is
r e p r e s e n t a t i v e n e s s tain
as
o f
o c c u r s
I n
t h e
w h e r e
s u c h
i n
a n
e l e m e n t .
t h e
o f
T v e r s k y
a n d
case
b e
c a n
a t t r i b u t e s k e t c h ) , o n e
e n t i r e
t h e a
t o
a
a n d
causal
T v e r s k y
c o n s i d e r
n e c t i o n s
t o
fall
t w o .
F r e q u e n t
case,
e x c e p t
e v e n t
D
h o w e v e r , A l l
l a n g u a g e First,
just
e x p l a i n i n g rate
o f
h a s
i m a g e s ,
T h e
p e o p l e
u s e
f o r m a t i o n
a o f
is e x p l a i n e d all.
A n d
t h e
| H)
a r e
a
b y
h a r d l y
b u t
|
H)
t y p e p ( D o f
s t u d e n t s
a t t r i b u t e t h e
(as
s e c o n d
f r e q u e n c y
w e
t h e
see
t h a n
a
w i t h / ( H ) ,
h a s
a n d
b a s e
rates.
f r o m
all
as
t h r e e
a n d
a n
a n d c o n -
b e t w e e n
a n d
S u c h
r e l a t i o n
causal
e q u i v a l e n t H
a
K a h n e m a n
d i s t i n c t i o n
t w o
t h a t
t o t h e
t h e
t h e
first
v a l u e
o r
i n t e r p r e t a t i o n ,
t h e
B a y e s '
o f
c o n c e p t s it
is
n o t p(H).
b e c a u s e
this
w h i c h
o b v i o u s
b y
is, n e g l e c t
f r o m
w h i c h
t h a t
t h e
p h e n o m e n o n .
t h a t
h a s
( b a s e -
a s s o c i a t i o n
p e o p l e ' s
t h e o r y
f o r
P r o b a b i l i t y
as
t h e
m e a n s
T h a t
| H ) ,
t h e o r e m
is e x p l a i n e d
P r o b a b i l i t y
m d p ( D
o f
t h e
v o c a b u l a r y
s u c h
n o w
b y
c o n s e q u e n c e s .
probability.
r e d e s c r i p t i o n
a n d
s h a p e d
c o n c e p t u a l
f r o m
S e c o n d ,
n e g l e c t
a r e
i m p o r t a n t
l a n g u a g e
heuristic,
| H)
p e r s o n a l i t y
g e n e r a l i z i n g
d e f i n e d
s y s t e m
e x p l a n a t o r y
insight.
t h e
identity.
d e v i a t e
t h e
s e c o n d
p r o b a b i l i t y .
r e p r e s e n t a t i v e n e s s
w e
t h e
o n e - d i m e n s i o n a l
v a r i a b l e s
f o r m a l l y
s u b s e t ,
r e p r e s e n -
c o n j e c t u r e ,
is
n o
p e r -
p s y c h o l o g y .
t h a t
c o n s e q u e n c e .
m a k i n g
a
less
o f
in
b y
a n d
a s s o c i a t e d "
b a s e - r a t e
c o n c e p t s p(H)
a r e
a n d
a r e
a
P r o b l e m ,
p a r t i c u l a r
class
a s t r o n o m y
T h e r e f o r e ,
f o r m a l
earlier
n o t
o n e
analysis
m o r e
o f
a
a
t h e
least
f r o m
a n d
b e t w e e n
i n t e r p r e t a t i o n .
o f
a n d
g e n e r a l i z i n g
j u d g m e n t s
called
n e g l e c t
t w o
(D
b e t w e e n
E n g i n e e r - L a w y e r
b y
b e t w e e n
t h e
T h i s
as a r e l a t i o n
e n g i n e e r s
p o s s i b l e
causal
m e a n i n g s
o f
f r o m
at
r e p r e s e n t a t i v e n e s s t h e
this
state
o f
a
r e l a t i o n
r e s t r u c t u r i n g
v a r y w i t h / > ( D
d i s t r i b u t i o n ,
t h e m s e l v e s
h e a d i n g ,
c h a n g e
is
o f cer-
t h e p r o b a b i l i t y p
r e p r e s e n t a t i v e n e s s
a n d
this
r e p l a c e d
p h e n o m e n o n
m e a n i n g ( U n d e r
87)
t h a n
" f r e q u e n t l y
g i v e n
is
p .
e l e m e n t s .
is itself d e r i v e d
" e x p l a n a t i o n "
t o
a b o v e
t h a n
first
case,
p e o p l e ' s
n o w
t h e
probability.
f r e q u e n c y
r e l a t i o n
b o d y
c o n s e r v a t i s m ,
w h y
neglect)
t h e o r y
f o r
a
a s s e s s m e n t
p r o b a b i l i t y .
as
t h e
f o l l o w s
o f
last
t h e
f o u r
o f
case
u n d e r
n o t
a n d
case
is d e f i n e d
s t u d e n t s
m o r e
a s s o c i a t i o n s
d o e s
t h e s e
t o
b o t h
n o w
first
r e d u c e d
class
is
t h e
s y s t e m
t h a t
is
case
f r o m
t h e
is
( 1 9 8 2 a ,
s u b s e t
f o u r t h
b e t w e e n
b e
t h e
s t u d e n t
t h i r d
t o
this
f r e q u e n c y
c a n
w h e t h e r
i n c o m e )
r e f e r
t h e
i n
s y m m e t r i c
e x a m p l e
t h i r d
d e r i v e d
e l e m e n t
I n
A n
K a h n e m a n
a n d
m e a n i n g s
o f
mind
t h e o r e m . )
q u e s t i o n
(e.g.
t h a t
e q u a l
is b e t w e e n
T h e
t h e
the
case, r e p r e s e n t a t i v e n e s s
r e l a t i o n
in
as
B a y e s '
s k e t c h .
as
t a t i v e
s u c h
s e c o n d
t h e
s o n a l i t y
see
r e p r e s e n t a t i v e n e s s
it
class a n d
t o
is a s s e s s m e n t
c o n d i t i o n s ,
m e a n i n g
easy
of
j u d g m e n t s s a y i n g
t h e y o f
t h a t
u s e
b a s e
inr a t e s
e n c o m p a s s e d t h e
p o s t e r i o r
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Statistics
p r o b a b i l i t y
is
calculated,
p h e n o m e n a
a n d
t h e
of
n o w
the
s e r v e
as
h a v e
t h e
p r o b l e m s
l o o k e d
s h o w n
for.
g e n e r a t e d s u c h
as
t o
a s k i n g
i d e a
t w e e n t o
0
e x p r e s s
jects
for
B u t
a r e
since
o f
t h a t t h e
a b o u t
t h e
c e r t a i n t y
is
3 5 %
s h e
t h a t
are
m o d e s .
i n d e e d
f o l l o w . s u c h o t h e r , e v e r ,
S u c h
as
t h e
r a t h e r
w h e t h e r ,
abilities
s h e
belief
b y
m a y s h e
a n
b y
o f
f e e l i n g
t o
o f
s h e
is
b e
o f
n o t ,
a n d
r e p r e s e n t e d
s w i t c h i n g s u b j e c t i v e
e s t i m a t e s certainty
is
o f o r
b y
f r o m v a l u e
o t h e r
m o d e s
recently,
still
e x p r e s s
are
h e r
m a y
m a y
u n -
m o r e
o f
n o t
b e
shift
c o n t a i n
b e -
u n c e r -
t h e n
shifts
s h e m a y
p r o b a b i l i t i e s ,
c e r t a i n
o r
a n x i o u s
t h a t
p r e g n a n t ,
b e t w e e n
p r o b a b i l i t y
o n .
p r o b a b i l i t y
t r a n s i t i o n o n e
o w i n g
N u m e r i c a l
a w o m a n
s o m e
s u b -
1 9 3 0 s
o n l y
s h e
o f
u n c e r t a i n t y .
m a y
p h a s e s
definitely
levels
o l d e r ,
u n c e r t a i n t y
b e l i e v e
b e -
a s k i n g
a s s u m e
R a t h e r
o f
l e a r n e d
o f
late
s u b j e c t i v e
t r a n s i t i o n
definitely
bit
this
c o n s i d e r
a
n u m b e r
e x p r e s s
h o w e v e r ,
t h e
a n u m e r i c a l
states
say
a
b y
t h e
d o
s e n s e
k i n d
topics.
all e v e n t s ?
t o
subjects,
it m a k e
d a t a
subjects
l e a r n e d
earlier t h o u g h t
this
t e r m s
little
for
illustration,
D o e s
t h e s e
o n
i n t o
i n
f r o m
a n d
w a y
a
o n l y
m i g h t
n u m e r i c a l
b e t w e e n
h a v e
w h e r e
f r e q u e n c i e s
t h a n
o n l y
T h e i r
A s
S t e v e n s
p r o b a b i l i t y .
u n c e r t a i n t y
relative
t h e
o f
a n d
( p r o b -
t h e m s e l v e s
g e n e r a t i n g
n u m e r i c a l
certainty,
t o
results
H e r
o f
shift
n o t
s t i m u l u s
p s y c h o l o g i c a l
is
w e r e
p r o b l e m
N o b o d y
u n c e r t a i n t y
h e a d s ,
d a t a
d u r i n g
b a s i n g a t h e o r y
p r e g n a n t ?
t w e e n
m a y
o u r
o f
t h e o r i s t s
N o n e
e x p e r i m e n t e r s
S.
q u e s t i o n s ,
r e f o r m u l a t i o n s
p r o b a b i l i t i e s .
o t h e r
o f
n u m e r i c a l l y ,
fixed
t i m e
t h e
G e s t a l t
b e t w e e n
p r o b a b i l i t i e s )
in
is p r e g n a n t .
r e p r e s e n t e d
o n e
b o t h
e x p l a n a t i o n s
k i n d s
a l o u d
m e a s u r e d .
for
i d e a
S t a n l e y
t h e
infer
e x p e r i m e n t a l
f o r
o f
t h i n k
t i m e
a n d
t h e
and
i n s t a n c e ,
t o
t r a n s l a t e
T h e
n o t
a
A t
i n
t o
o f
o r
u n t i l
as
tainty.
t h o u g h t
o c c u r
r e p r e s e n t e d states
r a t i n g s
r e v o l u t i o n .
s h e
is
usually
e x p e r i m e n t e r s
o t h e r
w h e t h e r
w a s
p r o b a b i l i t i e s
i n f e r e n c e
for
r e s e a r c h
W h a t
F o r
t h e
p r o b a b i l i t i e s ,
p r o b a b i l i t y
b y
a d d i t i o n ,
u s e d
w o r k
e v e n
u n c e r t a i n t y
r e p o r t s
l i k e l i h o o d s .
t h e r e
j u d g m e n t s R e c a l l
t o
d a t a ?
v e r b a l
t o
( b u t
t h e
t h i n k i n g ?
s u b j e c t s
n o t
n u m b e r s
o f
t h e
o b s e r v e d ,
s u b j e c t s
c o n f i d e n c e
a n d
v o c a b u l a r y
c h a n g e d
t h e i r
I n
for
a s k i n g
t h e i r
p a r t i c u l a r l y
n a t u r e
s t u d y i n g
1 d i d
significance
i n f l u e n c e
h o w e v e r ,
o f
a n d
also
( s o l u t i o n )
f o r
h a s
p h e n o m e n a
t h e s e
s u b j e c t s
e i t h e r
T h e
t h e
m e t a p h o r
i n s t r u c t e d
a n s w e r
t h e
d a t a
t h e
p r o c e s s e s .
e x p e r i m e n t e r s ,
data,
it
u s e d
r e s t r u c t u r i n g
a b o u t
d i d
s t u d y
a n d
a n d
t h e
p o s e d ,
D u n c k e r
s o l v i n g ,
l e m )
t h a t
B u t
225
e x p l a n a t i o n s .
N e w
W e
mind
0
state a n d
1.
t r a n s i t i o n t h e
t o
t h e
H o w p r o b -
a p p r o p r i a t e
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226
Statistics
d a t a
for
a
t h e o r y
o f
j u d g m e n t
of
u n d e r
the
mind
u n c e r t a i n t y
is a
q u e s t i o n
a l m o s t
n e v e r
p o s e d .
6 . 6
I n
t h e
f o r m a l
T H E
R E T U R N
e i g h t e e n t h
c e n t u r y ,
d e s c r i p t i o n
o f
as a p r e s c r i p t i o n n i n e t e e n t h
last in
t o
t h e
d e c a d e s ,
as
c e r t a i n
a
t h e
c u l a t e d t i o n s F o r
w o u l d
results
a r e
3 3 9 - 4 0 ) t h a t d o
this
i n s t a n c e ,
w h o
"it n o t
c h a n g e s
a n d
t h e
ideal
t h e
t h e
r e a s o n a b l e
o f
l e a r n
a n d
p e o p l e
(Slovic, results
b a c k ,
t h i n k i n g
d i s c o v e r e d
least
D i v i s i o n
d i s m a l l y
in
1 9 7 1 ) .
P e t e r s b u r g
p r o b l e m ,
m a t h e m a t i c s
a
o f
t h e o f
w i t h
t h e b e t t e r
t w e n t i e t h - c e n t u r y
least
t h e i r
test
F a c e d
t o
in
b u t
p s y c h o l o g i s t s .
at
at
" b l e a k
a
o n e
a n d
b e
cal-
D e v i a t h o u g h t .
" f o r
a n y o n e s u c h
( 1 9 8 3 ,
p p .
i n f e r e n c e "
u s e
in
a n d
s u c h
tasks
o t h e r s
r i n g
f o r
m a n y
L i c h t e n s t e i n ,
s m a l l t o
A m e r i c a n t h e i r
elite t h e i r
t o
1 9 7 6 )
f o r
h u m a n
b e
E v e n
case
d i c t a t e s
o f
s h a d o w
r e a s o n a b l e , t h a t
their
t h e
c o m e
s o
o f
t o
n e w
n o
colleagues
o n e
in
A s s o c i a t i o n
t h e p e r -
( T v e r s k y
s o l u t i o n
p r o b a b i l i s t s c o m m o n
t h e
a l m o s t
i n t u i t i o n s in
f o r m
e i g h t e e n t h - c e n t u r y
d i s m a y
statistical
h a d
t h e
P s y c h o l o g i c a l
a c o m p a r a b l e
p s y c h o l o g i s t s
in
W h e r e a s
e x p e r i m e n t s .
t h e
u n -
e i g h t -
t h e o r y .
i m p l i c a t i o n s
o n l y
e i g h t e e n t h - c e n t u r y fit
t h e
p r o g r a m s
a n d
in
m u s t )
A n d
c o r r e c t
F i s c h h o f f , h a v e
a s s u m e d
-
t h e
r e v i v e d
h a v e
K u n d a
p e o p l e
p r i n c i p l e s . "
t h e
statistician,
o f
as
1 9 7 5 ) .
i n d e e d
t h e s e
a n d
e r r o r s
h e u r i s t i c s
" l a c k
B o r g i d a ,
w a s
s e r i o u s
statistical
like
t h a t
i n t u i t i v e
t h e
p r o b a b i l i t y
h u m a n
c o n c l u d e
r e a s o n a b l e
t h e
in
t h e
in
w a s
a
a n d
in
a c t i o n
( i n d e e d ,
K r a n t z , J e p s o n ,
t h a t
t a s k s "
o f
a
a n d
p r o b a b i l i t y
( 1 9 7 2 )
m a n ,
m a s s e s ,
o f
p r o b l e m s
c a n
o n c e
2). B u t
v i e w
i r r a t i o n a l i t y
c o m m i t
r e q u i r e d
m a n
K a h n e m a n ,
t h e
as
N i s b e t t ,
t h e m e :
m i n d s
h a d
M a t h e m a t i c a l
t h e i r
t o
( N i s b e t t
p s y c h o l o g i s t s
f o r m e d
m a n
t h e
1 a n d
belief
t h e i r
a n s w e r
a n d
o f
p s y c h o l o g i s t s ,
t h a t
at
N
b e c a m e
p r o b a b i l i s t s
r a t i o n a l
m a t h e m a t i c a l
T v e r s k y
e x p e r i m e n t a l
r e a s o n a b l e in
a n d
statistics
n o r m a t i v e
o f
this
biases
" p e o p l e
j u d g m e n t a l
p r o b a b i l i s t s
w a s
t h a t
s a m e
t h e
A
d i s a p p e a r e d
c h a p t e r s
classical
a s s u m e
o f
r e v e a l
v i e w
t h e
(see
t h e
h i m ,
t h a t
r u l e s
d i s c o u r a g i n g . "
r a t i o n a l i t y "
a n
t o
r e s p e c t
finally,
T h e
t h e
is d i s t u r b i n g
i m p o r t a n t
a n d
K a h n e m a n
w i s h
o f
a n d
as
r e a s o n a b l e
irrationality
t w e n t i e t h - c e n t u r y
a n s w e r
c o n c l u d e
o n
w i t h
a n s w e r , t o
t h e
c o d i f i c a t i o n
M a n y
a c c o r d i n g
f r o m
a l o n g
t h e o r y
M
i n t e n d e d
i n t e r p r e t a t i o n
i n d i v i d u a l s m a n
w a s
a p r o t o t y p i c a l
p r o b a b i l i t y
o f
R E A S O N A B L E
t h e o r y
us. T h i s
m a t h e m a t i c i a n s ,
c o r r e c t
o f
d e s c r i b i n g
m a t h e m a t i c a l
s i t u a t i o n s .
o n e
o f
o f
r e a s o n a b l e
a n d
e e n t h - c e n t u r y o n l y
rest
r a t i o n a l i t y
p s y c h o l o g y ,
t h e o r y
p r o b a b i l i t y
w h e n
m e a n s
T H E
i n t u i t i o n s
t h e
c e n t u r y ,
m a t h e m a t i c a l o p p o s e d
f o r
t h e
O F
t o
h a d
r e a s o n . r e v e r e
a n d
t h e
St.
r e v i s e d H o w e v e r ,
t h e
m a t h -
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Statistics
e m a t i c a l
t h e o r y
c o m m o n F o r
t w o
r e a s o n
t h e
single
o f b e
a b o v e
c o r r e c t
m a j o r
a n s w e r
a n d
o f
s e c o n d ,
o f
t h i n k i n g
p . 1 1 2 4 ) .
A
bias
tial.
a n d
F o r
this
e x p l a i n e d
b y
i.e.
t h e
t h e
n o r m a t i v e
t i o n
g r o u p
w o u l d
c h o s e n , w o u l d
a n s w e r
a n s w e r .
s t a n c e ,
w a s
t h e
n e c e s s a r y t h e
t o
h a v e
o n e
r e p l a c e
a s s o c i a t e d p r o b a b i l i t y o n e
jectivity t h e r e F o r
n o
this
p r o b l e m s s e e m e d w o r l d ,
h a s
t o
h a v e
a n d
it
o r
t h e
c l a i m
v i d u a l s
n e w
t h a t
s e e m s
N e y m a n
in
c o r r e c t
a n s w e r 0.80
e s s e n -
f r o m
is t h e t h e
t h e
bias
t o
d a t a
itself,
d e v i a t i o n
f r o m
s o l u t i o n ,
t h e
o f
d e v i a -
0.80
b a s e - r a t e
s e v e r a l
o r
a n d
w e r e n e g l e c t
o n l y
s c h o o l .
s o l u t i o n s ,
o f
o n e
F o r
in-
it w a s
t h e o r e t i c a l
n o t
c o m e
P e a r s o n ' s
w h i c h
o f
t h e
in
t o
t h e
n o t
analysis
f r o m
h a s
m o s t
his
usually
a l l o w
e x a c t l y
a n d
p o s t e r i o r
o n e
c o r r e c t
usually h u m a n
in
at
least
t h e o r e m
S u b -
u r n s - a n d - b a l l s B a y e s t o
h i m s e l f t h e
P r o p o n e n t s t h a t
its
p r o b a b i l i t i e s .
t h e o r e m
lifetime.
t h e
a p p l i c a t i o n s
p r i o r
T h o m a s
o f
w i t h
e l i m i n a t e d .
i n c e p t i o n .
d i f f e r e n t
t h e o r y
t h e
(2)
o f
n o t ,
B a y e s '
b e e n
a n d
v i e w
r e a l - w o r l d
p r o b a b i l i t i e s ,
this
a r e
b e y o n d
his
first
s t u d i e s
t h e o r e m
d u r i n g
v o i c e
t h e
t h e y
e a r n e d
a p p l i c a t i o n
h a s
n o t
a b o v e
d e t e r m i n e
its
p r i o r
is
t h e
o n e
e m e r g e d
p r o g r a m ,
since
w i t h
p r o b l e m
It
p r o b a b i l i t i e s "
w a y
w i t h
rules
A l t h o u g h
p r o b a b i l i t y
i n f o r m a t i o n
s p e a k s
statistics.
since
a g i v e n
a n d
biases
1 9 7 4 ,
its
t h e
t h e
K a h n e m a n ,
G e s t a l t
for
f o r m a l
subjectivity
s u b j e c t i v e
t o
(1)
B a y e s i a n
p u b l i s h e d
d i f f e r e n t
s a m e
a
a b o u t
jects
t h e
like
criticized
n o t
b y
h y b r i d
a p p l i c a t i o n
i n t e r p r e t a t i o n
t o
t h e
f r o m
a
s o m e
P r o b l e m
h a d
o f
r e v e a l
s o l u t i o n
p r o b l e m
s o l u t i o n
t o
o f
s u p p o s e d
a n d
s e e n
c o r r e c t
o n e
r e a s o n a b l e
c o r r e c t
o b j e c t i v e
s u b j e c t i v e h a v e
m a n y
t h e o r e m ,
d o u b t s
w a s
a
b e
it is n o t
a
e x i s t e n c e
n o r m a t i v e l y
b u t
t h a n
t h e
W u r z b u r g
" s u b j e c t i v e
t h e
b e e n
a n d
statistics
T h e
B a y e s '
r e a s o n ,
z e r o
statistics.
l o o k
u n d e r
u n i q u e
i n s t a n c e ,
j u d g m e n t t h e
r e s p e c t .
e n t e r s
is
o f
r e v i s i o n
classification
if,
h a s
t h a t
B a y e s i a n
i m p o r t a n t
T h u s ,
m o r e
for
t h a t
p r o c e s s .
p e r s o n a l
w i t h
t h e
C a b
e x p l a i n e d ,
w h e t h e r
single
v i e w
i n s t i t u t i o n a l i z a t i o n
b e
insisted
i d e n t i f y
a v e r a g e
a b o v e
t h i n k i n g .
a
single
g r o u p
t h e
t o
b e
P r o b l e m
n o r m a t i v e
s h o u l d
t o
a
c a n
a n d
f r o m o f
t h e
j u d g m e n t
e x i s t e d
a n d
w o u l d
i n c i d e n t a l
T u m o r
a r e
c o n t r a s t ,
r e s t r u c t u r i n g
T h e
t h a t
o f
i n s t e a d
First,
( T v e r s k y
t h e
in
T h i s
in
deviation
o f
0 . 4 1
If t h e r e
d e v i a t i o n
"biases
t h e
t h e y
p r o g r a m :
a s s u m p t i o n
o f
d i f f e r e n t ,
I n
as
h e u r i s t i c
a v e r a g e s ,
d i s a p p e a r .
a s s u m p t i o n .
d e v i a t i o n
s o m e
b e
t h e
s o l u t i o n
o f
t h e
t h a t
irrationality,
u n c e r t a i n t y "
t h e
227
m a t h e m a t i c s .
h u m a n
t h e s e
u n d e r
mind
t h e
r e s e a r c h
u s e
m a k e s
c o r r e c t
fit
a b o u t
d e f i n e d
i n s t a n c e ,
s u p p o s e d b e
is
t o
n e w
the
statistics
i s a necessary t h e
h e u r i s t i c
a n s w e r ,
a n d
r e f o r m e d
c o n c l u s i o n
s t e p s
j u d g m e n t ,
p r o b a b i l i t y
of
real
o f
d i f f e r e n t
t h e r e f o r e
t h e s u b -
r e s p o n d
p r o b a b i l i t i e s .
T h u s
a n s w e r
i n d i -
for
all
c a m p .
h a d
m o r e
i n f l u e n c e
o n
t h e
insti-
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228
Statistics
t u t i o n a l i z e d
h y b r i d
t h e
o n e
issue
o f
statistics t h a n
c o r r e c t
N e y m a n
a n d
a n d
c o n t i n u e d
t h e y
j u d g m e n t s
P e a r s o n
in
t h e o r y
O f
-
o r
b o t h
o f
use o u r
the
s e e m e d
S i n c e P e a r s o n
o f
t h e o r y
also
let
u s
is t h e
h e a r t
o f
t h e
p u b l i s h e d
his
statistics
i n f e r e n c e . t a u g h t h a v e
o t h e r
tics s e e m s o f
t o
b y
n u l l
g o d s
b e
j u d g m e n t
T h e
1 9 3 5 ,
M e d i a t e d t h e
i n
w e
find
t h e
u n d e r
o b j e c t i v e
t h e
v e r y
t o
t h e
T h e
ical
a
m o r e
t h a t
t h e
r a t i o n a l
t h e
t h e y
W h a t P r o b l e m ?
n o t
T h i s
ask.
Is
t h e
such
t h e
n u l l
a
t h e i r
for
matters
the -
to
h y p o t h -
effects
a n d
N e y m a n
h y p o t h e s i s
p r e s e n t e d
o f
i n d u c t i v e
p s y c h o l o g i s t s a n d
t h a t
o n l y - o n e - a n s w e r n o r m a t i v e
Experiments,
H e
p r o b l e m
statistics
t e s t i n g
of
m e s s a g e .
t h e
a n d
o n l y - o n e - a n s w e r
Design
w r i t e r s ,
balls
v i e w
r a t i o n a l i t y shall
( f o r if
w h o l e
w e
a p p l y
o f
t h e t r u e
t o
t h e
v i e w
in
w e r e
t h o u
t h e
shalt
o f
statis-
p s y c h o l o g y
p e r s p e c t i v e
a n
o f
t h i r d t h e
level
t o
t h e
just
C a n
c o n t r a s t
a r g u e :
m o r e
in
N o .
c o n t e n t f o r m u l a e .
a n d b u t
m e c h a n e q u a l l y
1 9 8 7 ) .
P e a r s o n ' s
n o t
I n
shall
t h e
b u t
t h e o r y ?
a l t e r n a t i v e
see J e f f r e y ,
c h a n g e s ,
o f
p o s e d ? w e
illusion.
place,
r e p e t i t i v e
o f
a n
d e c i m a l
a d d i t i o n
t h a n
a n d
t h e
u n c o n t r o v e r s i a l ,
c o u r s e ,
c o n t e n t ,
e x a m p l e s
N e y m a n
is,
is
p r o b l e m s
in
o f
statistics
at
w i t h
m o r e
e x a m p l e s
i l l u s t r a t i o n
u n c e r t a i n t y , "
i m p o r t a n t
p r e s e n t
o t h e r
s a m e
filled
is
a n
"statistics"
in
u n d e r
a r e
c o n t e n t , W e
v i e w :
i n f e r e n c e
a n s w e r
" j u d g m e n t
a n d
t h a t
s i m p l y
b e c o m e s
T h e
is
i m p e r i a l i s m
r e a s o n i n g
h a p p e n s
o f
o f
t e x t b o o k
i n d u c t i v e
c o r r e c t
o f
u r n s
s o l u t i o n s
in
vary,
d i f f e r e n t
in t h e
t e x t b o o k s
f o r
single
calculation.
o f
a g a p
o f w o r t h w h i l e
influential
s o l u t i o n
o n e .
c o m p o n e n t
d i v e r g e
p r o p o n e n t s
d e p e n d e n t W i t h
b y
t h e o r i e s
g i v e
his
m e t h o d
this
p a r t
m o d e l
n o r m a t i v e
t h e o r y
q u i t e
e n t h u s i a s t i c
m a k e
d i s t i n g u i s h e d
likely class o f a d m i s s i b l e
t h e
w h o s e
f o r m a l
t o
itself:
j u d g m e n t
m a t t e r s
f o r
I n
o n ,
396).
" o n l y - o n e - a n s w e r "
q u e s t i o n s
statistics
p.
h a s
i n f o r m a l
i n
1 9 2 8
alternatives,
r e a d e r
mathematical
personal
in
u n c e r t a i n t y .
i n s t r u m e n t
Statistical
o r
t o w a r d s
among
clearly
s u b j e c t i v e
t h e s e
a
h y p o t h e s i s
a m a i n
s p r e a d
o f
statistics.
b e f o r e
n o r m a t i v e
i d e a
T h e y
a t t i t u d e
p a p e r
one
c o m p e t e n t
in o u r
1962,
e x a g g e r a t e d
T h e
left
Fisher,
h y b r i d
as
sufficient
c a n d i d a t e
t o
as if it w e r e
t h a t
n o
n o
t u r n
in
t h e
t h e i r
j o i n t
level, the m a g n i t u d e
(Pearson,
j u d g m e n t s
T h u s
t h e
n e i t h e r
significance
is
t h a t
process
p e r s o n a l
first
a p p l i c a t i o n .
us, w e
w a s
a p p r o a c h
as the choice o f the m o s t
utilities
v i e w .
first
-
appropriate
balance
to
mind
t h e i r
t h e i r
f r o m
a n d
intuitive
terminology
eses, t h e
p a r t
n e c e s s a r y
a m o r e
F r o m
e m p h a s i z e
f o r m a l
n e c e s s i t y , a s it
exercise
a n s w e r ?
p a r t i c u l a r
the
Bayes'. W h a t
p r e s e n t e d
t o
e v e r y
m a t h e m a t i c a l
of
t h e
t h e o r y t h i r d
t o
t h e
C a b
d e c i m a l .
T h e
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Statistics
f u n d a m e n t a l tial
for
a n d
in
a n d
u s e d
N e y m a n t h e
t h e
a n d
t h e
falls
that
t o
b e n e f i t c o u r t
m a y
cases
t h e
vary
s a m e ,
receiver
m i z e s t h e
exist
his
w e
n u m b e r
c a n o f
w a s
i n t o w a s
t h e
are
s e e n
c o m e s
o f
criterion
o f
c a n d i d a t e s
f r o m
illustration.
Let
o n
the
n i g h t
t e s t i m o n y .
L e t
u s
further
| B)
B l u e .
is
T h i s
(since
t h e o r e m B l u e o f
t h e
v i e w ,
o b v i o u s .
error
g i v e s t h e
w e
g i v e n
us
v i e w s
calculate t h e
o n
t h e
Bayes' t h e
that
o f
o f
s u c h
t h e
w i t n e s s
pairs for
t h e
t h e
t h e
S i n c e
t h e
o n
t h e b o t h t h e
o n
t h e
N e y m a n
a n d
f o r m a l
c h o o s e
that in
t h e a
calculus
t h e
t h e
that
w i t n e s s
cabs
in
m i n i m i z e s />("G"
has
m i n i k n o w s
t h e
t h e
city.
overall
| B)p(B).
T h e
a l t h o u g h for
ratio).
error
w i t n e s s
w a y
t h e
t h e
t w o
c a b
likeli-
I n s e r t i n g
p r o b a b i l i t y
statistical
T h e
that
t h e m
t h e
c a b
a p p r o a c h e s
c a n
essential
witness'
u s e d
P e a r s o n ' s the
c o s t -
"Blue."
different
a p s y c h o l o g i c a l
reflects
that
t e s t i m o n y
o n
t h e
p o i n t
T h e
G r e e n
is c h a r a c t e r i z e d
(located
a
the
that
a n d
p r o b l e m .
a n d
w a s
w e
a c c i d e n t
for
is
o n
T h e
w h e r e
t o
l i k e l i h o o d
it
" B l u e . "
k n o w
values
(as
v a l u e
is i n
n u m e r i c a l
specify
t h e o r e m
N e y m a n
n e e d
T h i s
that
1 9 8 3 ) .
w i t n e s s
" G r e e n "
First,
t w o
t h e
saying
a
are
as
c u r v e .
a s s u m e
0.82(!)
s a m e
o t h e r ,
+
is
psy-
if a subjective
\ G)p(G)
witness'
probabilities o f
t h e
cabs
in
c o n d i t i o n s
a s s u m e
s e t t i n g
o f
criterion
this is t w o f o l d :
research),
f r o m
t h e
k n o w n
( B i r n b a u m ,
it
w h i c h
B l u e
p("B"
is
w i t n e s s e s .
t h e
o f
that
6.1
N e y m a n
n o t
a d d i t i o n
u s
o f
a n d p ( G )
W e
in
e q u a t i o n
A p p l y i n g
G r e e n
visibility
( R O C )
shift
in
"errors" possible.
e x c e p t
in
( H e r e
d e p e n d i n g
d o
n e e d
s u m
a c o n t i n u u m
p o i n t
t h e o r y
for
w e
t h e
p e r s p e c t i v e
u n c e r t a i n t y b u t
that
t h e o r e m .
B a y e s i a n
it
t h e
vary.
characteristic
u s
t o
o f
q u e s t i o n
s h o w s
as
a n d
sensitivity
m a y
e r r o r s , -i.e.
different
e x a m p l e
the
criterion
m o r a l
t o
in
this.)
a n o t h e r ,
s a m e
his
actually
lead
n i g h t
t o
if
e s s e n -
T o d a y ' s
c o n t i n u u m
"hits" a n d
the
accident,
r a t e s p(B)
s e a r c h e d
T h e
o f
u n d e r
o p e r a t o r
p("G"
Bayes'
situation
t y p e s
research.
B l u e
" G r e e n , "
is
as stated
t h e o r y "
o f
w h i c h
Bayes'
this c o n t i n u u m :
calculate
actually
h o o d s
o n
in
b e y o n d
subjective
criterion
criterion
base
p r o b a b i l i t y
t w o
several
i n c o r r e c t
g o
d e t e c t i o n
says
o n e
his
hypothesis
acutal
N o w
t h e
t h e
p s y c h o l o g i c a l
calibrated
b y
o n
analysis
minimizing
a
subject
f r o m
b u t
so-called
T h e r e
course,
o n
criterion,
t h e o r e m
r e p r e s e n t a t i o n
h i t - a n d - r u n
w a s
a
d e c i s i o n
Bayes'
"signal
w i t n e s s
criterion
P e a r s o n
o f
o r
t h e
t h e
t h e
229
n o n - e x i s t e n t
c r i t e r i o n is a p o i n t
side,
t e s t e d o f
t o
refer
t h e
mind
j u d g m e n t - u n d e r - u n c e r t a i n t y
analysis o f
n i g h t
w e
d i s t r i b u t i o n s
o n e
criterion
a n d
theory,
t h e
w i t h
P e a r s o n
subjective
o v e r l a p p i n g Recall
arises
r e a s o n i n g ,
P e a r s o n ' s
c h o l o g y ,
a n d
f o l l o w i n g in
statistics a n d
d i f f e r e n c e
of the
in b y
this
S e e n
a single pair
o f
in
f r o m
j u d g m e n t - u n d e r -
h e
curve).
t h e o r y
f u n d a m e n t a l
errors.
t h e
t h e o r y ,
R O C
p o i n t
is
characterized
F r o m
criterion
duality
in
thereof,
the
latter
shift
N e y m a n
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b e a n d
230
Statistics
P e a r s o n ' s logical e x i s t
t h e o r y :
p a r t . m a n y
m o r e ;
w h i c h
d i s s o l v e
i n t o
t h e
f r o m h a v e t h e
If
w e
a r e
m a t i o n
p a c k a g e d ,
t h e y
t o
r e l e v a n t
n o t
w h o w e
a r e
L e t
v a n t
b a s e
v a l u e , t h e
b u t , b a s e
f o r m a t i v e , t h e
o f
b a s e
s u g g e s t o n l y called
it
a
f u r t h e r
is
close
d e r i v e d
r a t e s
W e
c a n
g i v e
c o n c l u d e
t h a t
o f
since o f
is
is
first
w e B l u e
s e c o n d
"causally"
" i n c i d e n t a l . " )
a n d
o f
t h a t
k n o w
t h e
t h e
l i n k e d
a b o u t
t o
H o w e v e r ,
is
w i t h
a
t h e
t h e
j u d g e
o r
as
i n
f o r
s u b j e c -
for
g e n e r a l
a n
o f
j u d g e s
t e s t i m o n y n e e d s
r a t e
n o t
t h e
t h e first
t h a t
t h e rele-
n u m e r i c a l
is r e l e v a n t . b e
a t
( K a h n e m a n o n
t h u s
o f
t h e
e x a c t
m a y
d e -
P e a r s o n ;
a c c i d e n t s
see
P r o b l e m .
a c c i d e n t
a n d
s h e
indis-
C o n s i d e r ,
C a b
t h e
r a t e
w h e r e a s m a y
a n d
E n g i n e e r ,
m i n o r i t y
b a s e
p u b l i c a t i o n
e v e n t ,
f o r
r e a s o n i n g
t h a n
t h e
o n l y
h i t - a n d - r u n
later
a n
t h e
N o w
b a s e
in a c c i d e n t s ?
t h e
t o
o f which
city? T h i s
f o r
t o p i c
r e a s o n i n g .
N e y m a n
n o t
w h a t
i n f o r m a t i o n
h i t - a n d - r u n
errs.
a
a b o v e )
o f
k n o w s
w i t n e s s
q u e s t i o n
t h e
in
S h e
c o n c e r n
i n v o l v e d r a t e
b e l o n g s
a b o v e ) .
H e r
in
s h e
t h e
e s t i m a t e
are, h o w e v e r ,
v e r s i o n t h e
as
t e r m i n o l o g y .
statistical
w i t h
p r e -
for,
a n d
r a t h e r
r e l e v a n c y o f
i n f o r -
" h e u r i s t i c , "
s h o w n
D u n c k e r ' s
r e a l - w o r l d
d e a l i n g
c a b s b a s e
in
a p p l i c a t i o n
t h a t
(as
o f
s u c h
t h e y
is
t e r m
o n l y -
already
s e a r c h
f o r
p e r s o n
t h e u s e d
c o n f r o n t e d
c a b s
a r e
as
n o t
a
p r o b a b i l i t i e s ,
j u d g m e n t s
place,
B l u e
n o w
is
c o n s i d e r e d
s e a r c h
t h e
issue
R a t i o n a l i t y
subject's
E v e n
it?
t h e
p r o b l e m s
rarely
u n c e r t a i n t y .
d i s c u s s e d
W h a t
t h e
r a t e
this
is
is
w o r l d ,
I n f o r m a t i o n
this w a s
B l u e .
d o e s
p r o b l e m :
t e x t b o o k
w h e t h e r
l i k e l i h o o d
rate.
-
t h e
a s s u m e
( s h e
issue
t h e
r a t e
j u d g e
in
o u t s i d e
v a l u e s
d o )
f o l l o w i n g
is
o f
d e c i d e
r e a l - w o r l d
t h e
q u a n t i t a t i v e
search,
a n d
e n t e r
w h a t
f r e q u e n c i e s
t h e
t h e
in
a n s w e r ,
calculation.
T v e r s k y
p e o p l e
h e u r i s t i c , "
s e a r c h
u s
a n d
t h e r e
b a s e - r a t e
(0.82)
b a s e
i n f o r m a t i o n
w i t h
w a s
o f
B a y e s i a n s
i g n o r e
w i t n e s s
it
p a r t
a n d
t o
i n f o r m a t i o n
t h e r e
s c r i b e d .
t h e
u s i n g
a n d
as
s o l u t i o n
o f
u n d e r
b e g i n
c a b
i n s t a n c e ,
A s s u m e
this
p s y c h o -
c o r r e c t
a b o v e
e n t e r
t h a t
r e l e v a n c e .
k i n d
(if t h e y
v a r i a b l e s
I n f o r m a t i o n
for
W h a t
r e l e v a n t ,
c a l c u l a t i o n
p e n s a b l e
i n d e e d
t y p e
f o r m ,
d i d
o f
s e c o n d
n u m e r i c a l
t h e
s t r a t e g i e s
a
a n d
in
" r e p r e s e n t a t i v e n e s s tive
d o
t h a t
a
( a n d
s u c h
single
g i v e n
K a h n e m a n
o f
j u d g m e n t
o f
w h e t h e r
w h i c h
j u d g m e n t
b e
i n t o
s e l e c t i o n
R e c a l l
it s h o w s
p r o b l e m s
i n t o
v a r i a b l e s
a p p a r e n t l y
b e c a u s e
a n d
P r o b l e m .
j u d g e
r a t e s
allegedly
s o l u t i o n
b y
s o l u t i o n s
p h e n o m e n a
t h e
(0.80).
b a s e
f r o m
r u n s
o f t e n
r e s e a r c h
0.80,
v i e w
C a b
t h a t
t e x t b o o k
s e a r c h
a b o v e
a l t e r n a t i v e
r e p o r t e d
t o
s u p p l e m e n t e d
a l t e r n a t i v e
1 9 8 3 ) ,
air.
T h e
b e
n e g l e c t e d .
l e a v e
o n e - a n s w e r
e x i s t
B i r n b a u m ,
e x a m p l e ,
v a l u e , c.
r a t e s
t h e r e
mind
m u s t
relative
a n s w e r
this
p a r t
d e f i n e d
a s s u m p t i o n
s a m e
t h e
t h i n
c h o s e n
b a s e
since
see
a r e
m e d i a n t h e
statistical
S e c o n d ,
n e g l e c t
t o
t h e
of the
v e r y
in-
n i g h t .
a n d
O r
T v e r s k y
g r o u n d s b a s e t h e r e
Is
t h a t
r a t e is
is
little
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Statistics
g r o u n d
t o
b e t
d i s h o n e s t y base
rate
t h e
for
t h e
All
their
o f
q u e s t i o n ;
their
application T h e
data
T h e
in
t h e
g e n e r a t i o n
t e n d e n c y
c o o k b o o k - l i k e
p r o b a b i l i t y
h i n g e s
randomly fact,
d r a w n t h e r e
t i o n e d l e m ;
t o
o u t
that
t h e
subjects
subjects
an
w e r e
" r a n d o m l y " t h e
in
o r
notice, t h e
a n d
w e r e
d r a w
e a c h
i g n o r e
rates
( G i g e r e n z e r ,
disappears S u c h f o u n d ject.
if
t h e
results
in studies d e p e n d s
If t e x t b o o k
m o s t i g n o r e
indicate
o f
t h e
base
that o n
p r o b l e m s
t h e
h o w
are
B u t
w h e n
as
d e s c r i b e d t h e
t o
W . "
o f
o f
that
p p .
is
t o
in
t h e
50,
base
c o m p l e t e l y s i m p l y
if care
a n
in
research,
subject T h e
t h e
w e r e
refer.
e v e n
the
m e n p r o b -
falsely:
e.g.
b y
o v e r
1988).
S m a r t
t h e
w o r d
subjects
l e t t i n g
t h e n
t h e
s t e r e o -
u n i n f o r m a t i v e .
that
I n
E n g i n e e r -
A m e r i c a n
s k i p
urn,
Bayes'
" m e d i c a l " In
esticlaim
(via
rates
b u t
t a k e n
t h e
t h e y
know
subjects
n o
Base-rate
l o n g e r n e g l e c t
explicit. o f
i n f o r m a t i o n
individual
t h e
is
Blank, m a d e
t e x t b o o k s .
is n o t
154).
m a t c h
m a n y
d e s c r i p t i o n s
t h e s e
a n d
q u e s t i o n
in
E n g i n e e r .
t h e
search
i n f e r e n c e .
t h e t h e
asserted, t o
b e h a v i o r a l
rate specified
s t u d y
"quality"
the
t h e
b u t
b e t w e e n
i n f o r m a t i o n
w h e r e
base
d r a w n ,
is
B a y e s i a n
parallels
t o o l s
is a n
w h i c h
d i s t r i b u t e d
K a h n e m a n - T v e r s k y rates.
s o m e
P r o b l e m ,
a n d
i n f o r m a t i o n
since
statistical m o d e l s ,
t o o l s
f r o m
Hell,
vari-
A n d ,
v a r i o u s
statistical
fact,
d e s c r i p t i o n
crucial
m e c h a n i c a l
less a t t e n t i o n
m a y
r a n d o m l y
t h e m s e l v e s base
I n
t h e
o r
m i r r o r e d
b e
o t h e r s
sift
c o r r e c t
is
1982,
t o
c o m -
w h a t
this crucial i n f o r m a t i o n
instructions.
d e s c r i p t i o n s
a n d
a s s u m p t i o n
o r
o f
t o
a s s u m p t i o n s
c o n s t r u c t e d
lawyer,
are
t o
s a m p l i n g
deliberately
o n e
m u s t
statistical
o f
Tversky,
r a n d o m
e n g i n e e r
m i g h t
a n d
p a r t
o f
a c c o u n t
" T o m
t h e
that
p e r s o n
t h e
t h e
j u d g m e n t .
w i t h
p r o c e s s e s
t h a n
p o p u l a t i o n
(e.g.
n o t
m u c h
t h e
crucial
t h e
Slovic,
P r o b l e m ,
o f
take
t h e o f
t h e
e x i s t studies in w h i c h
d e s c r i p t i o n s t y p e s
o f
at
probabilities.
t h e
crucial
l o o k
d e c i d e
c o n s e n s u s ,
m i n d
p a y
single
t h e
since
o t h e r s . S h e
a n d
a n d
that
relevant,
i n f o r m e d
t h e r e
E n g i n e e r - L a w y e r
o n
K a h n e m a n ,
L a w y e r
that
a b o v e
subjects s h o u l d
t h e o r e m )
t o
p r e s e n t a t i o n s
m a t e s
t h e
the
n e g l e c t
n e g l e c t
t h e
that
t o
o f
m i g h t
realize
o v e r
is n o
c o n c e r n e d A g a i n ,
t e n d e n c y
C o n s i d e r t h e
are
s t u d y
b e
variables
p o s t e r i o r
( m e a s u r e m e n t )
t o
t i m e
s h e
m a y
also
o f
i n c o m p e t e n c e
T h u s
g u a r a n t e e
application.
t e n d e n c y
its parallel
o r
it is a m a t t e r
different
t h e
c o u l d
t o w n
n o t
d r i v i n g
s h e
refer. T h e r e
d o e s
t o
b u t
r e l e v a n t
critical r e m a r k s
w i t h
scientists. has
part o f
rate s h o u l d
calculate
t h e s e
rather
o n e
etc.
231
c r i m e .
accidents,
night,
mind
b e t w e e n
h i t - a n d - r u n
o f
j u d g m e n t
will
link
p o t e n t i a l l y
this
i n f o r m e d j u d g e s
for
base
t o
in
t i m e
p r e f e r
i n f o r m a t i o n
s o l u t i o n
"causal"
h i t - a n d - r u n
t h e
m i g h t
a b l e ^ )
a
i n v o l v e d
t o w n ,
p a n y
o n
of the
probabilistic is p r e s e n t e d
b o o k l e t s t h e n
subjects
in
p u t
t o
t h e
c l a s s r o o m s ,
subjects are
r e a s o n i n g
are
i n t o
s u b as
likely an
in t o
e x p e r i -
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232
Statistics
m e n t a l
s e t t i n g
tion,
t h e y
are
h e l p
reconcile
w h e r e
less likely t h e
l u s i o n s "
r e p o r t e d
research
o f J e a n
r e a s o n i n g . o n i n g
t a k e n
c o s t
o f
t h e
child.
a n d
o n
adults
text,
s o
a n d
t o
m o s t
o n e
rational
m a y
m e c h a n i c a l l y
rational W e
s o m e
m i n d
is
p s y c h o l o g y b e g a n
t o
diversity sidered,
a n d
selective T h e
all, h a v e
a r c h e o l o g y M o r r i s o n g o v e r n
h i s t o r y
s h o u l d
k i n d
qua
first
tool,
itself
p s y c h o l o g y
a n d
a n d
c o n q u e r e d
C o w g i l l H e n k e l
application
E x p e r i m e n t e r s
u s
as
a n
r o u n d a
that
( 1 9 7 7 ) ( 1 9 7 0 ) . o f
c o n s i d e r e d
c o n t e n t
a n d
h y b r i d o f
t h e a n d
A
theory, o f
c a u t i o u s
j u d g m e n t s c o n t e x t .
utility,
c o n t e x t s .
A
w h o Bayes'
B u t
p r e s e n t a f e w o f
scientific
h y b r i d for
t o
o f
s u c h
a
e x p e r i m e n t e r s
t h e
t h e
is b y
m a i n a n d
social
b e
c o n -
here.
N e y m a n
e m p i r i c a l
b y
n o
a n d m e a n s
sciences,
as d o c u m e n t e d
a n d
d o u b l e
t h e
necessity
issues
w a s
s o c i o l o g y
G i v e n
d e c a d e s
a c c o u n t
a p p r o a c h ,
t o
e x p e r i m e n t a l
i n f e r e n c e
h y p o t h e s i s
subjects
in
Fisher's
M o s t
in
statistician.
t h e o r i e s
characteristic
statistics their
c o n -
statistician
a f t e r w a r d s
intuitive
o u t
e d u c a t i o n . b y
t h e
irrelevant
b e
s u c h
institutionalized
a n d
research,
non
as
define.
w a s
o f
-
a n d
m e a n i n g
w h i c h
all
t h e sine
b e e n
t o
in
Let
p r e s e n t e d .
b e
u s
intuitive
b e
c h i l d r e n
t h e
a n d
the
as
o f
t o
probabilistic
in
c o n t e n t s
o f
i n c o m p l e t e .
their
is
p r o b a b i l i t y
w a r n
against
the
a b u n d a n c e
o f
t o
m i n d
s e e m s
w i t h
c o n t e n t ,
s h o u l d
o f probability,
a n d
b y
t h e
T h e
a p p r o a c h e s
ideas t o
w h i c h
t h e
e x p e c t e d
i n d i s p e n s a b l e
at
a p r o b l e m
it
t o
e v e n
o f
( b e
all
p o s e d ,
j u d g m e n t
b y
u n is
o n
rather
u n d e r care
b o t h
o f
t h e
reas-
c o n v e r s a t i o n s
f o r m u l a
institutionalization
restricted
b u t
o f
a n d
w h e r e
subjects,
today,
-
t h e
j u d g m e n t
s a m e
statistics
t h e
-
n o r m ,
t h a n
that
a n
it
p s y c h o l o g i c a l
a n d
P e a r s o n ' s
n o t
as
o t h e r )
n a i v e
il-
probabilistic
a p p r o a c h ,
s t r u c t u r e
i n d e p e n d e n t
m o r e t h e
the
o n
casual
t h e
h o w e v e r ,
as
h a r d e r
s e e n
h a v e
i n t e r p r e t a t i o n
m u c h
c o n c e i v e o f
b e
t h e
m o d e l s .
m e t h o d
applies
o r
h a v e
t h e
b y
o n
crucial i n f o r m a t i o n
i n f o r m a t i o n
as irrational,
m i n d
t h e o r e m ,
w o u l d
in
that
m a y
" c o g n i t i v e
t h e p r o b l e m
a n d
available
s u g g e s t s
" n o r m a t i v e , "
f o r m a l
d e n i g r a t e d
in w h i c h
e v i d e n c e
o f
research
least
also
children's probabilistic
single-case
at
i n f o r m a -
u n c e r t a i n t y
( [ 1 9 5 1 ) 1 9 7 5 )
i n s t r u c t i o n s
n o r m a t i v e
a n d
a
t h e
u n d e r
c o m p l e t e l y
c o n d i t i o n e d
in
the
crucial
c o n s i d e r a t i o n
b e t w e e n
I n h e l d e r ,
uses
t h e w a y
p r e s e n t a t i o n
rates. T h i s
j u d g m e n t
t h a n
r e a s o n i n g ,
v i e w s
all its c h a n g e s
u s i n g
are
m u c h
n o r m a t i v e
"descriptive" in
P i a g e t
r e a s o n i n g ,
m a n i p u l a t e
I n h e l d e r
a n d
d e v e l o p e d
e x p e r i m e n t a l
is n o t
o n
B a r b e l
P i a g e t
b y
o r
c o n t r a d i c t i o n
n o n - s t a n d a r d i z e d
o f
a c c o r d i n g w i t h
t o
mind
feel,
base
child u n d e r s t a n d s
d e d u c t i v e
v a r i o u s
i g n o r e
a n d
Probabilistic
b u l k
see,
research
imply.
s t r o n g l y d e t e r m i n e d T h e
t o
t h e
b e t t e r
that e v e r y
t h e
in
P i a g e t
w o u l d
c a n
a p p a r e n t
A c c o r d i n g
is m u c h
certainty
t h e y
of the
o t h e r
t e s t i n g "rational"
a n d if
for
fields
s t a n d a r d
if
b y
c a m e
t o
i n f e r e n c e . t h e y
u s e d
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Statistics
Bayes' a n
t h e o r e m
t o
e n g i n e e r ) ,
P e a r s o n i a n d o u b l e logical. t o
their
h a v e
t o
s e e m
general,
e v a l u a t e
h o w e v e r ,
t h e y
statistics
In
b o o k s
test h y p o t h e s e s
b u t
s t a n d a r d
t h e m s e l v e s their
b e
m a i n l y
b e h a v i o r a l
o w n
laboratory,
in
effect
sized
years
(e.g. C o h e n ,
editorials a n d o f
F e g e r , the
t o
policies If w e
o f
state
for
t h e
p u t
o f
s o m e
t h e
statistics
d i f f e r e n t
E l e m e n t a r y r e c o g n i t i o n
in
P e a r s o n - W a l d
s c h o o l ,
tual
e s t i m a t i o n
a n d
a n d
i n d u c t i o n
c u r r e n t as
if
d o g m a t i c
o f
a n d
t h e
Zeitschrift
a d h e r e n c e
b y
r e a s o n i n g
b y
by
a
single
has
in
this
physics
a n d
a t t i t u d e
a n d
for
o f
p u b l i c
n o r m a t i v e
m u c h
F e r m a t ,
fication
T h e y
p s y c h o l o g i s t s
p r o b l e m a t i c a l H o w e v e r
h o w e v e r ,
b i o l o g y .
o f
o u r
o f physical a n d
chapter,
o n e
n u m b e r
w i t h
k n o w l e d g e ,
p r o g r e s s i v e
i n d e p e n d e n t
h a v e
editorial
b e e n
s e e n
eclectic
d i f f e r e n t
brain
f u n c t i o n s .
d i s c r i m i n a t i o n ,
the
o f
the
f u n c t i o n i n g , o f
p e r c e p -
P e a r s o n
statistician.
t h e
it
a n d
N e y m a n -
statistician,
K a r l
i g n o r a n c e
statistical
e m p h a -
earlier
a n
T o
s c h o o l , read
w o u l d
o t h e r s ,
t h e s e e m
a n d
by
s c h o o l .
v i e w
o r i g i n a t e d s t e m
f r o m
t o w a r d s v i e w
b e e n
a n d o f
in
c o g n i t i v e
a
tools.
their t h e
p r o c e s s e s ,
different T h i s
b l i n d
c o n s t a n t
m e a n s
a n d
N a t u r a l
h a v e
science
a n d
the
h a v e
that
l o n g
d o e s
for
t h e
discussed.
t h e
b e e n
n o t
in
peculiar
since
universal: has
t h o s e
a c c o u n t s
w e
o u r
d i s c u s s e d
f r o m
c h a n g e d
a l m o s t
k n o w l e d g e
w a y
tools,
s p o t s
as it h a s
t h e o r i e s
history,
statistical
p r o b a b i l i t y
objectivity. w h i c h
o f
biological p r o c e s s e s . T h e
i n t e r p r e t a t i o n s t h i n g has
o f
a Fisherian
a B a y e s i a n
in
t o
statistician
o f
A n d
C O N C L U S I O N
t r a n s f o r m e d
u n d e r s t a n d i n g
a
7).
non-significant
that
c o n t r o l
c o g n i t i v e
o p e r a t e d
6 . 7
P r o b a b i l i t y
o n
d u e
p i c t u r e
a statistician by
M o r e
t h e
( B r e d e n k a m p
d e t e c t i o n ,
c o n t r o l l e d
literature
t o
s e n s o r y
t e x t -
r e a s o n i n g ,
increasingly
f u n c t i o n s
t h e
m e t h o d s
c h a p t e r
w e l c o m e
errors
t h a n
s o m e
o f articles is
they
type-I
g e t
r e v i s i o n
h o m u n c u l i
that
this
o u t s i d e
Sozialpsychologie
c o g n i t i v e w e
as
causal
o p i n i o n
o f
1 9 7 0 s
significance.
statisticians
s u c h are
a n d
B a y e s i a n
(see
are
for
rather
territories
studies
fur
r e a s o n s
B a y e s i a n
d e c i s i o n s
that a c c e p t a n c e
achieved,
j u d g m e n t
p s y c h o l o g i c a l
e a c h
m e r e
h o m u n c u l i
statistics.
traditional
t h a n
v a r i o u s
m e m o r y
its
rather
t o g e t h e r ,
f u n c t i o n s
t h e
w a s
N e y m a n -
institutional
since
B a y e s i a n
inflation
1 9 6 2 ) .
a n d
d e s c r i b e d
a n d
T h e
a l t h o u g h
o f
significance
Fisherian
u s e
as judicial
explicitly
p e r s o n
rarely
p o w e r
t h e
t h e
still
a n d
o f
( M e l t o n ,
intuitive
w h e r e
that
c o r r e c t
rhetorical
o f
s u c h
size
1 9 7 7 ) ,
as
1 9 7 0 )
level
results
as
s u c h
o n
s o m e
233
h y p o t h e s e s .
scientists
c h a p t e r s
r e - e n t e r e d
u s e d
o w n
h y p o t h e s e s ,
e x p e r i m e n t e r ' s r e c e n t
mind
(e.g. w h e t h e r
test
t o
i n c l u d e d
has
of the
Pascal identi-
a
m o d e l
d e p e n d
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o n
234
Statistics
s e a s o n e d tive."
j u d g m e n t ,
P r o b a b i l i t y
p s y c h o l o g y , arrives
at
cally,
that
u n d e r
t h e
t h e
that
exist a n d
1 9 8 0 ) .
that
o f
o b j e c t i v e
k n o w l e d g e ,
v a l u e d
as
t e r m s b e
o f
o u r
science.
a
w a y
b y
t h e in
o u r
t h e
t o
a n d
s a m e
m a t h e m a t i c a l , m o d e l
sense,
c o g n i t i v e
v e r y
is
r e p r e s e n t
n a t u r e
m e t a p h o r , arbitrary
o f
a n a
illusion, p o w e r f u l like
a n d
h e n c e
t h e
m e c h a n i c a l ,
a n d
t h e in
reflect
o u t s i d e
o u r
o f
s o v e r e i g n t y capricious
o f
in
e s s e n c e
d e e p
for
c o m -
n u m e r i -
e v e r y t h i n g c o m p u t a t i o n
p u b l i c
m e c h a n i s m i n s u r a n c e
for is
b o t h
a c c o u n t s
a
a n d
m u c h for
p e r s o n a l
of'statistical o f
p e r -
o f
t h e
g e n e r a t i n g
c o m p a n i e s ,
d e c i s i o n s
in
i n d i v i d u a l
w o r l d
h e a d s
c o g n i t i o n
"objec-
k n o w l e d g e
w h i c h
idiosyncracies t h e
a n d
p e r s o n a l
b y
characteristic
p s y c h o l o g i s t s , t h e
for
p s y c h o l o g y
probabilities
partly
e s c a p e
t h e
a
mind
p r o c e s s e s
brains
Statistics
i m p e r i a l
c o m p r o m i s e d
in
t h e
" o b j e c t i v e "
t h o u g h
a u t h o r i t y
sense,
b e c o m e
subjective
T h i s
k n o w l e d g e ,
it
are,
a
that
t h e o r i e s
v i e w
s u n ,
in
h a s
m e a n s
C u r r e n t
t h e r e
( P y l y s h y n , sonal
w h i c h
t o
is,
t h e o r y
k n o w l e d g e
n u m e r i c a l . m i t m e n t
b u t
of the
h a v e
decision. l a w its
I n
c a n n o t
a d m i n i s -
trators.
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" Y o u
can't
fight
the
law
o f
averages."
—
G r o v e r
S n o o d
in T h o m a s
P y n c h o n
(1984,
p.
142)
7
rest
e n h a n c e d o f
m o r e
e x p e r i e n c e
255
b y
n u m b e r s o n a n d
this
h a s
b o o m
c r e a t e d
i n f o r m a t i o n p e r s o n a l
a n d
in
p r o b a b i l i t y
a n e w
k i n d
f o r m a l
j u d g m e n t .
N o t
o f
t e c h since
Numbers
236
P y t h a g o r a s
has
b o t h
a
b o o n
that
statistics
( m i s ) u s e d p o s i t i o n .
a n d
tivity
a n d
rules
o f
c a n
o t h e r
E c h o e s
L o n d o n
t o
r e a s o n s
for
o f
in
the
t o
t h e
States.
b y
e x t r a o r d i n a r y
p r o f e s s i o n a l
p e r h a p s
e v e n
w e a k n e s s
o f
elites. large
role
in m o s t
in t h e
o f
erally
b e e n
h a v e
t h u s
States. has also
d e c i s i o n
-
G r u b e r ,
b e
stratified
o r
t o
a p p e a l
o f
v a l u e s
clash
m a n i p u l a t e
a n d t h e m
is
o r
( 1 9 8 7 ,
p.
are e s t e e m e d
that
q u i t e
t o
t h e
fact,
political
2 8 7 ) .
T h e o f
elusive, their
-
recently,
in
f o r m a l ,
Its
role
p r o m i n e n c e e x p e r t s
plays
m o r e
p u b l i c
R u s s e l l
h a v e
g e n elites
U n i t e d scrutiny
p r o c e s s e s
a r g u e d
a
t h a n
has
a n d
that
t h e
traditional
e v e n
o b j e c t i v e
o f
as
m o d e r n t o
is
b u r e a u -
T e c h n o c r a t i c
decisions
subject
fields. m a t t e r
o t h e r
m u c h
t h e
M i l t o n
o f
e d u c a t i o n
o n .
facili-
entirely a
tests,
States
o f
M i c h a e l that
c a n n o t
a n
easily
b o t h
t o
a c c u s a t i o n s
o f
m a n i p u l a t i o n
in
t h e
o f
l e a d e r s h i p
t h e
d e g r e e
in
h a v e
s t r o n g
m e n t a l
d e -
e c o n o m i c
r a n g e
in
o f
m o r e
p a s s e d
a n d
T h i s
faith
analysis,
are
e v e n
c e n t u r y
institutions
o f
a n d
universities.
c h i l d h o o d
p e r c e i v e d
for
established
t r u t h
business, a n d
idiosyncratic
especially is
in
U n i t e d
risk
is a m a t t e r
w i d e ,
o f
in a w i d e
a b s e n c e
arbitrariness.
a n d
real
c o n s e n s u s
t h e
A m e r i c a n
t o
a n d
universities
implicit
p r e t e n s e
lead
o b j e c -
d i s c r e t i o n
institutional
o p p o r t u n i t i e s
q u a n t i t a t i v e
q u a n t i f i c a t i o n
statistics
o f
t h e
d e f e n d e d t o
an
early
o f
e x c l u d e
m a y
this
t o a w i d e r public.
at least until
at least
e x p e d i e n c y "
practical
are
in
s t a n d a r d i z e d
f r o m
T h e
a n d
a n d
at
m e t h o d s ,
A m e r i c a n
elites in t h e
o p e n n e s s
o n
a n d
o f
political
a
n i n e t e e n t h - c e n t u r y
t h e
o f statistics is n o t
m u c h
m u l t i t u d e
o f guidelines
capriciousness
in
a
b e l i e v e d
e x p l a i n e d
political
o f
h i g h l y
w r i t i n g
"absence
f o r m
w h e r e ,
e n c o u r a g e d
o f
authorities,
s e l e c t i o n
relative
w e a l t h
responsibility
E u r o p e ,
T h e
t h e r e
in g o v e r n m e n t ,
t h e
for
b y
has
i m p r e s s i v e
in
f o u n d
p r o b l e m s ,
s o
o f t e n
a b o v e
n a t i o n o f l e a d e r s h i p
n o t
s o
g r o u n d ,
statistical
m a t h e m a t i c i a n s
alternative
Statistics,
o f
p u b l i c i n f l u e n c e
reflects
said
impartiality
a p p l i c a t i o n a i m i n g
n o w
heard.
a n d
cratic institutions w i t h t o o l s
that
o p i n i o n
still
is
b e e n
s u p p o r t
it is t h e
the
has
are
p e r s o n a l
o n e
h i g h
Cle'arly
a n d
scientists
m o r e
statistical
are
o f
it
t h e y
parallel
e x c l u d e
t h e
If
their p r e t e n s i o n s .
bias, t h e
s e e k
practical
size
t h e a t t a i n m e n t
t h e
B o t h
this
r e a s o n e d
h o w e v e r ,
m e c h a n i c a l
a v o i d
a n d
e x p e r t s .
b e c a u s e
e x p e r t
B o t h
d e v e l o p m e n t
U n i t e d
this;
t o
great,
p r o v i d e
m u c h ,
e v e n
s o
is
e n c o u r a g e s
e x c l u s i o n
t h e
a p p l i c a t i o n
cisively
b o a r d
S o c i e t y
t o
m o d e r n
a n d
b e e n
that
t o o
e v e n
t h e
world
n e w - s t y l e
m e r e l y
bureaucrat.
t h e
Statistical
their
B u t
c l a i m
fairness.
o f
L e a d e r s h i p
tated
o f t e n
t h e
at
t h e
a n y t h i n g ,
c o n s i s t e n t
across
t o
n o t
o f
the
n u m b e r s
things,
m o d e r n
t h e
p r o c e d u r e s
in
p r o v e
that p e r m i t s ,
t h e
o f
t e m p t a t i o n
t e c h n i q u e s
e m p h a s i z e
fray.
a
If e x p e r t s
s y s t e m
t h e
p r e s t i g e
t o prove
social
a n d
t h e
rule
rather
pluralistic
n u m b e r s
o f
a n d
o s t e n s i b l e
t h a n
service
U n i t e d o f
k i n d .
d e m o c r a c i e s . t h e
States
W h e r e
t e c h n i q u e s
neutrality. W i t h
T h e
that statis-
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Numbers
tics,
h o t l y
d e b a t e d
issues
rule
c a n
the
world
s e e m i n g l y
b e
237
t u r n e d
i n t o
p r o b l e m s
t o
b e
m a t t e r s
o f
s o l v e d . T o d a y ' s daily
a p p l i c a t i o n s
c o n c e r n
t e c h n i q u e s in
its
a n d
reflect
t h e
a n d
d e v e l o p m e n t s t e s t i n g
n e w
e x p e r i m e n t s , o b j e c t i v e
o f
a
i n t o
as
in
p e r s o n a l
a r r a y
w h i c h
o p i n i o n
l a w
n e w
a n d
in
its o w n
a p p l i c a t i o n .
d o
a n d
t h e
l o n g i n g
for
t h e
r e m a r k a b l e
m e c h a n i z e d
c o u r t r o o m s ,
o p i n i o n
t h e
w h i l e
p o l l i n g
n i n e t e e n t h
t h e
c e n t u r y
m e a s u r e m e n t
m a d e
b e l o v e d o f
intelli-
trials
c o n t r o l ,
s t u d i e s .
c e n t r a l
a g r i c u l t u r a l
S u b j e c t i v e
in
a p p l i c a t i o n s
like
o f
p r e c i p i t a t i o n
a n d
a b o u t
w a s
T w e n t i e t h - c e n t u r y
r a n d o m i z e d
q u a l i t y
t h e
c o n t i n u e
Q u e t e l e t ' s
statistics.
t o m o r r o w ' s
it
r u l e s
h a s
-
n o t
success
i n
a n d
w e a t h e r t h e
p o s s i b l e
7 . 2
i n t e r p r e t a t i o n s ,
e x t r a o r d i n a r y
Statistics
is
h a s
i n d i d o w n -
t r a d i t i o n a l r e p l a c e d
t h e
t h e
v a l u e s
t h e
E
o f
W
t h e
O u r
rules.
w i t h
t h e
o f
e x a m p l e s e m p h a s i z e
w o r l d
like
t h a t
v a r i e t y
o f
daily
i n t e l l i g e n c e
i n d i v i d u a l i s m , w i t h
familiarly o f
a
i m p o r t a n t
s y m b o l i z e s , o f
i n
r a t h e r
n o t i o n s
f a s c i n a t i o n
n u m e r i c a l
b u t
m o r e
j u d g m e n t s
m a t h e m a t i c s
N
o l d
t h e m
u s e d
r e m a d e
all
flexibility
m o d e l i n g .
field,
h a s
r e d e f i n e d
m a d e
n o w
a n d
t h e
all its g u i s e s
It
t h a t o f
t h e
e x h a u s t
all reflect
c e r t a i n t y
a n d
m e a s u r e m e n t ,
t h e r e b y
t r a n s f o r m e d
n e w
e x p l a i n
i m a g e .
m e d i c i n e ;
v a l u e s ,
as
e x p e r i m e n t a l
t e c h n i q u e s
h e l p s
statistics
a n d
in
o f
a p p l i c a t i o n s
it h a s
i n t e r p r e t a t i o n
t o
f r e q u e n c y
c h a n c e
e i g h t e e n t h -
i n d u s t r i a l
c o n v i c t i o n
i n f e r e n c e ,
i n
b e f o r e ;
p a s t
o f
o f
play.
e x p e r i e n c e p u b l i c
t h e
m a t h e m a t i c s
p e a s a n t s .
p e a c e f u l l y
c o m p l e m e n t
a n
in
a n d
t o
w i t h
a n d
t h a t
h a v e
o t h e r
c o e x i s t
b o t h
d e s c r i p t i o n ,
w a y s
statistics
o f
t h e
full
m e t h o d s
m a t h e m a t i c a l
t h e r a p i e s ,
h o s t
r u b r i c
m u n d a n e
b y
s t u d i e s
f u n d a m e n t a l o f
t h e o r y
t h e
c o n t e m p o r a r y
w o r k e r s
m u c h
"statistics,"
m u l t i f a r i o u s
in
c o u n t a b l e
still
m e d i c a l
f o r m i d a b l e
-
is
i n f e r e n c e
w h e r e
c o m e
k n o w n
t h e
" m a s s "
f o r e c a s t e r ' s
T h i s
o f
t h e
a n d
u p o n
B a y e s i a n
s o c i o l o g i c a l
p r o b a b i l i t i e s
f o r e c a s t i n g ,
p o u r
in
d r a w
e i g h t e e n t h - c e n t u r y
o f
t o
p r o b a b i l i t y
a c c u m u l a t e d
h i s t o r y .
for
i n d e e d
a n d
citizens
a c o m e b a c k
d i s t r i b u t i o n
g e n c e ,
v i d u a l
m a d e
d i s d a i n
t o
n o r m a l
a n
statistics
t h e
a t t a c h e d
a n d
h a v e
d e s c r i p t i v e
w a y s
o r d i n a r y
i n t e r p r e t a t i o n s
l i n e a g e
rationality
t o
statistics
t h r e e - h u n d r e d - y e a r
c e n t u r y
t o
t o
o f
t h a n
e v e r
p a r t i c u l a r l y
N e w
objects,
n u m e r i c a l
a n d
p r e c o n d i t i o n s
f o r
u n c e r t a i n t y .
O B J E C T S
B a s e b a l l
B a s e b a l l g r u o u s s a n d l o t s
is a m o n g -
o b j e c t s a n d
t h e o f
m o s t
i m p r e s s i v e
statistical
-
b e c a u s e
m a t h e m a t i c s .
city streets, s u p p o r t e d
b y a c u l t u r e
T h e
s e e m i n g l y s p o r t
o f w o r k i n g
m o s t
g r e w m e n
i n c o n -
u p
f r o m
a n d
f a r m
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Numbers
238
b o y s , o f
i n f o r m e d
m a n a g e r s .
a n d
c a n
P a l m e r ,
b y
Y e t
t h e
n o t o r i o u s l y
statistics
e v e n
b e
1986,
p p .
t r a c e d 9
( M c K e a n ,
ff.).
tics
o f
t h e i r
t r a d i t i o n s a n d
b o t h
ball
Abstract.
s t o r y
is
h a v e
B o t h
o f
to
a n n u a l
t h e
m o s t
o f
Play
its It,
e x p l a i n e d
h o w
a
g a m e
n a t i o n a l
m e r
c r i c k e t
t e m a t i z e d this
" f r o m t h e
t h e
A s
t o
b y
w o u l d t h e
o r
hitters,
a n d
H e
l o b b i e d
i n g
e r r o r s
w o r s e p r e s s
t h a t
w i n n i n g p r e s s
h a d
o f
p l a y
o n
b a s e t h e
a r e
statis-
v e n e r a b l e cricket,
B i l l James
Base-
t h e
b a s e b a l l
d i d
g a m e . "
o f
as
sys-
c h a n g i n g
1868,
p .
w o u l d
12).
all,
t h e s e
baseball
in
h e
t h a t
statistics t o
e x -
h o m e ( p p .
r e a c h e d d i d
u s e d
w a n t e d
w a n t e d
" s h o w y "
clearly
p a r t l y
u s e d
C e r t a i n
t o
11).
b e
b e
d e p r e c a t e d
b a s e s
u p
statistics
C h a d w i c k
c o u n t i n g
g a m e
a g o
t h e
w i t h
t h e
years
A b o v e
o v e r l y
establish
"a
g a m e .
since
t o
c o n n e c t i o n
g a m e
H e
C h a d w i c k
d e v i s i n g
statistics
a n d
It,
for-
t w e n t y
(p.
Learn
A
t o
i.e.
g r e a t
E n g l a n d .
t h a t
latter.
c a t e g o r y ,
in
( C h a d w i c k ,
t h e
to
H e n r y
I n
o n
t h e
also a
a t t e m p t
i n t e r e s t s
r e c o r d e d ,
n o t ,
w a s
r u n
6 2 - 8 ) .
o n
n o t
field-
d e m o n -
66).
t e a m
hasty,
his
c r i c k e t
r e c r e a t i o n "
a v e r a g e s ,
m o r a l
loss o f
t h e
o f
t h e
a t e a m
loss p r o m p t e d
b e t t e r
b e t s
b e e n
u n c e r t a i n t i e s s o m e t i m e s
T h e
t h e
b i g
t h e
t o
a n d
How
1868,
s o m e
o f
w e r e
p r a c t i c e
p r o m o t e
i n v o l v e d
a
c o n c e r n e d
o t h e r s
r u n
t o
n o w "
i d e n t i t y
" m o r a l
p .
o f
it w a s
(literally)
t h e
(e.g.
t h e
rate,
b u t
Ball:
in
i n f l u e n c e
is
g a m e s
h o m e
b a t t e r s '
c o u l d
it
v e r y
a
s t o p
t h e
a n d
football,
t h a t
baseball
Base
o f
baseball
details
ball
o f
of
m o d e l
his
d e e m p h a s i z e ,
t o
skill
t h e
s o m e
t h e
, w h i l e
t h e
t o w a r d
r e c o r d .
o f
v i r t u e s
least
T h o r n a m e n a b l e
b a s e b a l l
r e c o u n t i n g ,
i n t e g r a l
e x e r c i s e
w a s
b e
b e g i n n i n g s ,
b e
a n y
a n d
p u b l i s h e d
w e r e
t h e
w h i c h
t o
h e n c e
Statistics i n s t a n c e
t h e
h a r d
o n
field
H e
t o
A t
o f
Wisdon
Game
It,
h a v e
g a m e
in
The
d i r e c t e d
p e r c e i v e d ,
g a m e
b a t t i n g
w o r t h
its
(see
c o m p l a i n
statistics
a r e
g e n e r a t i o n s
as A m e r i c a n
n e g l e c t e d .
t h e
his
U . S . ,
s i m p l e
s u c h
said
s p o r t s
e.g.
Teach
t o
c r i c k e t
b e e n
early p r o m o t e r s
statistics
b e g a n
t h e m .
at
I n
to
h e
real v i r t u e s
p u n g e ,
-
i n
f r o m
o f
p u r p o s e s .
r e c o r d i n g
w a y
p r o m o t e
r e f l e c t e d
s t r a t e
o f
t h e
n a t i o n a l
t h e
t h e
scientific
r e p r e s e n t
a r o u n d
i n f l u e n t i a l
f o r
C h a d w i c k
f o r m e d
o t h e r
b e e n
How
a l m o s t
m a n l y ,
t h e s e
s i m p l y
statistics.
h e
o t h e r s ,
a b s t r a c t s
r e p o r t e r ,
p u r s u i t ,
m a n y
w i s d o m
b a s e b a l l
h a v e
h a v e
baseball
p l a n
s p o r t s
o f
o u r
o f
a n c e s t r y
F a n s
f o r
and
p a r t
its
d e v e l o p m e n t s
e n o u g h
world
u n g r a m m a t i c a l
t o
t h a t
the
b e e n
T h e s e
d e v e l o p e d
h a v e
c h a m p i o n How
f a v o r i t e s
rich
O n e
1 9 8 2 ) .
h a v e
b a c k
statistical analysis in w a y s n o t
rule
h a d
" t h r o w n "
C h a d w i c k
p o o r e s t
g a m e s
o f
s o m e
g a m e
b e t w e e n
c h a r g e d : t h e
w h e n
w a y s
r e c o r d
f r o m
t h e
m a t c h u p
i g n o r a n t o f
a b e t t e r
a c c u s a t i o n s
s e c o n d
ball, a n d
w i t h
o t h e r
for t h e
" K n o w i n g fact least
t h a t
t h e
t o
as a
well. t e a m
w i t h
m e m b e r s t h e t w o
o f
p u r p o s e t e a m s .
n o t h i n g
t h o s e
a
t h e o f T h e
o f
s t r o n g e s t
e x p e c t e d , "
O n e
t h e c l u b s n a i v e
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Numbers
journalists
h a d
o v e r l o o k e d
m a t t e r
o f
c h a n c e
tegrity
o f
t h e
t h e
g a m e
(see
in
p p .
in
E r n i e
c a r e d
Lieb,
sort
w e
p.
6 3 ) .
E v e r y p a s s e d
m a i n l y
m a j o r
a b o u t
3 0 ) .
statistical as
t h e
u p
a
statistic o f
s i m p l y
n o
m o r e
t h e
a in-
errors
t h r o u g h o u t
t h e
t o
L a n i g a n , t o
in
year
J o h n
analysis,
this
statistics.
B r o o k l y n o f
o n
=
in
a
(
Life
+
A B
A B
p r e s u m a b l y t o
i n c l u d e
scores.
h i m s e l f
t o
in
in
as
statistics"
for
s o m e
referred
r e c o r d i n g
o r d e r
t o
e n t e r p r i s e
c o m p i l e r " baseball.
said
t o
m a i n t a i n
(see
t h e
t o
(Lanigan,
o f
is
o f
p r e v i o u s l y
" d e m o n
H e
w e l l
r e a s o n s
i n f o r m a t i o n
h i m .
l o o k i n g
especially
L a n i g a n
t h e
t h e
interest
jobs
w a s
b l u n t
t h e
h a v e i n d e -
i n t r o d u c t o r y
a n d
P e t e
Game
of
m a g a z i n e
baseball
o f
Baseball
( 1 9 8 5 ) ,
t h e
o f
d i d
this
a
m a n
at
specialist),
m a n a g e r
B r a n c h
n o t
o c c u r
e v e n t
characterize
p o s e d
statistical
a u t h o r s
statistics
r e c o r d i n g that
P a l m e r ,
t h e a
a n d
t h e first
o n e
tradition
calculator
R i c k e y ,
r e v o l -
until
m a r k s
b e h i n d
detailed
h a l f w a y o f
o f
t h o s e
baseball
( A l a n
h i m
p o i n t i n g
R o t h ,
t h e t o
burly a
l o n g
b l a c k b o a r d :
H
H
w h o ,
n u m e r i c a l
m a g n i f i c e n t
i n c o n g r u i t i e s
g r e a t
o f
w a s
baseball, o r
figures
b o x
t o
s e e m e d
baseball
T h e
D o d g e r s '
the
his
Cyclopedia
L a n i g a n
t h e
c o m p l e t e n e s s
Hidden
century.
In 1 9 5 4 ,
in
Baseball
i n baseball is in its
n e g l e c t e d
referred
T h o r n
The
t h r o u g h
g r e a t
C h a d w i c k ,
a b o u t
baseball
1 9 2 2 ) .
d e v e l o p m e n t
s e e m i n g l y
this
t w e n t i e t h - c e n t u r y
t h e m s e l v e s .
for
w e l l - p a y i n g
for
u t i o n a r y
AB
w a s
s u p p o r t e d
h a d
fact-filled
interest
e l i m i n a t o r "
w a s
t h e
statistics
r e g a r d
for
h e
g o a l
necessary
statistical
(
loss
also
a v e r a g e
really care m u c h
c a t e g o r i e s
n u m b e r
A c c o r d i n g
G
t h e y
early
o f
discussed,
fairness,
c o n c e i v a b l e
e q u a t i o n
t h e
statistics
o n
t h e
A l l m y
H i s
" d e m o n
I n
t h e
"I d o n ' t
already
Lanigan's
r e m a r k s
figure
h a d
a u t h o r
or m i n o r .
p.
h a v e
4 5 ) .
p e n d e n c e
t h e
h a d
239
that
instance,
C h a d w i c k ,
b y his c o n t e m p t
C h a d w i c k
(p.
possibility
F o r
t h e y
L a n i g a n ,
1 9 7 3 ,
r e c o g n i z e d
1 9 2 2 ,
world
i n d i v i d u a l
t e a m .
t o
his real interests:
e x p r e s s e d t h e
T h e
t h a n
c o n t r a s t
at ball g a m e s , (see
i m p l i c a t e d
q u e s t i o n
statistician,
a b o u t
1 0 4 ) .
t h e
the
1 0 3 - 7 ) .
Q u i t e
( 1 9 2 2 ) ,
(p.
rule
BB
+
+
B B
B B
+
HB
+
BB
+
HP
+
3 ( T B - H )
HP
4AB
R
ff
+
B B
\
+
ER
HB
H
+
BB
tfP/
SO
+
HB
8(AB
+
BB
\
+
HB)
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J
Numbers
240
T h e
f o r m u l a
o f w i n n i n g b a s e s h i t
h i t
b y
e a r n e d
c a n
e q u a l s
o f f e n s e
t o m
line).
b e
m o r e
T h e
t h r e e
b a s e p o w e r , "
score.
D e f e n s e r u n
ball
f r o m
t h e
m a n a g e r s
o f f e n s e in
a n d
t h e
g a m e
t h e
in
s u l t i n g
f r o m
baseball's i n g
o f
is n o t
t h e
t o
t o
t h e
s o
l o w
really
accepted
m y
t h a t
a b o u t
a n d
the
constructive
w a s
t h e
m a n
b e s t
k n o w n
H e
baseball
statistics.
b e
a
b r o u g h t
g i v e n b e
like
c o m e
t o
science
v a l u e s
later
c o n t r o l , " e q u a t i o n
c a p t u r e
b a s e -
i n t u i t i o n
9 6 . 2 %
o f o f
a c c u r a t e
p e r i o d .
o f
t h e
e l e m e n t s
instance,
t h e
s t a n d i n g s
w h e n
t o
t h a t
R i c k e y
s e v e r a l
fact
a
t h a t
p i t c h e r ' s
s u r p r i s e s
his
o f
s t r i k e o u t
( d e s c r i b e d
t r a n s f o r m e d
d o w n
o u t
S u b s e q u e n t
a l m o s t
t h e
m e
into
baseball
to
b y
r e -
Life
as
u n d e r s t a n d -
in
f o r
t o
a
-
h e
u p
l i t e r a t u r e h a v e
o f
b u t
b a s e b a l l
b e e n
a
values a n d
the
s a m e
at
opinions
u p o n
n e w
t h e
and
device o n
time
for
s o m e
startling
o f
truths
the
t i m e
j u d g m e n t l e a g u e s
scientistic,
a l r e a d y a
t h e
m a j o r
p e r h a p s
h a d
-
s o m e
51
m o s t
m e m o r y .
f o r e c a s t
6 9 )
c o m e
different
a n d
m a t h e m a t i c a l p .
by considered
statistics in
o r
C h a d w i c k
1868,
d e v e l o p m e n t s
p u t
m y
o p e n i n g
scientific,
are slow to change. F o r
have
reveals
o f m a t h e m a t i c a l
t h e
I
disconcerting
b a s e b a l l
( C h a d w i c k , in
ideas. W e
recently
theories. It
m o s t
G r a n t e d , o f
B u t
compelled
h i s t o r y
i n a u g u r a t e d
c a u s e s "
w o r k e d
to
is t h e
i m p o r t a n c e
players.
t h i n g
has
cherished
. . It
thing
m e t h o d s .
w h i c h
m o s t
g a m e .
S u c h
it
w h o
s u b c o m p o n e n t s m a d e
R i c k e y
( b o t -
a v e r a g e , "
T h i s
t h e
o f
T h e
efficiency
" p i t c h e r
r e p l a c e
o n e
(F).
b a s e
t o
baseball by personal observation,
statistical
baseball
oldest
w a s
(R),
g a m e :
years I have judged
m e a s u r i n g
final
B r a n c h
c l a i m e d
o n
t o
F o r
r u n s
b a s e
its c l o n e s
relative
T h i s
" o n
t h e
{BE),
c o m p o n e n t
t w e n t y - y e a r
s u g g e s t e d
Baseball people are generally allergic to n e w
by
a
balls
fielding
m e n
b e
m e a s u r e
w i n n i n g
a r e
c o u l d
p r e d i c t
a p p r o a c h .
l e a d e r " )
a n d
o v e r
o n
" f i e l d i n g . "
s t a n d i n g s .
crucial.
D \
is a
( A B ) ,
a n d
o f
a n d
f o r m u l a
(V4)
b a t s
a d e f e n s e
w e i g h t i n g
t h e
at
a l l o w e d , "
I B M
final
t o
b a s e s
o f f e n s e
hits
B y
(H),
—
W e a v e r s ,
r e v e a l
w e l l
statistical
" b r a i n i e s t
t h e
s o
w e i g h t e d
ability
E a r l
t h e
0
p e r c e n t a g e
b y
g a m e s )
(SO),
=
a v e r a g e , "
a b i d
( f o r
( T B ) ,
G
o f
s t a n d i n g s
f o r m u l a
w o r k e d
w a s
s t r i k e o u t
t h e
l e a g u e
c o n t r i b u t i n g
f o r m u l a
a v e r a g e
" s t r i k e o u t
a n d
h i t s
m i n u s
" a v e r a g e
o p t i m a l l y ,
m a j o r
u s e d
o r
calculation.
d e f e n s e
as
line)
" c l u t c h "
S t e n g e l s
w i t h
p r e d i c t i n g
( t o p
t o
G
s t r i k e o u t s
w r i t t e n
r e p r e s e n t
its C a s e y
R i c k e y
a n d
o f
b a s e s
s u b c o m p o n e n t s
a v e r a g e , "
its d e s c e n d a n t s
t e r m s
(ER),
s i m p l y
world
a p p e a r s .
t o t a l
r u n s
r e d u c e s
a n d
the
it
i n
(HP),
c o m p o n e n t
" e x t r a
" e a r n e d
t h a n
e x p r e s s e d
p i t c h e r
(HB),
e q u a t i o n a n
r e c o n d i t e
efficiency,
w h e n
b a t t e r s
is less
rule
c o n c e i v e d w h e n
c a l c u l a t i o n this
o f
p r o g r a m
statistics
p u b l i s h e d
" t h e
in
after
r a t h e r
t o
t h e
b l a c k
p h a s e o f
o f
s o m e -
g a m e
results o n l y
o f
will f r o m
b e g a n
t o
R i c k e y . m o r e
scholarly
Downloaded from https://www.cambridge.org/core. Newcastle University, on 03 Oct 2018 at 11:29:14, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.009
Numbers
o u t l e t s o n
t h a n
b a s e b a l l
t a g e
effect
b y
o f
b a t t i n g
statistical
s c o r e
a n d
1 9 6 6 ,
M I T
t h e
t o
P r e s s
t h e
Journal.
a l m o s t
statistics
statistics t e n s i o n f o l l o w
o f
o f
o f
a n d
a n d
N o w
his
his n o t
time,
Similarly, h e l p s
t o
d o e s
n o t
to
C o m p u t e r s
in
t h e
effect
t h a t
o n e
" t h e
t y i n g
t h e
1 9 6 3 ) .
I n
w r i t t e n
statistical
as
p .
analysis
t h e
b y
w i t h
b a s e b a l l
-
in
o f
b y
the
o f
to
the
s o m e
f o r
A m e r i -
t h e
r o o t
o f
for
Research
t h e
n a m e
w h i c h
o b j e c t i v e
o f
b a s e b a l l
k n o w l e d g e
h a v e t h a t
its
baseball?
c h a m p i o n s
always
e v e r y
o f
d o n e .
as
t h e
a
s i m p l e
T h o r n
ballplayer
c a l c u l a t i n g
I n e v i t a b l y ,
is
a n d
a n
e x -
P a l m e r
" i n t u i t i v e
p r o b a b i l i t i e s
o f
s u c -
shortstop
is
figuring:
probably
because
the
the
various
distance
Based
has
n o
the
chance
he almost f r o m
the
led
h i m
probabilities
o n
speed
of a
o f
d o u b l e
certainly has
hole t o
to
the
n o
b a g
conclude
is
that
play."
thinking
w h o
l e a d i n g
t h e
r e c e i v e d
y e a r l y Baseball
t h e g a m e o f
b a l l is h i t , h e
as a g l i m m e r
of any n u m b e r
statistically
p o s i t i o n s
r u n n e r ,
calculate
is, w h y
S o c i e t y
" s a b e r m e t r i c s , " s e a r c h
It
strategies:
third o f
t h e
S A B R ' s is n o w
" t h e
f o r e v e r
a n d
e s t a b l i s h e d .
7 0 2 ) .
s u g g e s t i n g 6 ) ,
w e l l
f o u n d i n g
p u r s u i t ,
m a n a g e r s
hard
m a n a g e r
a s k
a n d
hole,
c o n s c i o u s l y
r h e t o r i c a l l y
b e c o m e
t r a n s f o r m i n g
the
was
t h e
t h e
s o p h i s t i c a t e d
Baseball
o f
test
t h e
( L i n d s e y ,
Percentage
p i t c h e r
t o
t h a t
t h e
a h e a d "
little chance o f a play at s e c o n d ; a n d
so m u c h
e r a s e
1 9 8 6 ,
plays
calculation
t h e
a r e
a d v a n -
t h e
c o n c l u s i o n
resiliency
o r g a n i z a t i o n
d e f i n e s
in
t h r o w s
h e
o f
i n v o k e d
c o m b i n e s
c r e a t i o n
statistical
"percentage
yet
t h e
r e p r e s e n t e d
h o w
H e
first.
t h a t
s i m u l a t i o n s
o b v i o u s
o f
p u r p o r t e d
d e t e r m i n e d
t e a m
t h e
h a d
f r o m
t h e
c h a p t e r
is r a c i n g
play at
this
a n d
players
have
was
1 9 7 1
b a s e b a l l
b e e n
play; he m a y
this
in
( J a m e s ,
(see
as
s c i e n c e
Bill J a m e s
w h a t
r u n n e r s
s u c h
C a r l o
w i n n i n g
b a t t i n g
C o o k
t o
r e g u l a r l y
s t r a t e g y .
a l t e r n a t i v e
h e
-
p r o f e s s i o n a l
h a s
f o r
short,
p u b l i c a t i o n
p s y c h o l o g i s t s
W h i l e the
o v e r
a c r o n y m
statistician" cess
t o o k
R e s e a r c h ,
s c i e n c e
o f
t h e
b a s e b a l l
b a s e b a l l "
Is t h e
p r o b a b i l i t y
p u b l i s h e d
t h e
a n o t h e r
s e e m i n g l y
C o o k .
d e p t h
a n d
Y e t
p u t s
b o o s t
g u r u
1 9 7 4 ) .
h a s
o p p o s i t e
o u t c o m e ,
t h e
E a r n s h a w
1 9 7 0 s ,
T h e
a b o u t
t h e
in
M o n t e
t h a t
b a s e b a l l
B a s e b a l l
a n
justify
t o
o n e
a c o n s i d e r a b l e c a n
( F r e e z e ,
241
Research
h a n d e d n e s s
g a m e
o n
c o n s i d e r a t i o n s
a n a l y z i n g B y
o f
world
e x p l o r e d
o r d e r
m o s t
t h e
article
e m p l o y e d
s m a l l
m e t a l l u r g i s t
p h y s i c a l
O n e
the
Operations
A n o t h e r
r e s u l t s
a d d i n g
j o u r n a l
b a t t e r s
1 9 5 9 ) .
r e m a r k a b l y
r u n s
T h e
science.
e n j o y e d
( L i n d s e y ,
is
Life.
rule
s t o p
d u g o u t s
is
t h e m .
entered
( T h o r n
t h e
t h e
q u e s t i o n
the shortstop's h e a d
Palmer,
s h o r t s t o p ,
" p l a y i n g T h e
a n d
a n d
1985, p.
w h o
h i m s e l f
p e r c e n t a g e s , " t h a t T h o r n
e v e n a n d
in
5).
t h u s if
h e
P a l m e r
h e r e ? are, a c c o r d i n g
t o
s o m e ,
t h e
n e x t
n a t u r a l
Downloaded from https://www.cambridge.org/core. Newcastle University, on 03 Oct 2018 at 11:29:14, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.009
e x -
Numbers
242
t e n s i o n . S t e v e a
S o m e
M a n n ,
t h i n k
b a s e b a l l
d e s i g n a t e d
b a t t e r s , B u t
o t h e r
a n s w e r s . p u t e r b e r
w i t h
s u c h
c o n d e m n
d o e s
it,
f o r m i n g
h a v e
s t u d y .
N e w
G a l t o n
p r a y e r ,
u s i n g
c e r t a i n
b e f o r e
c l a i m e d s t u d i e s
t o
s e e m e d
statistics
A s
t o
is
o r
t h e
n o t
o l d
o f t e n
q u e s t i o n s
t h e
t o
s t a n d p o i n t .
W h e n
a r e
tables
case
in
a d d r e s s
n e w
i n t o
t h e
s o l d
p i t c h e s .
t o
t h e
a
n u m -
t h e
o f
Pearl,
o r
w i t h
availability
a n d
t o
h i t h e r t o
l a b o r a t o r y ,
l o o k
at
e l u s i v e t h e y
t a k e
statistics
a
o l d
-
h e r P e a r l
1 9 2 5 ;
p .
s u c h h a v e
6 7 ;
also
m a t h e m a t i c a l scien-
i n c o n v e n i e n c e .
n e w
t o o l
o n e s
i n s p i r e d
f r o m
f r o m
t h e
o n
a l t e r e d
a n
t o
b i o l o g i c a l
less
o f
of
w o u l d
1 9 3 9 ,
a n d
Design
R a y m o n d
t h e y
o f
p r a y e r
a d d e d
r e f i n e d
social
t h a t
c o i t u s , i n a g o
p o s s i b l e
efficacy
his
w a s
ff.).
scientific
p h e n o m e n a .
i n f e r e n c e
13
a n d
o f
t h e
b e g a n
a c e n t u r y (see
m e a s u r e -
s u g g e s t
m i l k
t r a n s -
a n d
m a d e
i n t o
t o
f r e q u e n c y
precisely,
h a v e
f o r
t o
statistical
e l u s i v e
w i t h
r e a s o n
o f
o b j e c t s
a n d
p o w e r f u l
t h e
v a r i e t y
i n f e r e n c e ,
p p .
for
e v e r y
h i t t e r s ,
i n q u i r y
taste
p o s s i b l e
issues
p h e n o m e n a
b r o u g h t
o f
h a v e
F i s h e r
1 9 3 5 ,
m o r e
science,
o f
g e t
b e e n
a
r a t e s
A .
t h o u g h
m o r e
a n d
b r a z e n n e s s
i m p r o p e r
it
in
w h e t h e r
g i v e
m a k e
a l t e r n a t i v e
t y p e s
d e s i g n a t e d
p r i v a t e ,
R .
( F i s h e r ,
t h e
f o u r
n e e d s
c o m -
P u r i s t s
n o t o r i o u s
tea?
3). B u t
m a n a g e r
1982, p . 3 1 ) . B a s e b a l l
effect
i n v e s t i g a t e
as
Says
s a m e
a l r e a d y
i n s u r a n c e
i n d u s t r y ,
g a m e .
t h e
inaccessible
w o r l d . t o
w e l l
s i m p l y
a
a
g e t
b u t t o n s
d e s c r i p t i o n ,
d i s c r i m i n a t e
t o
as
1 9 7 4 , p a r t
a n s w e r
h o w
a c o t t a g e
r e s e a r c h e r s
s c i e n c e
first
s a m e
a n d
this
t h e
a n d
s u b t l e ,
1 8 7 2
t a b l e s
really
t u r f
o f
m o s t
" W h e n
t h e
1 9 8 2 ) .
a h e i g h t e n e d
in
in
a f t e r
n o w
d i d
s o
t h e
h a v e
o f
p a r t i c u l a r
s a m e
baseball.
this
a n d
d r a m a
a n d
( M c K e a n ,
h e r e t o f o r e
p u b l i s h e d
i m p o s s i b l e
B o o r s t i n ,
tists
o f
l a d y
t h e
1 . 0 0 0 "
m e t h o d s
s h o w i n g
b e
a r e
find
t h e
a g a i n s t
( M c K e a n ,
m a t t e r s
p o w e r
b y
p u n c h
artificial
W e
t o
b u t t o n s
r e c o r d
m e a s u r e
w i t h
world
P h i l a d e l p h i a : t h e
" E d g e
just
m o r t a l i t y
w i t h o u t
c u p
n o t
s t u d y
F r a n c i s
a
t h e
m a t h e m a t i c s
q u a n t i t a t i v e
c a n
c a n
Statistical
m a d e
Experiments
o n e ' s
the
a d d
i n
p u n c h
t e a m s
g a m e .
a p p l i c a t i o n s .
w a s
as
a l o n g
t h e
e v e n
p l a y i n g p o k e r . "
p r o f e s s i o n a l
Statistics
m e n t
e a c h
w e ' r e
s y s t e m s
o f
he'll
m a n a g e r
N o w
will
c o n s u l t a n t
h i t t e r ,
a l o n g
t h e
t h e y
rule
a
n e w
s t a n d p o i n t
o f
c h a r a c t e r .
E S P
T h i s
n e w
c h a r a c t e r
p h e n o m e n o n
s t u d y
statistics
r e p l a c e d
i n t o
s t r i k i n g
t h e
i r o n y
t h e
scientifically
scientific
s i g h t s
b e a r s
o f
t h e
t h a t
in
visible.
w i t h
f r o m c a r d
r e s p o n s e
o f
in
t h e
w h i c h d e a r
g u e s s i n g t o
t h e
C o n s i d e r
s u p e r n a t u r a l ,
m e s s a g e s
f u t u r e
s t a m p
t h e
as
m e t h o d s
u s e d
t h e
r e m a r k a b l e
t h e
a p p l i c a t i o n
d e p a r t e d t h e
k e y
o p p r e s s i v e
a n d
t o
m a k e
case o f
o f
t h e
i n f e r e n c e
c l a i r v o y a n t
p h e n o m e n o n .
scientific
t h e
It
inis
a
d e t e r m i n i s m
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Numbers
that
s e e m e d
B u c k l e , a t i o n s
o f
in
o f
1 9 3 0 s
b e
t h e s e in
Britain,
analysis. J.
m a d e
t h e
m o s t
a feat h e
m u n d a n e
s e e m s
t o
arrive
h e n c e
c a n n o t
R h i n e
set
u p
w a s
part
o f
t h e
e x p e r i m e n t s
five
six
w o u l d
t h e
o r
e i g h t
b e
e x p e c t e d
n o n - e x i s t e n c e
T h e r e
w e r e ,
e x p e r i m e n t a l l i g h t i n g o n
t h e s e
lations,
field
o f o f
s u n
c h a n c e
o f
p s y c h o l o g y ,
leaders
w h a t e v e r tics w a s
E S P ,
o r
trials.
e v e n
a
t o
T h e
E .
c o u l d
G .
a n d
w a s
e v e n t o
o f
R.
it
i n d i c a t i o n
o f
Statistical d e m o n s t r a t i o n s
p a r a p s y c h o l o g y
b u t
as S e y m o u r
has
r e m a i n e d
respectability
a n
( M a u s k o p f
w e r e
n e v e r in-
w h e n
o n l y
R h i n e ' s
u n d e r
certain
initial
attacks
.
-
t h e
m a t h -
1 9 3 0 s .
R.
1 0
5 0
,
calcu-
e v e n
q u e s t i o n e d that
R.
t h e
t h e
that i n d e -
idea
o f
t h a t h e r e , as in all o f (see
i n v o l v e d a n d
t o
n o t h i n g
elusive a n d
as
a
least
a n
M i c h a e l
science,
M c V a u g h ,
his
t o
M c V a u g h
o n 1 9 7 9 ,
statis-
straight-
elicited issue
t h e
o f
that,
e x p l a n a t i o n
c i r c u m s t a n c e s c o n t i n u e
o f
several
his relatively like
e x -
n u m b e r
a n n o u n c i n g at
a
M a u s k o p f
i n s p i r e d
c o n c l u s i o n s ,
a n d
I n s t e a d
p r o b a b i l i t y
a p r o c l a m a t i o n
o f E S P
a n d
w i t h
t h e
i n d i s p e n s a b l e
w h a t
M a u s k o p f
in
s u g g e s t e d
o b j e c t i o n
that
rejected
t h e
small
Fisher,
R h i n e ' s
o f f e r e d
that,
classic
insisted
sign
10~
B u t
K e l l o g g
A .
as
s e c u r e
as
T o
h e 3 2 0
statistics
c o n t r o v e r s y
a d e e p e r
p r o c e d u r e :
b e
p u r -
w o r l d
science.
p r o b l e m s
his
t h e
w e r e
e n s u i n g
l o w
back.
B o r i n g
c o n t r o l s
validity
o f
C h e s t e r
statistics
t h e r e
clear
o n e
is
subjects
cards
at
his
replicable,
Perception,
o f
d u r i n g
inspiration
t w e n t y - f i v e ,
o f
t o o
w h o
series o f r e p e t i t i o n s
o f
as
t h e
n o n e
m e a n i n g l e s s , real
l o n g
o u t
d i r e c t e d
still
i n c l u d i n g
t h e
B u t
statistical
s t r e a m ,
a c a d e m i c
b e
w e r e
w a s
o n
u s e
f r o m
t o
statistics.
is n o t
H i s
Extra-Sensory
t h e
E d g e w o r t h
e x t r a s e n s o r y
that
guessing.
n u m b e r
p r o b a b i l i t y
A m e r i c a n
m i g h t
p h e n o m e n a . s t e a d y
o f
s o u n d .
f o r w a r d
1 9 7 9 ) .
luminaries,
a
t o m o r r o w .
w a s
I n
read
a l l u d i n g
successive
M c V a u g h ,
statistical
b e
real, b u t
k n o w l e d g e
g u e s s e s
as
t h e
Psyt o
o f
m i r a c u l o u s
probabilities
s u c h
statistics
d i s t r i b u t i o n
p e r i m e n t a l
w i t h
results
rising
b e
card
a p p e a r e d ,
if a n y
T h e
m a y
c h a n c e .
c o u l d
Clark,
n o t
c o r r e c t
b y
later
w o n d e r e d
t h e
t e n
E S P
i m p l a u s i b l e
p e n d e n c e
t h e
it
deal w i t h
t h e
for
also g a v e
l a n g u a g e
limit-
m e t h o d s
p a r a p s y c h o l o g i s t
t h e
t o
Francis
arid
w a s
S o c i e t y
statistical
f a m o u s ,
t h e
c h o s e n
T h e
enlisted
built his p r o o f s
t e c h n i q u e s ,
W i l l o u g h b y
a n d
o f
c o n d i t i o n s ,
e m a t i c a l
o f
o r
in
p u b l i c
o f
( E S P )
t e r m s .
i n v o l v i n g
u s e
D u k e
o b l i g e d
p o s s i b l e
statistics.
a n d
D a r w i n ,
d e m o n s t r a t i n g
i n s t r u m e n t s
t h e
reality
o f
t h e
p e r c e p t i o n
its
p e r f e c t g u e s s e r s , s o R h i n e v o l v i n g
t h e
243
B o i s - R e y m o n d ,
task
m e t h o d s ,
in a crucial m o m e n t b e
D u
a m o n g
R h i n e ,
o f
world
t h e
p i o n e e r e d
e x t r a s e n s o r y
s u c h
t o
clairvoyance,
B.
d e m o n s t r a t i o n
a c c o m p l i s h
t u r n e d
scientific
a n d
the
H e l m h o l t z ,
P r o m i n e n t
t e l e p a t h y
t h e
p o r t e d
in
s h o u l d
R e s e a r c h ,
i n v e s t i g a t e assist
f r o m
naturalism.
flexible
chical
f o l l o w
science
m o s t
t h e
t o
rule
f o r t h
o f E S P in
a
o b s e r v e ,
m a r g i n s
1 9 8 0 ) .
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o f
Numbers
244
rule
the
M e n t a l
A s
t h e
e x a m p l e
m e a s u r e
e l u s i v e
scientific v i o u s l y
b y
t h e
v e n t e d
d e f i n e d
N o r t o n factor,
v i e w
t h e
o f
result p o w e r
h i b i t
t h e
b e
o f
t r a i n i n g
abilities, a n d
t h e y
a v e r a g e b e i n g less
v a r y
o r
i n
e v e r y
t o
is
t o
B r i t a i n ,
n e u t r a l i z e
o n e
just
( q u o t e d
electricity,
( S p e a r m a n , results. t h e o r y
a n d
b y
n o
i n
1 9 0 4 ) .
B u t
t h e
first
m e a n s
f a c t o r s t o
m u s t
T h o m s o n w h i c h
in
i n d e e d n o t
t h e
a n d
w i t h
s u c h
t h e
t h e
" I t
a a
t h a t
o f
all
a n
o f
m e n t a l
c o u r s e
a
i n
h e
w r o t e ,
-
t e n d
a v e r a g e
i n
S p e a r m a n n o
n e w
i n t e l l i g e n c e
m e a s u r e m e n t .
real
o b v i o u s l y s c i e n c e
i n t e r p r e t -
g e n e r a l t h e
o r
t h i n g
" a n a r c h i c "
w a s
t h e
w a s
w h o s e is
-
factor,
m o r e
p h y s i c a l
rival
o f
h o t c h - p o t c h
g e n e r a l
is
t h e
necessarily
S p e a r m a n ' s
o f
-
e x -
p a r t i c u l a r
o n l y p o s s i b l e a
e n e r g y
n u m b e r
t h i n g s
abilities. T h o m s o n p r o d u c e r
as
o f
i n s t a n c e ,
p r o p o s e d r e d u c e d
o f
l a r g e
1 9 6 4 ) .
f o r
i m p o r t a n t e n e m y
in-
p r i m a r y ,
s u c h
a n o t h e r
m e a s u r e
n a t u r e ,
his w a s
w a s
m u s t
W h e r e a s
p r e c i s e l y
o f i n d e p e n d e n t
I n
m e a s u r e m e n t :
a n d
fact,
s u p p o r t i n g
factor,
a n y
T u d d e n h a m ,
this
in
e n d e d
r e s u l t s
g e n e r a l
t o g e t h e r .
s a m e ,
t h e
statistical
p e r t u r b a t i o n s
t h e
T h e
a n o t h e r .
b i o l o g y ,
i n t e l l i g e n c e
a h o s t
H o u s e ,
o r
G o d f r e y
o f
a n d o f
-
specific
i n d i r e c t
v i e w ;
like
m e a s u r e m e n t
t h e
h e
ability
p r o m i s c u o u s l y
t h e
a
g,
i n t e l l i g e n c e ,
ability w o u l d
w e r e
r e s u l t s
o n e
f r o m
o f
t h e
i n
w a s
physiological,
g e n e r a l
statistics
f r o m
c o n c e a l e d
a s u m
M o r a y
p o o l i n g
w i t h
" s a m p l i n g "
o f
e m e r g e d
a s s o c i a t i o n i s m
i n t e l l e c t u a l
t h e s e
m e a s u r i n g
d e a l
t h e
b u t
d e -
1 9 3 0 ) .
p r o b a b l y
e q u a l
p a s s i v e
statistical
called
i n t e l l i g e n c e ,
t h e
c o n v e n t i o n .
t o
w h a t e v e r " o f
social
o f
p r e -
i n
S p e a r m a n ,
t h a t
n o t
p o s s e s s e d
h a v e first
o f
t h e
is l a r g e l y
trait,
t o
s t u d i e s
S p e a r m a n ,
o f
o f
s e e m s
a c c i d e n t
t h e o r y
g e n e r a l
p r o d u c t
intelligence,
his
t o
h a d
c h a r a c t e r
a n d
f r o m
a s e n s e ,
S p e a r m a n
n o
c o n t r a s t
a n a l o g y
b y
o f
w a s
factor,
f o r
o f
f a c t o r
it
also
n e e d
s t u d y
a t i o n
i n
t h e
e l a b o r a t e l y
n a t u r e
w h y
t h a t
d o m i n a t e "
b y
a
C h a r l e s
c o n t e x t
m e a s u r e m e n t
c o m p l e t e l y
t h u s
t h e
abilities,
r a n d o m l y
as
isolate
v e r y e x i s t e n c e
p e r s o n s ,
o f
m e a s u r e m e n t s
m e a n
u n p e r t u r b e d
o f
" s i m p l y
c o n t r o v e r s i a l
analysis.
P e o p l e
o r
in
m e t h o d
h e l d
b r a i n .
w h i c h ,
w h o s e
t o
d i s t i n g u i s h e d
o f
u n d e r l y i n g
m u l t i t u d i n o u s
since
w h a t
1 9 7 9 ;
special
f o u n d
d i f f e r e n t o f
o f
v a r i o u s
statistics
all m a n i f e s t a t i o n s
active,
a s t r o n o m i c a l
f e a t u r e s c a n
s o m e
m o s t
o f
easily
e n t i t i e s
" m o n a r c h i c a l "
as
o f
a l w a y s
i n t e l l i g e n c e
s h o w n
t h e o r y
d i f f e r e n t
s t a n d a r d
t h e
p o w e r
s o m e t h i n g
b y
in
( N o r t o n ,
S p e a r m a n ' s t h e
h a s
m i n d
d e s p i s e d
t h e
analysis
u n i t a r y
h e
b y
n o t a n d
c e n t u r y ,
u n d e r l y i n g
f a c t o r
B e r n a r d
t o r
d e g r e e
t e s t i n g
t h e
t h e
A l t h o u g h
s m a l l e r
factor
facts
m e a s u r e
statistics.
c o n s t r u c t
t h e
t o
o f
is
p e r h a p s
m i d - n i n e t e e n t h
g e n e r a l
o r
I Q ,
s e e k s
o r
s h o w s ,
p h e n o m e n a
e x i s t e d .
g r e a t e r
E S P
C o n s t r u c t i o n
r e a s o n i n g , fined
o f
world
o r fac-
f o u n d e r tests
i n
B u t
h e
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Numbers
t h o u g h t b e
t h e
factors
r e g a r d e d
m o r e
'reality*
s t a n d a r d T h e
a n
rather
a n s w e r s
t o
o u t
that
p o s s i b l e
o f
t h e
d e f i n i t i o n
100,
t h e
a n
later I Q ,
s t a n d a r d
o f
n o t
u s e
r e p l a c e d
a c c o r d i n g
t o
S t a n f o r d in
the
p s y -
U n i t e d
factor
analysis,
o n
a d d i n g
w h o
relative
t o
the
in
first
age.
m e a n
recm a d e
for
-
effectively
w i t h
as
b y
p r o p o s e d
m o s t
f o r m
a d v a n c e
b r o u g h t
T h i s
initially
t o
c o r r e c t
t h o u g h t ,
c h a m p i o n e d
w h i c h
u p
h a d
T e r m a n
q u o t i e n t
d e f i n e d
4 2 ) .
S p e a r m a n ' s
q u o t i e n t ,
this
p.
a
t h a n
B i n e t
b u t
o r
rather
assessed
Stern,
living, 1 9 3 9 ,
t h e
a n y
B i n e t
it useful,
intelligence
o f
t e s t i n g
b a s e d
w a s
m a d e
d e v i a t i o n
w a s
A l f r e d
p r o c e d u r e It
c o s t
s h o u l d
w i t h o u t
( T h o m s o n ,
intelligence
d i d
a n d
t h e
intelligence
F r e n c h m a n h e
o f
coefficient"
unitary
b y W i l l i a m
o f
i n d e x
is p r o p e r l y
o f
W e c h s l e r
statistical a n d
-
a n
q u e s t i o n s .
c l o u d s
d e f i n i t i o n
T e r m a n .
o r
d e s c r i p t i v e
later r e n o u n c e d
b y
p o s s i b l y
a n d
intelligence
t h e
coefficients,
t h e
h e t e r o g e n e o u s
p s y c h o l o g y o g n i z i n g
m o r e
"statistical
p i o n e e r
m e n t o r ,
245
S p e a r m a n ' s g,
o f
t o
world
particularly
a c o r r e l a t i o n
l o o k e d
his
a
o r
the
a n d
a v e r a g e ,
T e r m a n ,
T e r m a n as
t h a n
c h a m p i o n
L e w i s
S p e a r m a n
a n d
t h a n
A m e r i c a n
States.
intelligence,
m o r e
d e v i a t i o n ,
c h o l o g i s t
b u t
as n o
o f
rule
a
e a c h
i 5
p u r e l y a g e
w a s
( W e c h s l e r ,
1 9 3 9 ) . T e r m a n
d i d
n o t
w o r r y
a c k n o w l e d g e d
that
h o m o g e n e o u s .
B u t
since
t h e y
m o s t
abstract, a n d a
n o t
mill
c o n c e p t u a l
h a n d
A l t h o u g h h a v i n g sisted in
o r
h e
that
A l r e a d y
o n
stress
o r
tests
test b e
o f
w h i c h
t h e
in
a test
a
single F.
N .
all called v a r i o u s yields
u s e
o f
t h a n
g,
m e a s u r e F r e e m a n ,
for
m a n y o f S.
i n c r e a s e d o f
a single
a b r o a d
s o m e o n e ' s
a t t e n t i o n
result
( R u m l , o f
a n d
is
p p . o f
traits, b u t g e n e r a l
a
year
a n d
c o n t e n t
firmly
b y
that
that
1 4 3 ) . E d w a r d
in-
c h a l l e n g e
character
t h e
as
level
" q u o t i e n t "
insisted
score,
1 3 1 ) .
g r a d e
H e n m o n ,
R u m l
as
age, a n d
s y m p o s i u m
B.
that
c h i l d r e n
t o
C .
t h e
129,
p r e p a r e d a
a n d
success
age.
particular
" s o m e
o t h e r s ,
m e n t a l
t o
o r
t h a n
d e t e r m i n e
o f
A .
1 9 2 1 , p .
d i v e r s e
intelligence
V .
strictly
w i t h
s p o k e
intelligence
I n
n o t
intelligences,"
c h r o n o l o g i c a l
c o n c e p t
C o l v i n ,
o f
1 9 2 1 ,
s h o u l d
H e
r e c o g n i z e
correlations
intelligence. S.
m u s t
p s y c h o l o g i s t s
q u a n t i t a t i v e
a v e r a g e
W e
their
t h e
is
p r o g r e s s ,
"hierarchy
l o w
latter
intelligence,
as p o s s i b l e "
e v o l u t i o n a r y
r o u t i n e l y
f r o m
this
a n d
realism.
i m p o r t a n t
( T e r m a n ,
o f
u n d e r c u t w e r e
metaphysical
aspects,
t h e
h e
t h e
r e p l a c e m e n t
t y p e s
as h o m o g e n e o u s
a t o p
m o t o r m a n "
rather
t h e r e
o f
society.
it yields
f o r m e r
o n
t o
s t a n d s
age, d i f f e r e n t
1 9 2 1
o f
a d v a n c e d
car
d i s t r i b u t i o n
m a n y
stages
" b e c a u s e
street
in
m e a s u r e
a n
t h i n k i n g
W e c h s l e r ' s
w a s w i l l i n g
h i g h e s t
issues
aspects are m o r e
m e n t a l
intelligence,
T h u r s t o n e
t h e
t h e s e
S p e a r m a n ' s
t h e
s t a n d a r d i z e d
o f
has
o p p o s e d
a g i v e n
s c h o o l .
this
s o m e
abilities
c o n d e m n
a b o u t
intelligence
r e p r e s e n t
useful
m u c h
L.
L.
traits, "in
a n y
s h o u l d
T h o r n d i k e d e n i e d
p o w e r
that
w h i c h
Downloaded from https://www.cambridge.org/core. Newcastle University, on 03 Oct 2018 at 11:29:14, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.009
re-
Numbers
246 sides
in
task"
h i m
a n d
d e t e r m i n e s
( T h o r n d i k e ,
1921, p.
rule
his
convention.
f o r m
the
R a t h e r
factor
it
analysis
ability
n o t
was
a
differently,
so
set o f perhaps
seven
s a m e
analysis
p r o p o s e d t h e m . (or
by J.
of
chapter R e a d
issue,
5). B u t
can
be
W h a t e v e r
m e n t a l
United
it
a n d
b o t h
g
-
influential. I Q deficiency,
preferred
n o t
a
according
m o r e
w e r e
n o t
t h a n
inferred
intelli-
I Q ,
to
the
o n e
often
the
has
1964, p.
that
used
in
the Russians
( W i g d o r
for
a n d G a r n e r ,
admission
fessional
schools
in
o f m u c h
criticism,
the for
influence
to
decide
U n i t e d
m e n t a l
constructs.
that
w h a t e v e r
w h a t e v e r
can
testing has
education,
its
alleged
colleges
association
in serving a n d
be
b e c o m e
c o m m i t m e n t
especially in
"secret w e a p o n "
States. Ability
1981,
516).
1982, vol.
selective
treat-
to
their statistical
a d d e d
o f
correl-
( G o u l d ,
d i c t u m
for
o r t h o g o n a l
impossible
statistician's
testing America's
w e r e
h u n d r e d
f r o m
g r o u n d s
a
s c h e m e
enthusiastic president o f the Educational Testing
w i t h
per-
points o u t in his elegant
reality o f
widely
to
to seven,
n o t generally
be
o f interpretation,
are
statis-
single
the P M A s
statistical
factorist
influential
it m e r e l y a
tests have quasi-legal standing in
a n d
called standardized
required
o n
( T u d d e n h a m ,
the difficulties
-
could
the
gave
and,
practice
" T o
it
to limit
P M A s
in the
the
T h u r s t o n e
fact give
S p e a r m a n
writes:
exist"
States. A n
its baleful
in
in
believed
once
are
is
measured,
m u s t
e n o r m o u s l y
did
t h o u g h t
intellectual
m o s t
abilities." These, a n d
giving
s e c o n d - o r d e r
T h u r s t o n e
'measured'
for
a
T u d d e n h a m
exists
o f
the
o f
for various special abilities, b u t
t h e m . A s S t e p h e n J a y G o u l d
this
b e t w e e n
capable
capacity
b e c a m e
that
impossible
since T h u r s t o n e ' s
i n d e p e n d e n t ) ,
m e n t
m e n t a l
it p r o v e d
P. Guilford,
M o r e o v e r ,
ations a m o n g
"primary
was
every
mistake.
a n d a range o f deviations
the
in
because h e
gence measure
real. U n f o r t u n a t e l y ,
world
126). T h u r s t o n e
critic o f the unitary I Q , t h o u g h tical
the
a n d
legitimating
tests
a n d
p r o -
the
eugenics a n d
an
contest
E T S
g r a d u a t e
testing has b e e n
w i t h
Service
in its
1, p . 9 5 ) , a n d
the
target
racism,
inegalitarian
or
capitalist
order. T h e r e f r o m
are,
T e r m a n
terpretation T e r m a n m u c h , o u t
to
it
m o r e
was
foolish for
A m e r i c a n
p r o v i d e d
A m e r i c a n
have than
for
the
to
favour
l o w
for
testing was
s e e m
could
parents
for
o r
W a r
language
T h e
(Kevles,
skills
as
in-
to
require.
never
achieve
teachers
closely linked
sterilization.
enthusiasts
a hereditarian
w o u l d I Q
I Q
o f "feeble-mindedness"
First W o r l d
English
criticism.
evidence
w i t h
sentimentality
g r o u n d s
such
t e n d e d
p e o p l e
evidence
in the
required
that
t h e m . I Q
stztcs
legal
recruits
clearly
reasons
fervor
suggested
any ambition
ations
g o o d
A r t h u r J e n s e n
w i t h
often
and
in s o m e
that
perhaps,
to
h o l d
to eugenics, in three
massive
a n d
gener-
testing
1968-69), using
well
as
a
o f tests
considerable
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Numbers
m e a s u r e
o f
nativist l a w s
p r o p a g a n d a
that
B u t h a v e
acculturation,
t h e
n e f a r i o u s
surely
rhetoric, scores
b e e n
( T e r m a n ,
o r d i n a r y
1 9 2 3 , p p .
p o i n t s
s t u d e n t s .
l e m s
o u t
W i t h
n i n e t e e n t h w a s
n e e d e d .
s t u d e n t s dary
e x i s t e d
w e r e
for
that
w a y
regard
o f
t o
c a n
l o w e r - c l a s s
i n e d u c a b l e .
T h e
p r e v a i l e d q u i t e
t h e r e
o f
i n f l u e n c e
G e r m a n y .
T h o s e
for It
s c h o o l s
d i c t e d
w a s
e v e n
T h e T h e r e
" t o n e "
b e c a u s e
W a i t e s ,
1 9 8 1 , u s e
s e e m
w o r k i n g - c l a s s
o f o f
p p .
o f
t h e
t o
s t u d e n t s t h e
their
b e
d o
b a c k g r o u n d s
results tests
o u t J e w s ,
m o s t
in
t h e
U n i t e d
c h i l d r e n
Intelligence
w i d e s p r e a d ,
a l m o s t h a v e t o
b u t
this.
a d m i s s i o n s ,
a n d
b e e n
used. a n
f r o m
a p t i t u d e
universal,
i m p o s e
b u t
e n d
h e l p
o f
t h e
learning
p r o b -
tests h a v e
rarely
as
alternative
as
e d u c a t i o n a l
e v i d e n c e
s y s t e m
o f
that s e c o n -
test
results.
In
test-
fact,
States, p e r h a p s
m u c h
less
districts in
s o m e w h a t that
G r e a t
scholarships
t e s t e d
a n d
Britain
b e t t e r
intelligence
b e -
c l a s s - b o u n d
t o a w a r d
p o o r l y
States
a p p e a r e d
in
1 9 2 6 ,
it
s o o n
a n d
t h e
t e s t i n g
intelligence
m u l t i p l e - c h o i c e
t o
has
o u t s i d e
is
C o l u m b i a
elite c o l l e g e s w e r e
T h e
t h e
t o
W a r
( S u t h e r l a n d ,
was, o f course, n o t h i n g equivalent
s c h o o l s .
California.
W o r l d
a d m i t t e d ,
m o r e
intellec-
S e c o n d
w a s
o n
t h e m
t h e
t h o s e
reliance
I Q
o p p o r -
for
"attain-
tests
that
that
t h e y
t o o
w o u l d
t h a n
their
tests
1 9 8 4 ;
also
E v a n s
p r e a n d
1 0 6 - 8 ) .
t e s t i n g
c h a n n e l e d
d i d
b e
British
U n i t e d
t h e r e
t h a n
o r
t h e
p r o v i d e d
w o u l d
s c h o o l ,
m e n t a l
their
u s e d
m u c h
scores
e x a m i n a t i o n s
h a v e
against
ability
that
e d u c a t i o n a l
1 1 +
c h i l d r e n
a r g u e d
w o r k i n g - c l a s s t h e
tests in
at
w i t h
n o t e s
after
t o
is
c l a s s - b o u n d
i n
o r
intelligence
s c h o o l i n g
test
until
i n d e p e n d e n t
far its g r e a t e s t
o f t e n
as
t h o r o u g h l y
s t u d e n t s
in interwar
e v e n
m e n t a l
testers
anti-egalitarian
A s i a n s
a n d
admissions,
Gillian S u t h e r l a n d
o f
i m m i g r a t i o n
d i s c o u r a g i n g
c h i l d r e n
c h i l d r e n
l o w
his
o f
a n d
b e
i d e n t i f y i n g
part
intelligence
tell
m o v e
universal
selective
i n t e r p r e t
that
o f
t o
fear
a reactionary
t e s t i n g
n e w
d e s p i t e
w o m e n
in E n g l a n d
m a n y
plish
m e n t a l
h e l d
e d u c a t i o n
m e n t . "
a r m y
h e
a d v a n c e d
tunities
t h e
a n d
t h e
not
for
t h e
b e c a m e
E u r o p e a n s . o f
b o o k
t o
g r a m m a r
that
1 9 2 3
t o
east
T e r m a n ,
a d m i s s i o n
u s e d
r u i n
In
n o t
b y
a
hardly
s o m e
r e a s o n s
e x e r t e d
cause
t o
d i d
E v e n
in
247
results w h i c h
a c h i e v e m e n t s
i n t r o d u c t i o n
against
e d u c a t i o n
t h a n
-
o f d i s c r i m i n a t i o n .
authorities
i n g
that
century,
a n d
c i r c u m s t a n c e s ,
m e n
world
c o n t r i b u t e d
s o u t h
a n d
2 4 - 5 ) ,
t h e
d i s c r i m i n a t e d f o r m s
a i m s
the
d u b i o u s
h a v e
against
teachers
tually equal t o w h i t e G o u l d
m a y
e x a g g e r a t e d .
c o u n s e l e d
u n d e r
p r o d u c e d
a n d
d i s c r i m i n a t e d
rule
b e e n 1 1 +
t h e in
test
i n s p i r e d in
f o r c e d
Scholastic g i v e n
u p p e r
t o
t h e
1 9 1 8 , t o
find
closely
e x a m i n a t i o n
s c h o o l s
difficult w a s
less
classes has
b e e n
in
t h e
T e s t ,
e x t r a o r d i n a r y
technical
a b o u t
results
h o p e s
Britain
e x t r e m e l y
o f
o t h e r w a y s
A p t i t u d e
in
t o
g e n e r a l i z e b y
s t u d i e d .
h o w
o f
the
s c r e e n i n g t o
for
a c c o m c o l l e g e
diversity
Downloaded from https://www.cambridge.org/core. Newcastle University, on 03 Oct 2018 at 11:29:14, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.009
a n d
Numbers
248
decentralization is
probably
the
or
system,
classes
T h e
a n d
certain
n o t
It
c o n t e x t
o f
h o p e d ,
possible,
at
frame T h i s
is t h e
studies, inspiring h i m legerdemain,"
n u m b e r s
E c o n o m i c
for
w i t h o u t
together
to
probabilistic the
f r o m
ways in w h i c h p e n d
an
exact
is
practical
character
w h e n
has not, science, of
to
the
w h o s e
E. B. W i l s o n
the p r o p e r
o n precisely h o w
a b o u t
o f its
just
founim-
measurement,
1984, a n d
have
in
the
rivals that
have p.
at
229).
being
a
a
index
o f the value o f the
less
o f
that
go
unit
o f
n u m b e r s
o f statistics, less
flood
measured.
c o m m o n
E d g e w o r t h
might
Because
o f I Q , have
b e c o m e
1880s, Francis
c o n c e i v e s it. O n e
1932).
A l t h o u g h
century
"statistical
c o m p o n e n t s
least
manipulation
this
is
the
medical
to p r o d u c e
w h a t
remarks,
n u m b e r s
In
the
has p r o v e n
certain
(Wilson,
it is p o s s i b l e
clearly
D u n c a n
m e a s u r e
o n e
p u r p o s e s
influence
collection
t h e m .
firmly
Certainly
statistical
abstract
p r o m i n e n t
analyzed
currency
the
m i g h t
de-
see the value o f g o l d
a real entity, u n d e r l y i n g all c o m m o d i t y p r i c e s a n d i m p e r f e c t l y i n d i c a t e d t h e m ,
b u t
n o t
reducible
to s o m e
function
best m e a s u r e
o f the value o f gold
according
the
v o l u m e . by
to
If,
o n
definition
than
o t h e r w h a t
t h e n
it
the
o f
w o u l d
their
hand,
the
can
buy,
price
o f
prices value
o f these prices. In w e i g h t
o f gold
m e a s u r e d
grain
calculation
should
o f
n o t
than
s o m e
be
w e i g h t e d
to the
index
n u m b e r s
n u m b e r that
it
merely
m e a s u r e
almost
entirely
t h a t it
b e
s o m e
l o n g - h i d d e n
entity
their
identical o v e r
m o r e
quantity
stable, unbiased,
to
as
average
pragmatic;
the
c o m m o d i t i e s
is c o n c e i v e d
by
all
highly
c o n s u m e d
1920s, m a d e h e
as by
that case
according
1888-90). Irving Fisher, writing in the early
the ideal index like,
these other
rather
that o f pineapples precisely in p r o p o r t i o n
( E d g e w o r t h ,
the
the to
c o m m o d i t i e s ,
stability
a
intelligence.
indirect,
( D u n c a n ,
advis-
m o r e
as s o m e it
for
intelligence
in.
for
measure,
use
a b o u t
b r o u g h t
tradition
a n n o y e d
i n d e x
the
o f
intelligence
defining
considerations
discussion
genetics
o f
D u d l e y
u p
m o n e y
plainly derive
in
Otis
m a k e
m e a s u r e m e n t ,
debates
is o f t e n
ever
a
"intelligence,"
designed
give
p r o p a g a n d a
n u m b e r s ,
this looseness. A s
the
t o a s s e r t t h a t critical analysis is b e t t e r t h a n
except
index
are
h o w e v e r ,
Galtonian
that
statistical m e a s u r e m e n t o f
tests
their
theory
weakness
change
w i t h
psychology
a convincing
testing
"legitimates"
aggregate
is o n l y p a r t l y o v e r c o m e
the
it
m u c h
m u c h
of m e a s u r i n g
least w i t h i n
n o t
respective
quantitative
r e n d e r e d
standardized
Perhaps
h e t e r o g e n e o u s
t o o
does,
elusiveness, w h i c h
statistical m e t h o d
to
their
does
system,
universities.
the
interfered
admissions.
g r o u n d e d
ders
selective
that
world
1982).
it e v i d e n t l y
of defining
the
States school
(Resnick,
b u t
"aptitude,"
has evidently ing
U n i t e d
entering
difficulty
even
the
inevitable
hierarchical o f
o f
rule
the
required
reversible, (Fisher,
o f a n d
1911,
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Numbers
1 9 2 7 ) .
In
c o n t r a s t
n u m b e r s really
-
I Q ,
in particular,
b e e n
at
m e a s u r e m e n t s u m e r
t o
a n d
issue. acts
t h e
w h o l e s a l e
t h e
price
decisions,
this
e c o n o m i c
lated
in
u s e d
t o
m o r e
t h a n
r e c o n c i l e
m a n a g e r s , t h e
M o s t
o n e
e c o n o m i c
w a y ,
s o
a n d
p r o c e s s
o n .
that
o p i n i o n
statistical
results
R e s p o n d e n t s t h e y
m a y
c h o o s e i n g
n e v e r
h a v e
are
I Q
o p i n i o n
m a y
b e
o f
w a s
n o t
p u b l i c
m u c h the
close
o f
in
its
W a r n e w
c o m p u t a t i o n s . "the
H e
ability
g e o g r a p h i c
a n d
d e v e l o p e d
w i t h
d e p e n d e n c e clinical t h e
o f
e n h a n c e d quantified. E l m o
o n
s e n s e
case
in
t h e
in
I Q , t h e
first
t h e
s a m e
t h e
statistics -
p i o n e e r s
w o u l d
h a v e
t h e
o r h e r e a n d
o f
least
b o n d
are
in
calcu-
s q u a r e s
are
attentively t h e s e
t h e
t h e y
o n
b y
n u m b e r s ,
t e n d e n c y
m e a s u r e
issues
a l w a y s
t h e
o f
t h e m .
a b o u t
are
t e r m s
socially
w h i c h
o b l i g e d
o f
t o
poll-
p u b l i c
c o n s t r u c t e d ,
o f
d e -
p u b l i c
t h e
a
for
large
( B e r n a y s , o f
f o r m e r
1 9 2 3 ,
like a n d
c h a m p i o n
better
t h a n
actuarial
a n d
s a m p l e s .
o v e r
w i t h
a
p p .
t h e
G e o r g e
d e n i e d
b e
s a m e o f
5 3 - 4 ) .
t h e
w i d e
m u s t
probabilities o f
d r e w d u r i n g
d e v e l o p m e n t
n a t u r e
s a m p l i n g ,
a
w h i c h
a n d
s a m p l i n g
t h e
r e c k o n e d .
w h i c h
scale
ability
t h e
statis-
tact as a
s u r v e y s
self-criticism
s t u d y
scientific
o f
political
p r o p a g a n d a
c o n s u l t a n t
o n
r e q u i r e d
b e
w a s
m e d i c a l
specialized
c h a n g e d
s e c o n d e d
s a w
u s e f u l n e s s
s u r g e o n " t h e
o f
a
b a s e d o n
enterprise,
success
relations
a
b e e n
c o u l d
L. B e r n a y s
1 9 2 2 ) . H e
is
that
that
reactions
has
o f p o l l i n g
o n e
E d w a r d
t h e
are
o p i n i o n
a d v e n t
b e c a m e
p u b l i c
area
that
d o c t o r
as
set
p u b l i c
p a i n s t a k i n g
e x p e r i e n c e
t o
a p p a r e n t
g r o u p
p s y c h o l o g i c a l t h e
clearly
a l m o s t
o r
g e n e r a t i o n
d e n y
e s t i m a t e
c o n -
different.
o p i n i o n s
h e l p
L i p p m a n n ,
n o t
o f
u n i q u e
m a n y
t o
t h e
a n d
n u m b e r s
W i t h o u t
q u i t e
w h i c h
s t o c k
w a t c h e d
m u c h
a n d
p i o n e e r s .
i m p o r t a n c e
T h e
R o p e r ,
t o
a n d
w i t h
p r o f e s s i o n a l d i d
for
it also
f r o m
(see
are
n e v e r
r e p o r t s
rates,
a k i n
m o r e as
R e v o l u t i o n ,
t h e
r o u t i n e
has
m a n u f a c t u r e d .
c e n t u r y ,
inspiration
t h e
b e i n g
t o
e v e n
i n v e n t e d ,
w i t h , a n d
o u r
in
i n d e x
t h e y will o n l y partly agree. I n addition,
b e
F r e n c h
relations
for
t o
o b v i o u s
First W o r l d
m o d e l
B u t
the
t o
all
-
b y
o p i n i o n
m u c h ,
w i d e l y ,
said
r e c k o n e d
tical s a m p l i n g T h i s
b e
at least
t o
w h i c h
case
s a m p l i n g ;
officials.
a s k e d
t h o u g h t
w i t h
i n v o l v e
p h e n o m e n a
o f t e n
b r o a d c a s t
c o m e s
Since
are
a
are i n d e x
s o m e t h i n g
displays
s h a p e
polls
a n a n s w e r
If
f o r c e
t o
t o
results
bate.
p o l l i n g
m e a s u r e d
currency
is
interest
a n d
P u b l i c
P u b l i c
this
N o r
g o v e r n m e n t b e
the
t e c h n i q u e s
results,
w o u l d
o f
m e a s u r e d ;
statistics
d i v e r g e n t
investors,
deflation
affect
s o
249
t h e p h e n o m e n a
p r o c e s s
a n d
world
results,
indices
prices, i n v e s t m e n t respect.
a n d
p o l l i n g
o n
the
reality o f
inflation
L i k e
b a c k
rule
t h e
A s
-
in
b o t h
o p i n i o n G a l l u p
t h e
it a n d
latter,
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for
Numbers
230 they insisted that tunity
to
m a k e
designed people could
to
thus
p r o v i d e a n d
be
o r
d o n e
key
this was
to
the
largely w o r k e d n e e d e d
a
a
admirer
o f
ferent
the
the
T h e
Institute
Archibald
l o n g
w h i c h
to
the
decisions,
the
public
and
unless
o f
the
w h o
better
than
R o p e r
studies, have derstand
to
1940, p.
they
w e r e
m a t h e m a t i c s
as
o n
the
the
A.
research, w h i c h t o o k that
the
color T h e
goes
to convince influential,
o f
for political
longer shape
find
or
s o m e
for
as m u c h
price
and
o p i n i o n
polls,
to manipulate
dif-
poll-
o f
o f
those i m p o r -
learning
like
public
to
see
opinion
a n a l o g y is like
to
success
those
w a y
1940, pp. 332-3). T h e
anticipate,
expect
m a k e s
research
1901).
i m p o r t a n t
business. I should
m a r k e t
per-
their roots in a
b e c o m e
n o w
can
the
and
h a d
size o r
o f
K i a e r
theory o f sampling
n o
public
o u t
N .
a n d
h a d
could
or
theirs
Marshall
this as a m o d e l
it
b u t
conjec-
1980; also Bowley,
Crossley, h o w e v e r ,
s o o n
director
M o r e
o f
334).
possible
saw
h e was unable
Mosteller,
a m a n u f a c t u r e r
be used
soundness,
e v e n
m a r k e t i n g
the p u b l i c as t o
un-
it.
Gallup,
R o p e r ,
vaulted into T h e
Digest
lists
o f
w o r k e d
c o m e
w h o s e
the time o f Laplace,
viability.
w r o t e
. ." ( R o p e r ,
could
distin-
objective opinions
statistical
its
a n d
principles
research to g o v e r n m e n t .
intellectually
Bowley, a s t u d e n t o f Alfred
purchased.
the public wants, h e application
o f
learned
public
H a d l e y
probability
w h a t
t h o u g h
1930. R o p e r a g o
t h o u g h t ,
w i t h
o p i n i o n
a v a i l a b l e since
N o r w e g i a n
(see K r u s k a l
by
agreed
R o p e r ,
public
they
old political arithmetic, insisting that
of Francis E d g e w o r t h ,
Gallup, a n d
society,
n o t
century. T h e
w h a t
w o u l d
"the m o r e
m a d e
o f
o u t
o f issues. Polling
sense,"
also
find
w h i c h
R o p e r
t h o u g h
230;
to
carefully
t h e m ,
mass
a n d
e s c h e w e d
the e c o n o m i s t A r t h u r
dictating
w h a t
p.
b e e n
a
c o m m o n
that
use of sampling, m a r k e t
things tant
o f
Statistical
"Business
while
1944,
sampling
facts.
large corporations ing:
G a l l u p
individual,
statisticians
it e x t e n s i v e l y
R o p e r ,
thing.
in
o p p o r -
sampling,
h u n d r e d
variety
d e m o c r a c y
citizen an
the pollster
several
extraordinary
1890s to use sampling,
International
used
an
(Cantril,
o f
Probabilistic
just
o u t in the twentieth
science
haps, was
heard.
" h a r d - h e a d e d
speculations
b e g a n in the
to give the average
contacting
a g o o d
nineteenth-century
was
by
to estimate error h a d
tures a n d
world
b y its a c c o r d a n c e w i t h
experts" m e t h o d s
the
all g r o u p s , p e r m i t t e d
average
h a p p i l y , is a t t e s t e d
T h e
voice
vigorous
possessed
realistic
her
for
surely
that
guished,
his
thinking
the
Cantril
theirs was the w a y
represent
w e r e
rule
the
h a d
Crossley
limelight b e g u n
potential o u t
and
in
g o t
1936
c o n d u c t i n g
subscribers
for
reasonably well in the
their
start
as a result o f presidential its first
sampling five
in
the
1930s,
t h e Literary straw
w e r e
Digest
polls
in
population.
attempts, a n d
a n d
1916,
Its
fiasco. using
polls
h a d
at least g o t
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the
Numbers
w i n n e r
right,
ness.
J u s t
f r o m
a n
t h e
earlier
o f
t h e
w i s d o m
y e a r s
a
financial in
t h e
years,
f o r t a b l e
f r o m
w i n
b y
w o u l d
b e
bility lasted p r e d i c t e d m o r e
c o u l d
until
t h e
t h a t
( G a l l u p ,
H e
w o u l d
shifts
m a k e
m o s t h e
p o l l s
1 9 4 8 ,
p .
o f
t h e
v a l u e
t o
in
3 4 - 5 5 ) .
R o p e r o f
k n e w
d i d
for
o f f
t h a n
d e c i d e d
in o f
n o t
just
p o l l
t o
a g e ,
sex,
t h e
first
t i m e
o f
t h e
c o m -
R o o s e v e l t
Literary
G a l l u p ' s o f
w e l l m o s t
t h a t
t h e
a
air
Digest
o f
i n v i n c i -
P u b l i c a f t e r
O p i n i o n
t h a t
t o
b e
t o
a v o i d
f o r e c a s t i n g
t h e
n u m b e r s .
M o s t
c h a r m i n g l y ,
his
a n d
a n d
l e a r n e d
Digest,
p e o p l e ,
I n s t i t u t e H e
b e f u d d l e d
m o r e
a c c o r d i n g
far
o u r
{Literary
f o r e c a s t
h o w
t o
h a v e
b o t h
his
5 4 %
t h e
t h e y
1 9 3 6 ,
t o
c o i n
b e n e f i c i a r i e s
p r e f e r e n c e s
o p i n i o n ,
t h a t
w e r e
off"
a n d
n o t
n o t o r i o u s l y ,
l e a r n e d
in
d i d
a p p l i e d
1 9 3 6 . G a l l u p
a n n o u n c i n g
v i n d i c a t i o n
a n n o u n c e d
W e
Digest,
feel
w e r e
T r u m a n .
e r r o r
a d v i c e
political
p p .
available
c o m p e l l i n g
" h a v e
h a v e
his A m e r i c a n
d e f e a t
c a u t i o n a r y
g u e s s e r s ,
w h o
t h a t
p r e d i c t
1 9 4 0 ,
s m u g -
e d i t o r s
d i v i d e d
k n e w
o f
freely
m i l l i o n s
fail i n
t h e
t o
R a e ,
w e
o n e ,
o f
T h e
t h e
G a l l u p
a b l e
1948, w h e n
t o
t o
w a s
s o
6 ) .
p o l l i n g
h e
a n d
p .
w e
fact
m e a s u r e
infallibility.
a n d
t h a n
s e p a r a t e d
p i e c e
p e o p l e
stratified
H e n c e
s m a l l
critics s e c o n d o f
in
n o
b e e n
w h e r e
likely
a c k n o w l e d g i n g
c o n c e i v e :
a f f i r m
a
a n d
late
o n l y
B u t
m a r g i n
D e w e y
b u t
also
g a p
p o o r .
a b o u t
just
w a s
o n .
( G a l l u p
o n l y
release
s o
w i d e
t h e i r
m e t h o d ,
b u t
a w i d e
t h a t
o u t c o m e ,
c l u d e d
a
u s
h a s
L a n d o n ,
m o n t h s
7).
affluent,
t h e
careful
p r e s s
p .
p o p u l a t i o n ,
f o r t y
p o l l
t o l d
t o
1 9 3 6 ,
" H o s t s
f e w
Digest's
status, a n d
w o u l d
a
1 9 3 6 ,
relatively
r a n d o m
i n
3 1 ,
called
251
this
claims
w h i c h
f o r
h i n d s i g h t :
h a v e
14,
t h a t
v i c t o r y
world
q u o t e d
n o
a c c u r a c y '
the
d i s p l a y e d
it
m a k e
T h e y
p o l l i n g
N o v e m b e r
t h e m
o f
Digest
O c t o b e r
result.
a b o u t
a d v a n c e
" W e
a s w e e p i n g
a c t u a l
t h e
e l e c t i o n
Digest,
t h e
o f
t h e
' u n c a n n y
b y
s c o r e
1 9 3 6
year:
{Literary
p r e d i c t e d
m o r e
b y
b e f o r e
p h r a s e
p o l l s "
a n d
rule
o f o f
his t h e
p e o p l e , "
t h e s e
c h a n g e s
p r o f e s s i o n
t h a t
A m e r i c a n
p e o p l e
w h i l e
o n l y
2 8 %
in-
G a l l u p still
d e n y
it
6 ) .
7 . 3
N
E
W
V A L U E S
A t t i t u d e s
I n t e l l i g e n c e
a n d
t h a t
t h e
I Q
b e i n g
a n d
t h e
G N P ,
n u m e r i c a l ,
solidity
t h a t
i m p l i e d
b y
d e v i a t i o n entities,
f r o m a n d
m e a s u r e
n e i t h e r
a n
m e a n
a c q u i r e
n e v e r
u s e d : o f
e c o n o m y
r e d e f i n e
i n d i c e s
o r i g i n a l s
t h e
o f
in effect,
t h e s e
t h e i r
t h e
vitality
I Q a
c o r r e s p o n d s
h a d .
t o
t h e
c o m m o n
t h r o u g h a p p a r e n t T h e y
d e f i n e d n o r m a l
a r e
m e a s u r e m e n t . p r e c i s i o n
also
as m e n t a l
a n d
a c q u i r e a g e
d i s t r i b u t i o n e v e r y d a y
if v a g u e
a n d
a r e
s e n s e
n e w
o f
I Q
q u i t e t h e
n o t i o n s
B y a
d i n t
o f
k i n d
o f
m e a n i n g s d e f i n e d
as
d i f f e r e n t w o r d
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"in-
Numbers
252
telligence."
M o r e o v e r ,
e d u c a t i o n a l
p a t h s
b e
e v a l u a t e d
less m a i n l y s y s t e m o u t
t h e m
a n d
t h e
( B o u r g u e t ,
p.
studies
w h i l e
i n t o
rich
is
w e r e
Statistical
p u r p o s e s : G r a h a m
s t u d y
W a l l a s
a n d
1984,
1 6 2 - 8 0 ;
p p .
T h e
m o s t
t h e
for
s u r v e y s
a l m o s t is
is
m e t r i c s , "
their equal.
as
T h e
T o t o
a
u s e s
t o
s u p p o s e i g n o r e
o f
m u c h
t h e y t h e
g u t
m o s t
are s p a r k
the
s u c h
is
n o t t o
o f
t h e
o f
t h e as
r e d u c e
t h e
originality
o r
t w o
science
o f
stereoreleased
(see
B u l m e r ,
individuality, intellectual strikingly
since
polls
rational
t h e
o f
t o o
j u d g -
a c a d e m i c
t o
c o m -
" s c i e n t o -
p u b l i c a t i o n s o r
its a n d
q u a n t i f i c a t i o n
t h e m s e l v e s ,
university,
o r
o f
o r
a g e
i n h o m o g e n e o u s
for
b o o k s ,
scholar
that
for
t o
b y
a n d
t h a n
in
field,
are
all p a p e r s ,
o f
m o s t
rather
scholars
a r g u e d ,
n o t
largely b y
individual,
a
w i t h
1 8 2 - 5 ) .
intellectual
o f
u s e d
ideas,
n u m b e r
in
t w e n t i e t h
a s s u m e d
s t a n d p o i n t
resistance
the
p a r o l e
displays
feelings
vitality
it -
for
F l o r e n c e
associated
o b v i o u s
p p .
attitudes,
serious
t h e
is
m o r e
individuals
political
o f
b o u r -
( F l o r e n c e ,
first
v i o l a t i o n
1 9 2 3 ,
c o u n t
s e n s e "
b e
n e w
F r a n c e
b e h a v i o u r
d e t e r m i n e d
is e v e n
f o r m
c o n c e r n s
c o u n t e d ,
m e a n
o f
all, f r o m
t h e
indices
m e a s u r e
b e
w a s t h e
classification
for
that
t h e
t o
in
K e l l e y ,
i n d e e d
p r o b e
directly
o b j e c t s
n u m b e r
w o r k e r ,
that
w h i c h
researchers c o h o r t .
b e e n
w h i c h
o f
t h e
i n t o
c o u l d
insulted.
statistical
w o r k ,
until well
classi-
t o
closely
rationality
o p i n i o n s ,
a n d
w a s
e x a m p l e ,
t o
S a r g a n t
c o m m o n
c r i m e
a s s u m e d
area o f
o f
i n t e r e s t i n g
o n e
for
statistical
always
has
w h e r e
1 9 6 4 ;
b y
i n q u i r y
irrationality
individuality,
there
m u n i t y
s t u d y
for
b e
c e n s u s
distinctive
o f
w i t h
especially
b e
s u b j e c t e d
h o u r s
select
carry
t o
t o
sense
P.
d o u b t -
t o
are
sense,
N a p o l e o n i c
w a g e s ,
t h u s
d e n i e d ,
are
will
things.
a
it m a d e
t h e
e d u c a t i o n a l
t i m e
s t u d y
In
r e m a r k e d
a n d
m a s s
t h e s e
sciences.
t h i s is
s a m e
statistical
p e o p l e )
l i k e l i h o o d
G o u g h ,
H e r e
disdain
It
in
problematical
a c h i e v e m e n t s .
w h i c h
basis
statistical
m e n t s .
a n d
o f
d e c i d e
s t u d e n t s
t h o u g h
the
of
c o n t i n u a l l y
b e h a v i o r ,
o t h e r s w a s
prejudices, w h o s e
n e e d e d
at
t o
that
intelligence
uses
t h e
a c c o u n t e d
nutrition,
v o t i n g
a n d
criminals,
are
p r e d i c t i o n ,
o f
t h e
statistical
labor,
o r
as t o w h e t h e r
b u d g e t ,
a n d
I n d e e d ,
Statistics
in
noticeable,"
family
-
individuality
that
p o o r
d e s c r i b e d
o f p o v e r t y ,
o p e r a t e .
is
i m p l i e s
a n d
E S P a n d
o n e ' s
( u n l i k e
t h e
their
2 1 8 ) .
century.
is
"It
m e a s u r e s
a d e c e n t r a l i z e d
b e h a v i o r a l
h a v e
they
1 9 8 7 ) .
"that
1 9 2 9 ,
a n d
d o u b t s
since
o f
p r o b l e m s
c o n s i d e r a b l e
citizens,
t h e
t o
c a u s e
n a t u r e
s h o w s
g e o i s
e n q u i r i e s
is
a p t i t u d e
inevitably
m e a s u r e
ethical
social
a n d
o p p o r t u n i t y
B o u r g u e t
w e r e
t y p e s
t h e
c o u n t e d
t h e r e
o f
v i s i o n
a n d
I Q
world
t h a n as individuals
t h a n
t o
o f
the
s t u d e n t
a t t e m p t s
in
M a r i e - N o e l l e
1 9 2 9 ,
a
o f
m a x i m i z e
intellectual
p r o n o u n c e d fied
t o
rather
t o
T h e
certain
T h e
u s e
statistically rather
d e s i g n e d
a
o p e n
a n e f f e c t
elites.
t h e
rule
t o
m a k e s
o r a n for
scientists,
are
a s s e m b l y - l i n e g r e a t
science.
Downloaded from https://www.cambridge.org/core. Newcastle University, on 03 Oct 2018 at 11:29:14, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.009
Numbers
T h e
p o i n t ,
rarely
o f
a p p l y
T h e
c o u r s e ,
it
v a l u e s
e x c e p t
f o r m
b y
A m e r i c a n
f r o m in
t h a t
1 9 2 4
cess,"
o f
o f
this
m o s t ,
like
o f
this
s c h o o l
o f
s o c i o l o g y ,
o n
The
p e a s a n t s ,
h a r d . t o
i n s t e a d
p e a s a n t ,
b u t
o b j e c t
a m e l i o r a t i o n
s p e n t
p s y c h o p h y s i c s a t t i t u d e s
o b j e c t
o f
w o r d s
a n d
i n g o f
c o u l d
for
o t h e r
s t a t e m e n t s
p l a c e
t h e
b l a c k s
o n
o n
t o p
e r r o r t h e
each,
a t t i t u d e s
m e n t s
w i t h
t h e s e
t h e
u n i t
individuality, h e
s o u g h t
m o r e a
visceral
single
axis.
i m m i g r a n t s ,
a
o f
t h e y
i n d e e d
t h a n T h i s
in
t h e
t h e
C h i c a g o b o o k o f
for
A m e r i c a b e
o f
P o l i s h a n
v e r y
i n a d e q u a t e
p s y c h o l o g i s t
a t t i t u d e s
social
t h r o u g h
b e h a v i o r
T h u r s t o n e ' s
m u s t
s u i t a b l e
u s e f u l
a n d
a
m e a s u r e
t h e
a t t i t u d e s
t o p i c s
-
f o r
p r e s e n t i n g H e
e x a m p l e ,
w a s
o p i n i o n . "
b e i n g U s i n g
set
t h e
o f
m o s t
b o t t o m .
t o
assign
this scale, h e
h e
as
t h e b o t h
o r
w i t h
lika
t o
h o s t i l e
t o
F r o m
t h e b e -
d i s c r i m i n a l
c o u l d
b a s e d
set
s u b j e c t s
d i s t a n c e s
" s t a n d a r d
subjects,
if
u n d e r l a y
s u b j e c t s
t h o s e
t h a t
b o r i n g
m i l i t a r i s m ,
first
t h e
1 9 2 7
w e i g h t s
t h a t
his
w i t h
also
less
a n d
t h e
at
a b l e
e x p e r i m e n t a l
o n
m e a s u r e t h e
s t a t e -
a g r e e m e n t .
p r o c e d u r e
virtually
rationality, n u a n c e s b y
u s e d
f a v o r a b l e h e
lot
t h e
T h u r s t o n e ,
a r o u n d
as p r o h i b i t i o n ,
b y
b e c a m e
w o r k .
d e c i d e d
l e n g t h s
e x p r e s s e d
a n d
o f
w o u l d
t h a n
o f
c o g n i t i v e ,
t h e p o o r ,
m o r e
m o s t
set
a
life
p r o -
i m p l y i n g
a t t i t u d e s
social
C h i c a g o ,
q u e s t i o n .
o f
ideas, o r
w a s
L.
m e a s u r e m e n t
o f
as
fully a p p r o p r i a t e
r a t h e r
r a n k i n g s
s e c o n d
n o t
lot
s u c h
o r d e r
statistical o r
w a s
at
s t a t e m e n t
w h i c h
T h u r s t o n e ' s
c a r e e r
t h o s e
in
o f
his
a
L.
nationalities,
in
a n d
o f a single
o f
t o p i c i n
s t a t e m e n t s
d i s c r e p a n c i e s t w e e n
t h e
flexible
r a t i o n a l
Z n a n i e c k i e ' s
n e w
t h e
S c i e n c e
h a s l o c a t e d
w o r k
c o n d i t i o n
u n d e r l y i n g
w o u l d
a n d
w a s a
a
F l e m i n g
t h e
t e r m i n o l o g y
Political
o f
in
p r o m i n e n t
" a t t i t u d e s "
T h e
w h i c h
w o r l d ;
r e s u l t
c o n c e r n i n g
races
o f
classic
t o
o n
r e s u l t
America.
-
clearest
d i f f e r e n t
F l o r i a n
m a t e r i a l
a
m a d e
H e
s c h o l a r s
3 2 2 - 3 0 ) .
p r e j u d i c e s
r e s e a r c h . d e e d s
o f
a
t h e
t h e
a n d
m o r e
a t t i t u d e s
b e
a n d
rigid
t h e i r
p p .
as
in
and
m o d e r n
1 9 6 7 ,
m o s t
t h a t
b e c o m e
T a b l e
s p e a k
a d a p t a t i o n
elicit
m e a s u r e m e n t
also
t o o k
t h e
s u b r a t i o n a l
o f
o f
o n
5 1 ) . D o n a l d
Europe
m a d e
t o
c u r i o u s
a l r e a d y
b e
t o
T h o m a s
b e c o m e
h o w
is
a r e p e r h a p s
R o u n d
n o t
a t t i t u d e s
h a d
( F l e m i n g ,
T h e s e
w i t h
W i l l i a m
i n t o
t h e
1 9 2 8 , p .
h e l d ,
l e a r n
r e f o r m s
( R i c e ,
in
t h e m
253
it
h a d
insisted
n e e d
Peasant
M e r e
b r i n g
w h o
Polish
t h e y
o l d - w o r l d
w h i c h
R i c e , p r e f e r r e d
c o n c e r n
b u t
m e a s u r e m e n t
scientists
" o p i n i o n
r a t i o n a l i t y
s o u r c e
1 9 2 0
o p i n i o n
social
S t u a r t
world
t h e m s e l v e s .
e n t e r p r i s e ,
t h a t
the
validity,
t h e pollsters. A l t h o u g h
r e s o l v e d
still less o f
s o m e
t o
u n d e r l y i n g
a c a d e m i c 1 9 3 0 .
h a s
rule
in
his
p r e s u p p o s e d e x p e r i m e n t a l
o f o p i n i o n ,
w h i c h
t h e
b u t
s u b j e c t
a n
subjects.
s t a t e m e n t s c o u l d
t e c h n i q u e
for
d e a l i n g
w i t h
m i n o r i t i e s ,
t h e
u s u a l s u b j e c t s
a b s e n c e
b e
o f
o f
W h a t feeling,
l o c a t e d
w o r k e r s ,
o f
a l o n g
w o m e n ,
sociological
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in-
Numbers
254 v e s t i g a t i o n , m a n
says
t h i n g
that
that
w e
t h e
W e
b e c a u s e
carriers
o p i n i o n s "
o f
t h e
n o t b e e n
t h e
rather
o f
m e t h o d s . t h e
n o t
latent a s k e d t h e
S a m u e l
a variety
interest? is
E v e n
g i v e s
h i m g i v e
g o o d
t h e
o t h e r
is
f r o m
t h e
in
lay
w i t h
n o
w o u l d
effect,
for
t h e
m a k e
t h i n k
h e t o
a n s w e r s o f
variation m i s t a k e s
B o t h
t o
assess
w a r s
g a v e
situation
their
services
b e
s e e m
t h e
w a s
I Q
o f
t h e
c o m m o n
also
b y
h a d
h a v e
t h e
t h e a r m y
a n d
t h e
w i t h
for
P a u l
t o
war,
particularly
b u t
w e r e
tests o f
b e c a u s e
f a v o r e d
H e
w a s
soldiers
I Q
t e s t i n g
i n d e b t e d his
t o
statistical
Lazarsfeld
s o u g h t
identified
t h e
t h e
a r m y .
p r i m a r y
w a s
f a v o r a b l y
are
all f a v o r a b l e
o r
is
a n s w e r s
t o
is
articulating
in
o n e
t h e
w a s
t h e
t h e
t h e s e
o u t
o f
a r m y ,
a n d
D i d
for
his
N o n e
t h e
a
w e r e
p r e s e n t :
a r m y ?
i n f e r e n c e o n l y
soldiers
o f
latent
that
q u e s t i o n . w a y
t o
e x a m p l e ,
l o o k i n g
a b s e n c e
trait
s o m e t i m e s
m a t t e r s
o f
statistics
for
T h e
character
a r m y
t h e
u s e d
p o s i t e d ,
p r e s e n c e
in
a n d
o f
t h e
in
p o t e n t i a l
partici-
Lazarsfeld
p o s s e s s i n g
W h a t
p u r p o s e
w h o s e
a n d
if t h e
s p e a k
r e s p o n d i n g
interest.
a n d
h e
T h e
3 4 - 7 ) .
t o w a r d
ascertain
S e c o n d
subjects
just as T h u r s t o n e
a t t i t u d e
t h e s e
t h e
select
t o
w e r e
w e r e
attitude,
p p .
as
s h a r p e n
e n d
in
c o n s c i o u s n e s s .
t o
p r o b a b i l i t y
t o
also
o p i n i o n s ,
r e s p e c t
r e a s o n s
o f
certified
1 9 4 9 ,
a n d
life.
their
t h e
G u t t m a n ,
al.y
pri-
test a n d
argues,
L o u i s
D i d
soldier's
o f
t h a n
o n
b e l o w
a r m y ?
a r m y
w o r k
surface
discharge,
r e s p o n s e s ,
subjects,
et
o f
s e r v e
e n d o r s e
m o r a l e ,
civilian
s o c i o l o g i s t s
attitudes,
q u e s t i o n s
h i g h
m a y
o f
o f
if t h e a
his
f a v o r a b l e
decisive
trait.
T h e
" n o t
t h e y
First.
o p p o r t u n i t y
t o w a r d s
t h e
a t t i t u d e
d u r i n g
t h e
a n a l o g i e s
h a d
o r
a t h e
e v e n
o n ,
b e c a u s e
recruits
t o
( 1 9 8 5 )
policies
-
like
A f t e r
for
w i t h
character
B u c k
d u r i n g
t h o u g h
t h e
m e a s u r e m e n t
( S t o u f f e r
that
b y
c y n i c i s m
S t o u f f e r ,
factors
traits
soldier
t h e s e
just
T h e
o r
t h e
w e n t
e x p r e s s
n u m b e r
attitude,
P e t e r
analysis.
c o n t e n t
identify
o f
a r m y .
as s u c h
h e
" W h e n
G e r m a n y ,
rather
p r e s e r v e
the
w i t h
s t i m u l u s
p l a c e
b a c k
3 6 0 ) .
5 3 7 ) .
b i g
a n d
u n l i m i t e d
p e r s o n n e l
abilities
N o t
as
its
later,
b u t
rather
5 3 1 - 2 ,
c h e c k
v a l u e d
i n c r e a s i n g
factor
p r i m a r y
m e n t a l
T h i s ,
w h o
h e l p
w a r
o p i n i o n s , "
p e o p l e p p .
p.
o f w o r d s
b u t
social science
t h e
h i g h l y
w i t h
t o
t o
and,
b y
A t t i t u d e
T h u r s t o n e ,
w a s
t h e
string
t e s t i n g h a d
b e e n
s t u d e n t s
h a v e
t h e m s e l v e s .
h a d
1 9 6 7 ,
as it stands,
r e c e i v e d
virtually
m o r e
war.
t o
u s e
a
e n t e r i n g
c o n t e n t
t h e
1 9 2 7 - 2 8 ,
o f a nascent
e n c o u n t e r e d
t h e
o f
life
e n j o i n e d
o n
p l e a s e d
d e a l i n g
world
( F l e m i n g ,
in
c o g n i t i v e
a i m
a r m y
o n
w a s
p r e v i o u s
t h e
t o
t o o l s
lost
their
tests
u s
s e n t e n c e
b e
s y m b o l s
I Q
practitioners
p a t i o n
t h e
the
really t h e
just as intelligence
h e r e
a d a p t a t i o n
their
o f
m e a s u r e m e n t
a r m y
officers;
u s is n o t
( T h u r s t o n e ,
W a r ,
like
a m i s t a k e
"shall
o f
o r
A t t i t u d e W o r l d
p e o p l e
m a d e
m e a n i n g
speaker."
marily
w i t h
interests
i m m e d i a t e t h e
n o t
rule
o n l y
T h a t
h e
s o m e t i m e s
o f
attitudes
probabilistic. attitudes.
A s
T h e w i t h
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Numbers
T h u r s t o n e , t h o u g h t , t h e s e
b u t
w i t h
o f
t h e
able,
h o w e v e r ,
v i e w s
w a s
o f
h e l d
h a v e
m e n
T h e
r e s p e c t
b y
R o p e r .
t h e s e
w e l l
o f
P e r h a p s
t o
statistics
t h e
in
o f
t h e
their
i m p l i e d
that o f
attitudes,
o r d e r
t h e
o r
acquire
t h o u g h t s ,
o f
for
less
b e h i n d 1 9 6 7 ) .
t h e
t h a n
struc-
o p i n i o n s
It is
o f
q u e s t i o n -
c o n s i d e r a t i o n
w h i c h
d e m o c r a t i c t h e
for poll-
a v e r a g e
m a n
their o b l i g a t i o n
c o n c i s e
large
lie
a u t h o r i t a r i a n
officers.
a n y
in
that
rational
F l e m i n g ,
effusively
e s t e e m
t o
also
s o c i o l o g i s t s
that
t h e
c o n s c i o u s ,
a t t i t u d e s
1 9 5 0 ;
s u i t e d
t h e
t o
d i d
w i t h
s o c i a l r e s e a r c h e r s is less d e c i s i v e
t o
a b o u t
255
n o n - r a t i o n a l
a p p r o a c h
t h a n
world
c o n c e r n e d
c o m p a r a b l e their
the
Lazarsfeld,
n o t e , w a s
w h e t h e r
r e c o u r s e
m a t i o n
1 9 5 0 ;
m a y
w a s
a n d
n o t
unarticulated
their subjects
G a l l u p
is
( S t o u f f e r ,
military.
enlisted
sters,
the
a p p r o a c h , w e
t h e s e
t h e
researcher
r e s p o n s e s
T h i s t u r e
t h e
rule
a n d
reliable
n u m b e r s
o f
t o
i n f o r -
individuals.
I n s u r a n c e
T h e in
quality
d e b a t e s
o f
t h i n k i n g
o v e r
e x p e c t a t i o n ,
t h e
rationality
either
in
e c o n o m i s t s
a n d
tradiction
b e t w e e n
b e
i n t e r e s t e d
b u t
o n
the
t h e
s t a n d a r d s
c e n t u r y a m e n d h o n o r t h e
o t h e r ,
o f
a n
p r o b a b i l i t y
t h e
u s e
t h e o r y
a n d
a s k e d
6.6)
t o
a c c o u n t
here,
face
d e s c r i p t i v e
t u r n
o n
that
h o w
o f
t h e
claim,
statistics
u n l i k e
that
its
o f
has
t h e
t h e y
p r o f e s s
d o
r e a s o n ;
irrational
their are
u n w i l l i n g
p e o p l e has
d o
n o t
codifipractical
success
e x p e c t a t i o n in
t o
b e c o m e
w i t h
financial
its w o r t h
b y
e i g h t e e n t h -
t h e o r y
spectacular
p r o v e d
t r a p p e d
m a t h e m a t i c a l
b y
o f
c o n -
o r
p r o b a b i l i t y
r e a s o n i n g
issue
s a m e
fact
m o s t
P r o b a b i l i t y
m e r e l y
at
n o t i o n
t h e
in
rational
e v i d e n c e
t h e
h a n d ,
e x p e c t a t i o n
e q u a t i o n t o
o n e
p e o p l e
c o u r s e ,
n o t
p o i n t
t h e
b e e n
T w e n t i e t h - c e n t u r y
d e s c r i p t i o n
subjects
O f
o f
f o r m s .
m u c h
in practice.
they
T h e s e
c a u g h t
o f
their
this
also
O n
u p h o l d e r s
d e f e n d
has
in
1.5).
rationality,
o f t e n
are
a n d
(see
in t h e
moyen
m o d i f i e d
theory.
t h e o r e m s
industry: o f
o r
(see
today's
I'homme
g a m b l i n g .
p r o n o u n c e
e c o n o m i s t s
insurance
s i m p l e
e m p i r i c a l
practical
W h e n
o f
probabilists
t h e y
p r o b a b i l i t y
rationality,
w i t h
o f
b y
p r e s c r i p t i o n
p r e d e c e s s o r s ,
arbiter
the
in
its a x i o m s
cation.
its
p s y c h o l o g i s t s
e i g h t e e n t h - c e n t u r y t o
d i s p l a y e d
o f
c o u p l e d
the
m a r k e t -
place. H o w e v e r , i n g
o f
t h e
realities o f
i n s u r a n c e
p r e m i u m s
c l a i m s u g g e s t s . in
t h e
m o s t
It is t r u e
a p p l i c a t i o n p e r v a s i v e .
asters d i v e r s e
o f
t h e
o f
are
W o r l d "
c o n s i d e r a b l y
that i n s u r a n c e
statistical
D a n i e l
i n s u r a n c e
a p p l y i n g p r o b a b i l i t y
D e f o e ' s has
m a r k e t .
a n d
T h e
p o s t
m o r e
t h e
probabilistic
d r e a m
a l m o s t
w a s
o f
c o m e o f
t h e
a n d
first
actuary
t h e
a n d
against
today's has
pric-
t h a n
g r e a t practical
m o d e l s ,
in
t o
c o m p l i c a t e d
i n s u r a n c e t r u e
statistics
this
success
it is still "all
t h e
t h e
D i s -
e n o r m o u s
a n d
e v o l v e d
f r o m
Downloaded from https://www.cambridge.org/core. Newcastle University, on 03 Oct 2018 at 11:29:14, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.009
that
Numbers
256
o f
a
l o w l y
firm,
c l e r k
o n e
a d e v e l o p m e n t
t h e
i n s u r a n c e
his
a u t h o r i t y
i m p r e s s i o n
t o
a c t u a r i e s
t h a t
Y e t
all
in fact
e v e n
a n d
h u n c h e s
if
n o t
t h o s e t o
a n d
c a n n o t
m e n t
a n d
s c a t t e r
a
o f
p r i c e
b e
h a n d
t h r o u g h
m u s t
s t r i k e
a
m a k i n g
a n d
t h e
s u c h
1 9 5 1 , p .
m a r i t i m e
d r e d
y e a r s t r a d e
T h i s
a g o , as
m o d e l .
b e
a n d
t o
m o b i l e
a n d
life
h o m o g e n e i t y s a t i o n m u s t
o f t e n
w r i t e r s i n s u r e
o f
i n s u r a n c e
d e n c e .
p a y
F a c e d a r e
t h e
l a w
t h e
risk
( a n d for
class
a fortiori
t h e s e
t o
find
t h a t
a
criteria
T h e y
o f fife
t h e
s o m e t i m e s b e t w e e n
a n d
large
t h e
t h e
as
t h r e e
fire h u n -
is k n o w n
in
6 7 ) .
o f
p a r t
statistical l a r g e
e q u a l l y
likely
o t h e r .
A u t o -
n u m b e r s ,
b u t
w o r k m a n ' s
c a t a s t r o p h e s a s s u m p t i o n
like o f
t h e
e n o r m o u s
u s e
a
o f
o f t h e
t h e
c o m p e n floods) i n d e p e n -
reality,
f o r m
t h e
class,
t h e
a n d
o f
p h e n o m e n a
t h e
e a c h
d i c t a t e s
c u r v e
b u s i n e s s
s u c h
t h e
f r o m
m o d e l
t r u s t
t h e
t h e
w h e t h e r
a n d
a g a i n s t
b e t w e e n t o
o n
free-
a n d
w e r e
p .
a
q u a l i f i c a t i o n
w e l l - d e f i n e d
o n e
e x t r a c t s
f o r
w h a t
c o n d i t i o n s
n u m b e r s ,
d e s t r o y
r e l u c t a n t
c o m p r o m i s e
t h e
d o u b t f u l ;
disparities
statistics. a
is
t h e
o n
j u d g -
a c u r v e
in
t h e y
a b o u t
i n d e p e n d e n t
i n s u r a n c e
disasters
u n d e r s t a n d a b l y t o
large
a c t u a r y
o n l y
1 9 5 6 ,
w i t h
i r r e g u l a r
a n
i n s u r a n c e
as
o f
yields
t h e
o f
f o r m
m o r t a l i t y
e x p e c t e d
L u d d i s m
d o u b t s
g u e s s w o r k
t h e
b u s i n e s s ,
reliance
t o
m e t h o d s ,
o f
e x p e r i e n c e
f o r m s
5).
m o d i c u m
t h e
a n d
c o n s t i t u t e
o f
m e e t
t r i c k y
(Pfeffer,
satisfy
b y m i s f o r t u n e ,
i n s u r a n c e
w i t h
e n t i r e l y
p r o b a b i l i t y
w e l l - f o u n d e d
a
t h e m
fortified
t r a d e ,
figures
statistics
d u e
p .
i.e. b y d r a w i n g
h e a v i e r
t o
s h o u l d
-
l o n g
o f
s i m p l y
t h e
w h i c h
o n
o l d e s t
b e s t
r e g u l a r i t y
o l d e r
n o t
f r o m
d o w n
is
e v e n
really
o f
e m e r g e d ,
j u d g m e n t "
p o l i c y h o l d e r s
s t r u c k
h a v e
is
s h i p w r e c k s
p r o f i t
t h e
c o n s e q u e n t l y
also
is a
o n e
o f
" a c t u a r i a l
o f s u c h
is t h e
w i t h o u t
f r o m
T h i s
i n n o c e n t
" u n d e r w r i t i n g
T h e
e n o u g h
a
t h e
m o r t a l i t y
t e c h n i q u e s "
d i s t i n c t i o n s
as
d a t a
c u r v e ,
nice
c o n s e r v a t i s m
fires
t h e
b e t w e e n
a l m o s t
b u t
t h e
p o i n t s .
O t h e r
a n d
o f
e d u c a t e d
i n s u r a n c e
w a r h o r s e
f r o m
t r e n d s
w i t h
1.6),
t h a t
n e w
3 3 5 ) .
a r e
u n d e r w r i t e r s like
b a l a n c e
t h a t
(see
Life
o f
a n
r e p u t a t i o n
1 9 5 6 ,
u s e
o w e s
w i e l d s ,
p e r f o r m e d
g r e a t
t h a t
m a t h e m a t i c s
m y t h
(Pfeffer,
a m o u n t
fair
t h e
t r u e
w h o
h e
t h e
t h e
c a l c u l a t i o n s
b u s i n e s s
o f
is
o f
inject
e v e n
o f
s u c h
i n s u r a n c e
e x p e r t
t e c h n i q u e s
m a k e
s m o o t h
c l o u d
a n d
t h e
It is a l s o
n e w - s t y l e
o f i n s u r a n c e
" g r a d u a t i o n
t h e
" i n d i c a t i o n s "
( S p o e r l ,
b y
a
t h e
s o p h i s t i c a t i o n
t h e
a
w i t h i n
last c e n t u r y .
c o m p l a i n e d
t h e
G r a p h i n g
n o t
p o w e r
I n d e e d ,
a n d
i n s u r a n c e
eye.
o f
p r e m i u m s .
c o n s t r u c t e d
g o o d
c u r v e
m u s t
B u t
a n d
t h e
a n d
h a v e
f r o m
t h e i r
b a s e d
p o i n t s ,
m o r t a l i t y
for
d o
in
e x a m s .
statistics
t e c h n i q u e s .
table,
p r e s t i g e
a m o u n t
all b r a n c h e s
t h a t
world
i n f o r m a t i o n
e c o n o m i s t s
t h e
the
p r o t o t y p e
t h e
u n c e r t a i n t y
m a t h e m a t i c a l l y d a t a
t h e
a r c a n e b y
s o m e as
a n d
g r e a t
a c c r e d i t a t i o n
p e r f e c t i o n , " e l i m i n a t e d
is
t h e
f o s t e r e d
o n
o f
a l r e a d y o b v i o u s
a c t u a r y
r e q u i r e d
t o
t o
rule
s u m s
u n d e r t h e y
s u b j e c t i v e statistical
Downloaded from https://www.cambridge.org/core. Newcastle University, on 03 Oct 2018 at 11:29:14, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.009
Numbers
m o d e l i n g
a n d
f r o m
bility"
t h o s e
t h e
o f
risk
factor
rule
j u d g m e n t :
e x p e r i e n c e
r a n g i n g
f r o m
0
the
w h e n
world
237
individuals
o f
the
class,
t o
1 0 0 %
are
actuaries
as a
r o u g h
s u s p e c t e d assign
o f
deviat-
a
"credi-
t h e m
a d j u s t m e n t
t o
t h e
class
average. T h i s
a s s u m e s
that
B u t
s o m e
base
rates are available:
o n
t h e
h a n d s
d e n t e d p l a n t
f o r m s
o f
t h e
o f
disasters
fixes
assets,
u p o n
and,
o p i n i o n
-
o f
c r e w "
t h e
c o v e r
h u m a n
s h i p o w n e r , 1 9 5 6 ,
p.
n o
t h o s e
t h e practice
t o
m o d i f y
o r
skill o f
t h e
statistics w h e n o f
r e d u c i n g
j u d g m e n t -
a p p l y
m o d e l h o w
is
t h e
o f m a m m o g r a p h y
t h e
principle
cells, h a v e
a n d
is
that u s e d
a b i o p s y
all
s u c h
l e m f r o m
is
tests, h o w
H e r e
the
h a v e
base
rules
a n d
rates
for
h e r e
statistical
w h e n
a n d
t o d i a g n o s e
a n
p e r s o n a l
p r e d e c e s s o r g a u g e s
t h e
in
" t h e
quality
in-
o f
t h e
is
lies
n o t
e v i d e n c e history, a
n o t
c a n c e r
S u c h
in
the
in
differently
w h e t h e r
t h e
o r
a
usually
s o m e t i m e s
a n d
initial m o d e l s
a n d
a b o u t
are as
t h e
s o m e in
t h e
w o r k s
o n
f r o m
b e n i g n
p a t i e n t
s h o u l d
d o n e
u n d e r
g e n -
in infection.
Like
T h e
clinician's
m a m m o g r a p h y
s y m p t o m s ,
b i o p s y
t h e
j u d g m e n t s
j u d g m e n t s
o f
d r e a m
probabilistic
i m p o r t a n c e ,
accurate.
f r o m
tables
T h e
M a m m o g r a p h y
p r o c e d u r e
m a m m o g r a p h y
breast
d e c i d e
1 0 0 %
irrational
t h e
e s c a p e
situation,
X - r a y s
in scars a n d
a n d
c a n n o t
p r o p o r t i o n a t e
h e l p
necessarily
statistics are at h a n d
t h e
a b s o r b
t o
results
the
t h e
o f
e x p e n s i v e
p e r f o r m
o f
in-
c o m p a n y ' s
in q u e s t i o n .
a n d
breast cancer.
cells
physicians
difficulty
p o w e r w h o
o w n
his
t h e o r y
rules
s t r a i g h t f o r w a r d .
s u b t l e t y
p e r s o n a l
accuracy
-
clearcut
case. E v e n
o f t e n
t o
t o
p r o b a b i l i t y
a p p r o x i m a t i o n
w e i g h t
w h e t h e r
p r e d i c t i v e
t h e p h e n o m e n a
m a m m o g r a p h y
t o
family
d e c i d i n g
that
it is n o t
m a t c h
o p e r a t i o n ,
eral anesthesia
s h o w s ,
n o t
m a l i g n a n t b y
the
his
officers,
o f
rules are n o t
u s e
o n
L i k e
c a n o n s
the
c o n s i d e r a b l e
u n p r e c e -
nuclear
u n d e r w r i t e r
ship's
o r
d i a g n o s i s
actuaries
j u d g m e n t s
r e a s o n a b l e
o r
n o
policies
u n d e r w r i t e r ,
factor,
t h e
t h e particular a
o f
d o
w h e t h e r
t o a p p l y
t i m e s
t h e y
ineffable
o f
t o
aside
bizarre
it.
w h i c h
L o n d o n ' s
claims a n d
i n v o l v e d .
for
for
6 8 ) .
o f i n s u r a n c e
set
a
also
t h e
available
e v e n t s
F l o r i d a
t o
m a r i t i m e
M e d i c a l
A s
in
possible is
are
L l o y d s o f b u t
h e l p
b e t w e e n
today's the
singular
just t o
p e r f o r m a n c e
V e n i c e ,
o r
pianist,
are
o f
statistics
blizzards
statistics
c o m p e t e n c e
(Pfeffer,
a n d
rare
c o n c e r t
the p r o p o r t i o n
t h e
large,
e x a m p l e ,
H e r e
s i x t e e n t h - c e n t u r y tegrity
is
this applies n o t
for
w h e r e
o f
i n s u r a n c e
a c e l e b r a t e d
e x p l o s i o n s .
stead
class
o t h e r
p r o b -
w i t h
that
particulars
in
n o t . availability
has
various
b e e n
o f
statistics
e x t e n s i v e l y
p o p u l a t i o n s
-
n o r
-
t h e
studied, in
t h e
as
exis-
Downloaded from https://www.cambridge.org/core. Newcastle University, on 03 Oct 2018 at 11:29:14, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9780511720482.009
Numbers
258
t e n c e
o f
s u c h
a
p r o b a b i l i s t i c
s i t u a t i o n s
statistics
i n
also
t h e
talk
q u i t e
l a n g u a g e
R a t h e r ,
it
m e d i c a l
l i t e r a t u r e
fuse
t h e
c a n c e r ( t h e
lies
in
t h e
g i v e n
a
cancer)
( E d d y ,
c h a n g e a b l e , o r
o f
t h a t
h e
t h a t
s o m e o n e
a
is is
it is t h e
r e t r o s p e c t i v e
m a m m o g r a p h y
w i t h
a
m a g n i t u d e E v e n a n d
t h e
b i o p s y .
o r
p a t i e n t
breast.
t h e
t h a t
b o t h
p a t i e n t s
e v e n
f o r
icians, i g n o r e t h e
a n
b i o p s i e s b u t
a
h e r e
t h e
( t h e
o f
t h e
w i t h
o f
t h e
r e p o r t
g i v e n
a p r e d i c t i v e is a t
t h e
c a n
s u r v e y
are
s o m e o n e
is
w i t h
g i v e n
t h a t
in
t h e
r e s u l t
c o n -
a c c u r a c y
inter-
a
g i v e n
m a n
p r o b a b i l i t y h e
7 9
e r r o r s
h a s
m e a n s
is
t o
a
m a n .
9 0 % ,
clinical d e c i s i o n
in
h a s
p a t i e n t
t h e
o f
t h e
p a t i e n t
t h e n o
is
o f
r e g u l a r l y
t h e
t h a t
a c c u r a c y
issue
t w o
A
b y
S t a t e s
t h e m s e l v e s
r e t r o s p e c t i v e
S t a t e s
U n i t e d
t h a t
its
o f
q u a n t i t a t i v e .
p h y s i c i a n s
t h a t
U n i t e d
a n d
p r o b a b i l i t y
fits
m i s t r u s t
p h y s i c i a n s
p r o b l e m .
t h a t
t h e o r e m
clinician's
probabilities
accuracies,
t h e y
m u s t
h e r
o f
s a m e
e a c h
h a v i n g
t h e
m e d i c a l
a
little
still
b e c a u s e o f
o f
s h e
h a v i n g
p a t i e n t
d e a l
o f
a n
b u t
t o
g o
o r d e r
o f
h a s
t e x t s
p r o b a b i l i t y ,
like
is
g r e a t l y
in
t h a t
a
a
t h e o r e m
s h o w s
i n c r e a s i n g
t h e
probabilistically
a
l e a r n i n g ,
c a n
i n
b e
t h e p h y s -
usually
e v a l u a t i n g n u m b e r
in
If
that,
cases,
t h e m ,
p r o b a b i l i t i e s
h e r
clinic.
p r a c t i c i n g
i n s t r u c t
in
d i f f e r e n t
b o t h
Y e t
this
I m a g i n e
l u m p
s c r e e n i n g
in
o f
cancer.
r e a s o n little
p r e d i c t i v e
signficiantly
sharply.
p r i o r
t h e
breast
B a y e s '
j o u r n a l s
t h e s e
d o
i m p a c t
a c c u r a c i e s
m a m m o g r a m ,
P h y s i c i a n s
w i t h
e x a m i n e d
d i v e r g e
a n d
t h e
d i s c o v e r e d
c a n c e r
p r e d i c t i v e c a n c e r
c o r r e c t l y
h a v i n g
m a m m o g r a m s ,
u n d e r w e i g h t
p o s i t i v e
d i s t i n g u i s h
p r o b a b i l i t y
d o c t o r
p o s i t i v e
t h e
o f
p r i o r
p r o b a b i l i t y
p e r f o r m e d .
h e r e
T h e s e
t o
drastically
i m p o r t
test
a b l e
h a v e
f o l l o w i n g o r
o f
B a y e s '
q u a l i t a t i v e
p r o b a b i l i t y
a s y m p t o m a t i c
a s s u m i n g
p r o b a b i l i t i e s
f o r
b o t h
a r e
patient's
p r i o r
f r o m
t h e
E q u a t i n g
c o n s u l t s
H e r
case,
t h e
m a m m o g r a p h y
a c c u r a c y
p h y s i c i a n s
r e t r o s p e c t i v e o n
in
-
m o r e .
w h e n
e v i d e n c e
t h a n
P r e s i d e n t
o f
lie
r e v e a l s
t h e
2 5 4 - 6 ) .
P r e s i d e n t
S t u d i e s
a h e a d
p o s i t i v e
m o r e
s h e
it
p r o b a b i l i t i e s ,
o f
d e c i s i o n s
m a m m o g r a p h y )
1982, p p .
a n y
d o e s
i n d i v i d u a l
a c c u r a c y
world
s u c h
m a m m o g r a p h y
p o s i t i v e
p r o b a b i l i t y
N o r
t h e o f
f o r
the
c o n c e p t u a l i z a t i o n
o n
p r e d i c t i v e
m o d e l
well.
d i a g n o s i n g
rule
s u c h
a
o f
cases,
d a n g e r o u s
t h i n g .
P r o b a b i l i t y
T h e
a t t e m p t s
w i d e n i n g carry
h o w
circle
w i t h
r e c e n t
t o
a p p l y o f
t h e m
a
a p p l i c a t i o n s
t h e
w o r l d
statistical
p h e n o m e n a , c e r t a i n
o u g h t
t o
a n d
f r o m
v i s i o n
i n m e d i c i n e
a n d
a n d
b e , as w e l l
o f t h e
t h e
l a w
p r o b a b i l i s t i c life t h e l a w
as h o w
m o d e l s
e x p e c t a n c i e s n a t u r e
o f
s o m e t i m e s
t o
t h e s e
t o
e v e r -
traffic
snarls,
t h i n g s .
O t h e r
b e s p e a k
it is. M e t h o d s
a n
a v i s i o n
o r i g i n a l l y
o f
i n t r o -
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Numbers
d u c e d a n
t o
test n e w
ethical
as
viduals
b e
cine
l a w
o r
w e l l
t h e
t h e
t o
T h e right rent
o f
cases
case o n t h e
a
the
t h e
e n e d
t h e
a r g u i n g that
t h e
firing
v i c t i m s
t o
o f
actuarial
t h a n
fairness d e c i s i o n
a n d
t h e r e
as s u c h : t o
t o
just
as
c h a m p i o n i n g
t h e
g r e a t e s t
o f
o c c a s i o n a l
indim e d i -
statistical
c o n t e x t
p e r s p e c t i v e
b e f o r e
t h e
case
d e c a d e s
o f
p o r e that
w h e r e
statistics g o o d
for
injustice
t h e
t h e
( o r
a l m o s t
a n d
t h e
o f
m o r e
t h e
a n
t h e
t h e
o f
o n e
in
b a s e d
its a n d
c o u p l e
r e v e r s e d
p r o o f .
d i s c r i m i n a t e
o r
recently
w i d e n e d
l o n g - t e r m
m i n o r i t i e s
n o w :
a n d
a n t i - d i s c r i m i n a t i o n
c o n s i d e r a b l y
o v e r
Statis-
interracial
H o w e v e r ,
t o
cur-
d e f e n d a n t s
u l t i m a t e l y
i n t e n t
o f
a u t h o r s h i p
p r o s e c u t i o n
b e t w e e n
i n s t r u m e n t
heart
a c e n t u r y
establish
the
traditional
c o u r t r o o m .
cases w e r e
has
an
the
for
d e s c r i p t i o n
discredited.)
f a s h i o n
in
t o
a n d
lies at
quirks;
m a t c h
in b o t h
as
l a w
b e l o n g s
h a n d w r i t i n g
t o
case
t h e
w i t n e s s e s
o f a r a n d o m
n o w
situation
A n g e l e s
t o
c h a r g e d
o r
n o t
is in
t h e m
u n k n o w a b l e
as
l e n g t h
t h a n
t h e
a n d
t h e
d e e p -
R a t h e r
against
p a t t e r n
t h a n
this
o f
o t h e r
principle
v o i c e s
o r
h i r i n g
s e x
w e r e
sense
e a c h
insisted
g r o u p s o n
t h e
a failure
individually
as
t r o d
t o
it
individual
is
are
right
t o
T h e
possible
as d o
life. Individually,
rather
a d d i n g
C h i e f t o
t h e
e v e r y
that
industry,
b e
o f
face
the
J u s t i c e t r e a t e d
'individuals'. in
the
(again,
inevitability
individuals
t o
o n
S u p r e m e
i n s u r a n c e
t h e
treat w o m e n
f e m a l e
individuals
c o n c e r n e d . o f
its
t h e r e f o r e
gingerly,
t h e
o n
b y
b r o u g h t
e m p l o y e e s
a n d
"fairness
c o u r t
suit
d i s c r i m i n a t o r y
colleagues.
r e v o l u t i o n i z e
that
large
restrictions
t h e
t o
m a l e
o f
w a s
f e m a l e
a v e r a g e
t h e
P o w e r
p l a n
f r o m
o n
as in
a n d
p e n s i o n
their
H o w e v e r ,
w h e r e
o f
W a t e r
l o n g e r
i n t e n d e d
n o
o f
the
live
m o r e
d i s s e n t i n g
p u t
statistical,
c o n t r i b u t i o n s
t h e y
classes."
a p p r o a c h
" T h i s
that
larger
that
w a s
w e r e
is intrinsically
D e p a r t m e n t
u p h o l d i n g
in effect
treat
statistics
this
D r e y f u s
statistics
their
b e n e f i t e d
a g r e e d ,
B u r g e r
o f
r e q u i r e d
this
is
t h e
g r o u n d s
statistical
that
I n
California,
t h r e e
l a w y e r s
T h e y
a v e r a g e )
C o u r t
o f in
traditional
L o s
e m p l o y e e s . it
o f
r e q u i r e
h a v e
discrimination.
t h e
b e c a u s e
t h e y
values,
objects.
statistics
the
a n s w e r i n g
m a k e
S o m e t i m e s against
in
Collins
role
n e w
e x p e n s e
s t a n d as e x p e r t
u s e d
past
t o
utilitarian
( C o n v i c t i o n s
t h e
legal
t h e
w h e t h e r
a r g u m e n t s
individual,
a n d
this
c o m p a r i s o n
car.
o f
in
t h e
v.
statistical
legislation
o v e r
b o t h
a y e l l o w
at
since
o b j e c t i v e l y
individual.
i m p r o b a b i l i t y
culprits,
w i t h
e v e n
m o r e
a p p l i c a t i o n
n e w
as a n i n d i v i d u a l
w a s
People
T h e
t o
259
d i s c r i m i n a t i o n
utilitariansim,
that
t a k e n
b y
like
o f
world
willy-nilly
t h e m
b e t w e e n
t e s t i m o n y
letters
o n
o r
controversies
their
users
the
c o m p o n e n t ,
a v e r a g e d .
its
n u m b e r ,
treated
ticians h a v e
t o d e t e c t
technical
a n d
v e h i c l e
this
b e
o r
c o m m i t t e d
conflict
t o
a
c o m m i t s
g r e a t e s t
w o r s e )
as
classified
m e a s u r e m e n t b e c o m e s
d r u g s
rule
.
.
It
o f
the
w o m a n
has
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Numbers
260
t h e s a m e i n g
o n
feasible
or,
E n g l i s h
j u d g e
o f
as
a p p l y i n g
h e
p.
t h e
o f
t h e
a n y
statistical
a g g r e g a t i o n
d e c i s i o n s p o w e r , "
v o t e
in
(Finkelstein, b a l k e d
at
cations
filter
g i v e n
o f
D e s p i t e hostility,
B u t
I n d e e d , t e r m s , a
t h e
statistics
in
t h e
inevitable,
s e v e r i n g
( D e f o r t
et
d i s m a l
al.y
-
h a v e
a v e r a g e m a n
Britain
o n l y
tables
m a n ,
o r
his
a g e "
h a v e
t a k e n
t o
par-
resisted
t h e
t o
o f
" s u m -
m e a s u r e s
s t r e a m l i n e
judicial
e x a m p l e ,
" v o t i n g
F o r
will
cast
t h e
r e a p p o r t i o n m e n t
m a n y
legal
t o
that
w i t h
fair
o f
a n
h a v e
simplifid e c i s i o n
statistical
individual e x e r c i s e
a
tiecases
scholars
m a t h e m a t i c a l
essential
h i n t e d
t h e
c o n s i s t e n t
i n d i v i d u a l
that
t h e
o l d
a n d
h a v e
a n d
liability,
c a n c e r
o f
correlations.
F o r
I n
justice
in is
average,
j u d g m e n t
I n
t h e
o f
all b u t a n d
d o e s
o f
past
accidents o f
a
t h e
w i t h
t h e
legal
e x a m p l e ,
t h e
for
-
in
e v i d e n c e
standards,
t o
w o r k -
o f
also
a n d
suits
so-called
o f
c a u s a t i o n p r o v e
necessary
e p i d e m i o l o g i c a l
c o n "toxic a n d
cause a n d
say,
m o s t l y
t h e
a p p e a r
the
b e i n g
o f
r e s p o n s i -
d a m a g e
linking,
like
idea
safety
t h e m
that plaintiffs
u n d e r s t o o d
central
o f
o n
startling
a n c i e n t
forseeability a rash
the led
t h e
m a d e
c o n c e p t s
r e q u i r e d
these
c e n t u r y
t h e
v e r g i n g
c o n c e p t s
a c c i d e n t s
carcinogens
e p i d e m i o l o g i c a l m e e t
legal
e l i m i n a t e d
d e c a d e
c a u s a t i o n
n o t
s u s p i c i o n
k e y
e m p l o y e e
e q u a t i o n
altered
t h e
m o d i f i e d
w o r k p l a c e
occupational
a n d
o f
t h e late n i n e t e e n t h
that
legal
statistics
h a v e
traditionally
H o w e v e r ,
i n g
t o w a r d
e m p l o y e r
similarly
C o u r t s
l u n g
a n d
n u m b e r
1 9 7 7 ) .
torts"
t e r m s .
a n
c o n t e n d i n g
i n t r o d u c t i o n
a i m
a n d
t h e
predictability
t h e
e n v i r o n m e n t a l
c l a i m
intent.
b o t h
c e r n i n g
ficient
a n
b e
h a v e
it replaces
legislation
o f
T h e
t o
case,
n o t
all cases.
c o u r t s
probability
a n n u a l
w o r k p l a c e .
o r d e r
B u t
u n c e r t a i n t y
u n d e r m i n e
m o r e
a p p l i e d
m i g h t
t o
t h e
a n d
h o l d i n g
that
a t t i t u d e
a n d
c o m p e n s a t i o n
i n t e n t i o n .
t h e
generality,
judicial
responsibility
bility
also
t o
that
c o u r t s
for
b u t
b e
G r e a t
h a v e
p r o p o n e n t s
m i g h t
b o t h
t h e
n e g l i g e n c e , liability, a n d
m a n ' s
in-
rules.
this
regularities
bas-
are
m o r t a l i t y
a v e r a g e
t h r e a t e n s
b e t t e r
p r o b a b i l i t y
particulars
w i t h
3 6 9 ) .
irreducible
a n
T h e y
criterion
s u g g e s t i o n s ,
case
application
a single
election,
in
h a n d
b e
T h e i r
a n
1 9 7 8 ) .
trial.
t o
t h e
c o n t r a d i c t i o n at
p u r p o r t
as
o u t
p.
p l a i n t i f f is a n
o f
that
individuals,
n o t i o n s .
s u c h
1980,
particular
States a n d
p e r s p e c t i v e .
o f
a p p l y i n g
d e f i n e d
b r e a k i n g
a n y
that
U n i t e d
i n n o v a t i o n
judicial
legal
b y
e x p e c t a t i o n
o f
3 9 7 ) .
o f
statistics"
t h e
t h e
t h e
e s s e n c e
d e t e r m i n a t i o n s
i n v o l v i n g
f r o m
t o
is t h e
Player,
a n individual
c o u r t s in the
v i e w
i m p o r t a n t
case
g e n e r a l i z a t i o n s
for
ticularity
o f
a n o t h e r
c o n c l u s i o n
o p p o s i t e
1 9 8 2 ,
a j a u n d i c e d
in
t h e
T h i s
i n d i v i d u a l
( q u o t e d
o n
live
I n general,
m a r y
world
w h e n
c o m m e n t i n g
c a n say w h e t h e r
will
( D o w n t o n ,
statistics
i m p o s s i b l e "
statistical
" n o b o d y
that
reliable
h e r e ,
precisely
that
the
statistical possibility o f o u t l i v i n g m e n .
d e c i s i o n s
d r e w
rule
in
suf-
s m o k -
assertions
c o n c e p t
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o f
Numbers
"attributable g i v e n
risk,"
t o x i c
o b s e r v e d
c o r r e l a t i o n
that
t o
t o w a r d
studies
f o r c e d
c o u r t s
A s
in
lation,
t h e
t h e
o f
a t i o n
b o t h
are
fact o f ciated
the
a n d
a
t a n g l e d
t e n d s -
a n d
in
t o w a r d
a r e c o r d
d r u g
-
c a u s a t i o n
m a s s
suffices
for
a n d
these
w o m e n
for
epi-
H o w e v e r , t e r m s
the
individual
in
hired, o f w i t h o u t
o f
case,
caus-
a n d
v a l u e s
w h i c h
legis-
p e r s o n a l
chains
traditional
has
direction.
o u t
t h e
this
o f
d i s c r i m i n a t i o n
has e d g e d
t h e
o r i e n t a t i o n
5 1 - 2 ) .
statistical
t h e
c o n v i c t i o n
" b u t
its
a
c h a n c e ?
s a m p l e s
p p .
b e h a v i o r i s m ,
f e w e r
for
w i t h
paradoxically,
ethical
o f
t h e
in
-
t o
is
b y
e p i d e m i o l o g i c a l
in
u n c e r t a i n
t h e
-
1985,
c o m p e n s a t i o n o f
criterion
d u e
likely
o c c u r r e d
larger
in
n o t i o n s
H o w
h a v e
pass"
Carter,
responsibility:
certain
m a t t e r
w i t h
a n d
t o o
Statistics
w o r k m a n ' s
t o
the
c o u c h e d
o l d e r
cases o f a disease
for"
t o
t h a n
a n d
statistical v i e w s
i n t e n t
u n a m b i g u o u s sense.
o f
rise o f
e l e m e n t s
revise
" b u t
c o m e
specifically
t o
case
legal
rather
( B r e n n a n
legislation
e x p o s u r e
h a v e
e v e n t s
r e g u l a t o r y t h e
n o t
261
probabilistically:
a n d t h e
world
o f all n e w
r e c k o n e d
o f disease
w o u l d
particular
d e m i o l o g i c a l
is
s q u a r e w i t h
d a m a g e
the
t h e p r o p o r t i o n
s u b s t a n c e ,
T h i s is difficult act,
o r
rule
t o
m a k e
t h e
s i m p l e
birth d e f e c t s f u r t h e r
t o o
asso-
p r o b i n g
o f
m o t i v e s .
M e d i c a l
T h e
ethical
i n d i v i d u a l in
a n d
m e d i c i n e ,
T h e as
clash
ethical
a n y
h a v e
t o
e v i t y
a n d area
rates
b e e n
p u b l i c
constitute
g e n e r a l
b y
o f
W i l l i a m
m o r t a l i t y
fever,
b y
o f
t h e
relevant
s o
o b v i o u s l y
o f
variation
(see
p r o c e d u r e s
t h e
c o u l d
Ironically,
t h e
n e w
issues,
m e a s u r e s ,
a n d
L o u i s - R e n e d u r i n g
a n d t o
T h a t
1 9 7 9 ; o f
C o l e m a n ,
scurvy,
e n a c t
t h e
are
reluctance that
the
w a s
w h o
t h e
o f
t h e
is
e n o r -
t h e
1830s,
t o
l o n g -
for o f t h e
the
t h e
n e w
in
d e a t h
r e s o l v e
the
differ-
p u e r p e r a l reluctance
statistics
b y
w e l l
p i o n e e r s
t o
as
b o l s t e r e d
a d v o c a t e s
are
s t u d i e d
S t u d i e s
legendary, that
disciplines
t h e y
greatest
r e s p o n s i b l e
m e a s u r e s
c o n s e q u e n t i a l
since
years,
1 9 8 2 ) .
balance.
c o n t r i b u t i o n
V i l l e r m e ,
w e r e
t h e
c o n t r i b u t e d
m a i n l y
t h e
sharper
in
m e d i c i n e
the
o n
e v e n
p e r t i n e n t
Statistics
c h o l e r a
that
h a n g
the in
P e r h a p s
is
this are as
m e d i c a l
Farr
sanitation
o f
c e n t e r e d
a v e r a g e s
in
e f f e c t e d
i m p o r t a n t
v a l u e s
o f t e n
b u t
w o r l d .
statistics
n o t
all
f o r m u l a t e d .
m o s t
Eyler,
dictate.
N o t
t h e
authorities
t o
d e a t h
in
a n d
S e m m e l w e i s s ,
in
the
t a k i n g
issues implicit
t h e s e
especially
h o u s i n g
ential
t o
o f
a n d
science.
h e a l t h
h e a l t h
district,
c o n d i t i o n s
life
sharply
b y m u c h
w e r e
o f
m o d e r n
a t t e n t i o n
h a v e t h e
m a t t e r s
b y
p r o f e s s i o n a l
necessity
e p i s t e m o l o g i c a l
m u c h
m o u s l y
traditional
statistical
w h e r e a n d
g i v e n a n d
this
t h e
p r e s e n t e d
k n o w n
that
b e t w e e n
t h e r a p e u t i c s
s e e m e d
p e r s i s t e n c e r e m e d i e s
o r
explain. standards
o f
e x p e r i m e n t a l
statistical
d e m o n s t r a t i o n
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Numbers
262
e n u n c i a t e d
b y
agricultural easier.
R.
A .
research
F i s h e r w h o
t o b a c c o
F i s h e r h a v e
h a d ,
industry, s m o k i n g
w i t h
m e n t a l
p r o t o c o l
h a d
t i o n
that
t h o s e
l u n g
cancer
m o n o t o n i c a l l y is full
o f
factor
that
1978, w e
p p .
n e e d
n o t
t h o s e
s p u r i o u s
t o
b e e n
4 7 3 - 6 ) .
A n
t o
a n d
t h e
cancer
rates
v a r i o u s
s m o k i n g
o n
ician
o f
a n d
this
Fisher
t o
t w o
take
a n
a n d
p e r b e
t o
can
cause
t o
e x p e r i m e n t
t h e
b e
a
w o r l d g e n e t i c
(see
B o x ,
t h e
issue;
their
s m o k i n g
t h e
resulting
actual
at
o f
n o n - s m o k e r s ,
analyze
w o u l d
t h e
settle
m a i n t a i n
d e t e r m i n e
rates
b y
a n d
q u e s -
increased
cancer
c o u l d
t h e n
e x p e r i -
n o
B u t
c a u s e d
s m o k e r s
t h e y
his
risk
day.
t h e
s t u d i e s
h i g h e r
t h e
a n y
t o
h e a l t h
c o u r s e ,
that
b e l i e v e d ,
W e
o f
o f
research
that
m u c h
m i g h t
that
t r e a t m e n t s
s u c h
h a v e
g r o u p s ,
care
w a s ,
s m o k e d
o n e
p u b l i c
r e a s o n
i n d e e d
s m o k i n g
e x p e r i m e n t .
B u t
therapies
c o n t r o l
p o s s i b l e
a c c o u n t . detail safe
-
-
a n d
d o
b u t
t h e
is
r e a s o n it
n o r
u n n a m e d p a t i e n t M i k e
b y
a n d
Sinclair c o n t r o l s
A r r o w s m i t h d u a l
m i s s i o n
lation.
H e
ister it t o rest
as
o n c e
effect
o f
i m p o s s i b l e
n o v e l
o f
e n d i n g
is c o n f i d e n t o n l y
h a l f t h e
refuses
T h e t o
result
t h e
o f t e n
less
-
c o n t r o l s
t h e r a p y
in
it,
t h e
d i l e m m a . for
is,
a d d i n g
t o
e l e m e n t
o f
b e
in
g r o u p
t o
t o
al-
solidity
o f
at
'flipping
a
lives
n e i t h e r
w h o
anguish
if
its
w h i c h a n d
b e
B u t
far m o r e
believes the
that
c o m p l e t e
used.
t h e
o f
o n
s h o w n
are
if
s a v i n g
T h e r e
in
s u p e r i o r
e v e n
c o n t r o l
t h e
p r e s s i n g
can o n l y
w h o
in
t h e
least o f
a
o n e
cancer
coin'
"
(see
6 7 8 ) . t h e
m o r a l
a n d
o f
p h a g e
a c c e p t
m e d i c a l
i n f e s t e d his
n e w
effective,
e n t h u s i a s t
i n o c u l a t i o n
until
in
w i t h
t e s t i n g 1 9 2 5 .
p l a g u e
h e
p l a n s
areas, a n d
w h o
t o
w i t h
t o
t h e
i n o c u a d m i n -
leave
a c c o m p a n i e s
A r r o w s m i t h
w i t h
M a r t i n
b a c t e r i o p h a g e b u t
at least in s o m e
h e a l t h t h e
island
b e
o f
p u b l i s h e d
testing
will
p o p u l a t i o n , p u b l i c
delicacy
first
a C a r i b b e a n it
e x p e r i m e n t a t i o n
p r o c e d u r e s ,
is i n
a n d
u n d e r s t o o d
w i t h h o l d i n g
Arrowsmith,
t o
n o t
e x p e r i m e n t a l
irrational
p.
is
e x p e r i m e n t a l
will
p h y s -
scarcely
all t h e r a p i e s
justification t h e
is
g r e a t e r
d o u b l e - b l i n d
t h e
p o r t r a y e d
controls.
S o n d e l i u s ,
" n o
j o u r n e y s
ethics
m e c h a n i s m
k n o w s
1 9 7 7 ,
his
o f
justify
n e w
i n t r o d u c i n g
in
H e n c e
t h e
t o
h e i g h t e n s
L e w i s
studies.
attained
T h e
G o o d ,
h e a l t h
a d e q u a t e
t h e r e b y
researcher,
s u p e r v i s i o n
virtually
s u p p o s e
physician
e x p e r i m e n t a l ,
m e d i c a l
w h o s e
difficult
run.
closer
p r o b l e m
w h e n
t o
is
l o n g
p a t i e n t
p u b l i c
that i n c l u d e s
k n o w l e d g e t h e
i n v o l v e
t h e r a p y
effective
ternatives, t h e
t h a n
A n y
a n d
t h e r e
in
cancer.
a n d
c o n t e x t
unethical.
T e s t s
is
t h e
t o
t h e
as a c o n s u l t a n t
o f
s i m p l e
in
m e d i c a l
m o n e y
T h e r e
cigarettes
a n d
t h r o u g h o u t in
n o t ,
e x p e r i m e n t ,
at r a n d o m ,
v e r y
o u t o f
f i n d i n g s
f o u n d
p r o m o t e
habits
a n d
o f
o n l y assign individuals
in a d v a n c e
t h e
t h e
d i d
t h e m
p r o b l e m s
f o l l o w e d .
correlations, b o t h
world
a c c e p t e d
w e r e
w h o
n u m b e r
t e n d s
t h e
a c c e p t for
the
w o r k e d
n o t o r i o u s l y ,
s m o k e d
w i t h
h e
m a d e
cancer,
w h o
t h a n
after
n o t
r e f u s e d
l i n k i n g
rule
t h e h i m ,
a g r e e s
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t o
Numbers
r e n o u n c e
his
later
o f
dies
e v e r y o n e .
c r u e l t h e
T h e
a n n o u n c e s
e x p e r i m e n t
p l a g u e ,
his
g o v e r n o r
o f
t h a t
"as
v i v i s e c t i o n i s t s
f r o m
( L e w i s ,
p .
m e n t ,
1 9 2 5 ,
t h e
d e s t r o y s c o n t r o l
t a x e d ( W e
t o
a n d
s h o u l d
p o s i t e d : m e n t a l
since
w e
h a v e w e
r a n d o m i z e d , i n
f o r e i g n
s e c u r e
e n o u g h
b e n e f i t
o f
U n i t e d
S t a t e s
g e n e r a l l y trials.
o f
l a w
m o r e
is
p r o b l e m
in
p o s t w a r
lifts
test
t h e
u s e
b u r d e n
p r o m i s i n g
l e n i e n t
o n
justifying
t h e
u s e
p u r p o s e c o u n t i n g
o f
t h e
erases
v i c t i m s , o r
c e n s u s , t h e
all
o f
o f
o n l y
o l d
E
W
d i s t i n c t i o n s
t h a t
c r u e l
m e d i c a l t h e
f o r
statistical
o f
t h e
w a s
it
t h a t
u s e
w h a t
o f t e n
e x p e r i t o
b e
first a
l a r g e -
s t u d y
r e a s o n
s h o r t t o w a s
s t r e p t o m y c i n
p o l i c y
f o r
t h e
i n
t h e
F e d e r a l
in, a p p r o v e d justifying
n e w
o f
it
k n o w l e d g e
c o n t r o l
a n
i m p o s s i b l e
C u r r e n t
o f
is
t h e
as likely
F o r
o r
rigid
clinical
t h e
d e p r i -
p o p u l a t i o n .
p u r p o s e s ,
c o r r e s p o n d i n g l y
l a w
T h e
a n d
t h e
a g g r a v a t e d .
R U L E S
j u r o r
e x p r e s s i o n s u n i t s
t h e
g r e a t l y illness.
c o n t i n g e n c y .
after,
d r u g s
s t u d y
m o d e r n
c o n v e n i e n t
m a d e
6 8 2 ) .
f r o m
B a y e s i a n
t h e
p .
b y
o f i g n o r a n c e
s o u n d
e x p e r i m e n t e r s
e x p e r i m e n t a l
T h e
p a t i e n t s ,
d r u g s
N
s e c u r e
d i f f e r e n t
t r e a t m e n t
7 . 4
C o u n t i n g
a
t o
his
p e r m i t t i n g
i g n o r e d )
t h e
w h i c h
e v e r y o n e .
1 9 7 7 b ,
f r o m
( o r
1 9 4 6 ,
b y
o f
s e r i o u s
a n d
P e r h a p s
in
o b l i g a t o r y ,
o f
n e w
trial,
w o u l d
d e a t h
s o m e t i m e s
it is j u s t
justified
t r e a t
t h a t
is
efficacy
total.
m o r e
all.
bizarre
t h a t
e x p e r i -
s a v e
b y
cases o f
t h e
p l a n ,
c o r p s e s "
c o n t e m p o r a r y
o f
Britain,
( T u k e y ,
o f
truly
is rarely
t h e
t o
Y a n k e e
his
u n e t h i c a l
e q u i d i s t r i b u t i o n
w a s
e v e n
in
w i t h
y o u
will
B u t
after
p r e d a t e d
clinical
t o
r e s u l t
a n d
p h a g e
s a n g u i n a r y
e x p e r i m e n t
s t u d i e s
c a m e
t h e
A r r o w s m i t h ' s
o f
r e s e a r c h e r s
t h e
g i v e
p r e v e n t
c e r t a i n l y
k n o w l e d g e
a d v a n t a g e
t h e
t h e
p r o v i s i o n a l l y
p e r h a p s
t a k e s
is
t i m e s
a n d
o f
universally,
c o m m e n c e s
t r e a t m e n t
o f
i g n o r a n c e
p a t i e n t s
a h i g h l y
o f
B u t
careful
p e r m i t s
v a t i o n
a s s u m e
t o l d
t o
this little island.
m o s t
real
s t r e p t o m y c i n
f u t u r e
T h a t
n o
a p p e a l
c o n c l u s i v e
m e d i c a l
L a p l a c e ' s
p h a g e
c e r t a i n l y
w r e c k s
m o d e r n
t u b e r c u l o s i s ,
a
a
t h e
t h a t
t h e
u s as a l o t
c o n t r o l l e d
t h a t
in
c u r r e n c y
in
h e
d o u b l e - b l i n d
l e g i t i m a t e ,
available
o f
263
n o n e t h e l e s s
e x p e r i m e n t
like
as n o t .
o f
w a s
o u t
shall
r u n
r e c e i v e
h o w e v e r ,
t r e a t m e n t ,
ethically
t o
a n
w h e n
u s i n g
o n
a n d
i n g e n u i t y
S o m e t h i n g
s t r e p t o m y c i n a g e
n o w
p r o c e d u r e s
i m p r o v e m e n t scale
lost
d o u b l e - b l i n d ,
e x p e r i m e n t a l m e t h o d s . )
will b e
c a r r i e d
I
i n a n d
l o n g
fictional
a d d ,
e x p e r i m e n t s
p o s s i b l e
t h e
t h e
justify
island,
i n
world
w o r d s
A r r o w s m i t h
p o p u l a t i o n
the
a d m i n i s t e r
d y i n g
his icy r e s o l v e ,
A r r o w s m i t h ' s s t a n d a r d s ,
as
a n d
t h e
c o m i n g
t h a t
lives i n A s i a t h a n w i f e
far
3 7 6 ) .
c o n f i d e n t
rule
o f o p i n i o n
a r e
m a t t e r
identical. s o
i m p l i e s B y
crucially
its t o
that,
f o r
v e r y
n a t u r e ,
t h e
t h e
i n d i v i d u a l
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264 -
t h e
m o t i v e s
for
statistics
c r e a t e d ations k i n d
t h e
o f
culus
statistics
o f
t h e
n u m b e r s
f o r g e
for
o f
S i n c e d r a w p r o v e b u z z
o f
m o r e
t h e
n o
w a y
its
t h e
Bayes'
a n d
are
t h e o r y
cite
t h e o r e m the
d o e s
a t t e n d
n o t
a d d u c e d
t h e o r y
I n t r o d u c i n g t h e
" i n n o c e n t
until
o f
difficulties probabilists
p r o v e n
Bayes' o f
( K e y n e s ,
o f
o f
a n d
i n f e r e n c e a z e r o
Bayes' guilty"
i n f e r e n c e s
t h e s e
in
1 9 2 1 ) .
violate
t h e
p r i o r
t h e
this
o f
a x i o m
1978,
c o u r t r o o m
p .
o f
t o
b e
p r i o r
reason,
m o s t
o f
q u e s legal
s i m p l y
a
c o n p r o -
u n i f o r m ,
a n d
that
o f
lay
in-
p r o b a b i l i t y
c o u n t e r s
o f
that
it
d o e s
e v i d e n c e ,
it
e v i d e n c e
o f additivity
in
1 4 5 ) .
guilt
dramatically w o u l d
m a k e
principles A n y
probabilities, are
t o
also
a b a n d o n e d .
i g n o r a n c e
a
leads
already
w o u l d
t i m e - h o n o r e d
h a v e
is
se. M o r e o v e r ,
p r o b a b i l i t y
s u p p l y
state
F o r
p e r
t h e y
is
a l t h o u g h
b o d y
t o
t h e r e
s o u n d
effect
for
e v a l u -
t h e
T h e y
o p p o s i t i o n
K o r n h a u s e r , i n t o
so.
c a n o n s
certain
e v i d e n c e
w o u l d
a
a
o n
n o t
t h e
r e a s o n i n g ,
g i v e n
m a y
d o
t o
t h e
T h e
d o
S o m e
e x c i t e d
i n f e r e n c e
o f
t o
h o w
S i n c e
explicit,
studies
t h e o r e m ,
m u s t
t o
in
t h e o r e m
if jurors
t o
a n d
s h o u l d
t u r n s
Bayes'
t a u g h t
legal
t h e
e v i d e n c e
t h e o r e m
fixing
b e
1 9 7 0 ) .
i n f e r e n c e
Since
a p p l y
that
a c c o r d i n g
m o d e l
( B r i l m a y e r
B a y e s i a n
t o
s h o u l d
w e i g h t
B a y e s i a n
essentials
a n d
ersatz
t h e
has
scholars.
t h e
p s y c h o l o g i c a l
o t h e r
trial p r o c e s s .
i m p o s s i b l e
c a t i o n
t h e
(or,
c a p t u r e s
Fairley,
o f
a n d
t h e i n t o
a n
i n s t r u c t e d
statisticians)
that
-
d e c i s i o n - m a k i n g .
b e
cal-
j u d g m e n t s
i n f e r e n c e ,
d e b a t e
a r g u e s
a n o t h e r
classical
p r o v i d e
t h e
m u d d l e d
a n d
t o
t h e o r e m
w h e t h e r
associ-
t h e
m a t h e m a t i z i n g
Bayes'
lawyers,
r e n d e r i n g
flawed
t o i m p e a c h
p r o b a b i l i t y
t h e y
o f
s h o u l d
e x p e r t
as
e x p e r t
intuition,
faction
o f
s t r e n g t h t o
d o e s
r e c e n t
is a
b y
judges,
t h e o r e m
t h e n
( F i n k e l s t e i n
u s i n g
r e a s o n i n g ,
h o p e l e s s l y
m e a s u r e
it
Bayes'
s u c h
jurors
r e a s o n s
probabilities
i n d u c t i v e
e x a m p l e ,
o r
r e a s o n a b l e
t o o l s
o n e s :
m e t h o d s
for
t h e
subjective
o l d
origi-
D e s c r i p -
H o w e v e r ,
t o
s a m e
translate
t h e
empirically
t h a n
a d v a n t a g e s
consistent, tuitions
test
dictates,
-
r e p l a c e d
a m o n g
t o
o f
o l d
t o
t h e
b a c k
t h e
m e c h a n i z e
w h e t h e r
p r o - B a y e s
v e r s i o n
t o
claim
T h e
t o
t h e
its l o n g s t a n d i n g
irrationality.
h a r k e n s
are
e v i d e n c e
v e r d i c t s
w h e t h e r
r e a s o n i n g .
o f
f r o m
c o n t r o v e r s y
o f
f o r m
issue
i n e d u c a b l e ,
c o r r e c t
f o r m a l
equally
1 9 7 0 ,
o b v i o u s l y
alter
are
a n d
s e e k s
stance,
c i r c u m s t a n c e s
h e n c e
e x p e c t a t i o n ,
m o t i v e s
a political
g l o b a l p a t t e r n s visible.
U s i n g
s t a n d a r d i z i n g
e v i d e n c e .
b e
century.
p e r p l e x e d ,
b y
for
c o u n t e d ;
v o g u e
t h e o r e m ,
legal
t o
in
world
i n d i v i d u a l
c o n d e s c e n s i o n
T h e
t h e
i n f e r e n c e s
article
probabilists
rules.
p r o b l e m s
a t i o n
t i o n
o f
c o n s e n s u s
t h e
o r
the
t o m a k e
w h a t e v e r
m u c h
Bayes'
a n d
rationality
o f
n o w
g e n e r a t i o n
a r g u m e n t s
m a s k
e i g h t e e n t h -
t h e
in o r d e r
sociological
probabilists n e w
t h u s
-
act, attitude,
w i t h
rule
suicide,
nality o f a m o n o g r a p h tive
Numbers
n o t o r i o u s t h e
like appli-
a n d
t h e
a m o n g
e x a m p l e s
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t o
Numbers
d a t e
t r e a t
i d e n t i f i c a t i o n
e x a m p l e , g i v e n t h e
a c c u s e d
cases B u t
w e r e
it
t o
d e s c r i b e h o w
is t h e
is
b e
t h e
-
t h e y
t o
a r e
o n l y o f
vis-a-vis
"soft."
p u s h
q u a n t i f i c a t i o n
O n c e
c o n s i d e r a t i o n s
" O n e
c o n s e q u e n c e s u c h
again,
f r o m
s u c h
e l e m e n t s
as
h a r d
v a r i a b l e s
t e n d
i d e n t i t y t o
a n d
t h e
T h e
c o n t r o v e r s y
tise:
w h a t
c o u r s e b o t h
is
i n
t h e
r e s t
i n s t a n t
b e
o f
o f
u s
(see
e x p e r t s
i n f l u e n t i a l
o p p o s e r e t o r t
T h e s e
t h e m
-
t h a n
of
o f
f o r t h e t h e as
r e a s o n i n g r e p e a t
a n d
-
f o r
a n d
b e
if t h e
e v i d e n c e
shift
t e n d
t o
t h e
a n d
f o c u s
t o w a r d s t h a t
t h e
1 3 6 6 ) .
R .
a n d
t h e
is
in
a n d
w h a t
a
a
a
i n
e v i d e n c e . J u s t
as
is
fledgling
albeit
t h u s
t h e i r
t o
a
m a k e
o f
t h e
e n o r m o u s l y this
all s c h o o l s ,
c o u l d b u t
i n t i m i d a t i n g
t h e
f o r
t e c h n i q u e
l e i t m o t i v
l a y m e n .
a
u n t u t o r e d
F i s h e r ' s
t h e y
a n d
c r a s h
m o d e l ,
b e c o m e s
o f
e x p e r -
a p r e s c r i p t i o n
t h a t
h a r d e s t
l a y m e n ,
j u r o r s
p r i n c i p l e ,
f o r t h
o v e r
d e s c r i p t i o n ,
A .
I n
o f
lay
t h e o r e m
e x p e r t s
in
a
a m a s s e d ,
since
t h e
r e f r a i n
is
E x p e r t i s e
set
l i k e n e s s e s
p .
f r o m
p o l i t e l y
is t h e
b a d
e v e n
r e a s o n s
t h e o r e m
r e a s o n ,
( 1 9 3 5 ) .
b e t w e e n
t o
g i v e
d e r i v e it
t o
g a p
r e a s o n
a g a i n s t
a c o n t r o v e r s y
B a y e s '
s u g g e s t
t e c h n i q u e s ,
a
is
b a c k g r o u n d :
i n t e n t ,
1 9 7 1 ,
B a y e s '
i n f e r e n c e
t h e
s a m e
w o u l d
m i n d s
e x p e r i e n c e
like
w a r n
b e
a n d
t h e
r o o t
w h o
is d e f i c i e n t .
lies w i t h
this
n o n -
risk
t h a t
e x p e r i e n c e
w i t h
n u m b e r s ,
i n t o
m a y
( T r i b e ,
j u r o r s
t o
i n t o
i n t e n t
t h e n ,
is at
Experiments
t e c h n i q u e s
t h e m e s
a n d
statistical
w i d e n e d
r i g h t
t e a c h
m a t t e r s
e x p e r t i s e ,
h a s
t h a t
T o
o n
c h a r a c t e r
t h e
1.8).
t h a t
t o
precisely
m e t h o d s
i n f e r e n c e s
legal
state
p r o b a b i l i s t i c
p r o b a b i l i s t s ,
b e s t
t o
e v i -
likely
a n d
T h o s e
h o w
is m o r e
t h a n
1 9 7 5 ) .
f o r e n s i c
" h a r d "
s o f t "
b e l i e v e
e v e n
c o n c l u d e
p a t e r n i t y
(Fairley,
m a t h e m a t i c a l
k n o w l e d g e ,
j u r o r s
it?
o f
t h e
r a t h e r
Design
d e m o c r a t i z e
e m a t i c s ,
w o r d ,
s u c h
l i t e r a t u r e
t h e
h a s
t h e o r y
h o w
o f
a b o u t
m a s t e r e d ,
a p p l i e d
fact
t h e
o n e ,
o f
r e a s o n i n g t o
w h o
e i g h t e e n t h - c e n t u r y
s c h e m a t i c t h e
a n d
B a y e s i a n
p r o b a b i l i t y
s e n s e s
f o r
it,
o v e r
s o r t
e x p e r t
" r a r e "
1 5 0 0
o v e r w e i g h t i n g
p r o o f ,
P r o b a b i l i t y
s o m e
o f
o c c u r r e n c e
s w a m p
t h a t
a n t i - B a y e s i a n s
m o t i v e
as v o l i t i o n ,
is t h e p r o b a b i l i t y
f o r
p o s s i b l e
t h e
statistical
o f i n d i v i d u a l
e l e m e n t s
as
a n d
o f m a t h e m a t i c a l
a w a y
as
a n
c o m b i n e
e v i d e n c e
f o r
this
r u l e
-
p r o - B a y e s i a n s
m u c h
o f
t h e
h a n d p r i n t s
e v i d e n c e :
P o l a n d ,
f o r m
a p p r o x i m a t i o n s ;
s p e c i o u s
I n
t h a n
s o m e h o w
T h e
as
r o u g h
d a n g e r s
o f
tests, w h a t
analysis
q u a n t i t a t i v e
m a t c h
e v i d e n c e .
r a t h e r
265
quasi-scientific
child?
p r o b a b i l i s t i c
in
world
u s i n g
a g i v e n
m u s t
t r a n s l a t e
the
b l o o d - t y p e
e x c e p t i o n
j u r o r s
m a t h e m a t i c a l
o f
t o
accidental
r a r e
e n o u g h
f a t h e r
p r e s e n t e d
a n
p r o b l e m s
results o f
s u b m i t t e d
s i n c e
d e n c e
t h e
rule
m a t h -
T h o s e
allegedly b a t t l e
is
discipline
in
w h o
p o r t r a y j o i n e d . o f
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risk
Numbers
266 p e r c e p t i o n . e x p e r t s risk
a n d
i n
e v e n t
a n d
-
far
assess
risk
is
easy
f r o m
statistics,
disasters are t h e
t o
risk
in
d i s m a y :
c a n
rare
" W e
w a n t
A n d
k n o w l e d g e )
r e m e m b e r
w e I
r e a d i n g
e x p r e s s e d d a m a g e
i n
c u r r e n c y
o f
d i s c u s s i o n b u t
o n l y
s p e n t w o u l d a g e s
t h e y
cases
risk
r e s o r t t h e
in
services
r e d u c e
F o r
t o
t h e in
c h o i c e s
e x a m p l e , k e e p
( a b o u t w h e r e
t o risk
q u a n t i f i c a t i o n
o f
r a r e
o r
o f
e v e n
c e r t a i n
t h e
w h a t
1 9 8 3 , p .
n u m b e r
h a v e
d e a t h s
d e a l
o f
i n
t h e
q u a n t i f i e d , w o u l d
o f
o f
say t h e
b e t h e y
d a m -
risks
risk
o f
t o
assess-
c o n s t r u c t -
a r g u e
y e a r
o f
C u r r e n t
i n d i v i d u a l s
p e r
b e e n
w o r t h
w h a t
h a z a r d s
w a s
H e r e ,
b e
p r o b l e m s
I
v a l u e s .
also
o b j e c t i v e
d e l i c a t e
o f
h e
180). C o m p a r i n g
c h i e f
. .
t a c k l e
dollars'
o f
w e
m u s t
a m o u n t ?
o c c u p a t i o n a l
n u m b e r
o r
lost?
b y
m o r e
t h i n k
c a n
s o
risks.
v a l u e s
life
h a n d s
i n f o r m a t i o n
c o m m e n s u r a b l e .
o f
t h e
I
m u s t
w h e t h e r
a
o f
o u t c o m e
life?
is
o f
t w o
t h e i r
q u a n t i f y ,
level
m a n y
c a p a c i t y
( M o o r e ,
t h e
i n d u s t r y ,
t h e
t h e m
t o
o u t c o m e s o
s u b j e c t i v e
u p
p e r s e v e r e
assessors
t h e
d e a t h
i n s p e c t o r s
o b j e c t i v e
s u b j e c t i v e
o f
p o s e s
o f
risk
e a r n i n g
a m o n g
1 0 0 , 0 0 0
t o o
t h e
s a v e
t h e
q u a n t i f y i n g
t h a t
e x a m p l e ,
m a k e
o f
a n d
n u m b e r . '
T h o s e
d e r i v e d
collected,
said
is
b e
b e e n
i n
'All
c a n
o u t c o m e
h a v e
difficulties
q u e s t i o n
c o u r t ?
t r a c k
in a g i v e n
is e i t h e r
t h e
t e r m s
c o m p a r a b i l i t y
l i f e t i m e
I n t h e
t o
s h o u l d
e m p l o y e e s i n g
o n
r a t i o n a l
u n i t s .
b u t
n o t
h o w :
t o d a y ' s
n o r
d i s c u s s e d
w a n t
o f q u a n t i f y i n g
f o r
c e n t e r s
m e d i c a l
a n d
-
-
s o m e h o w
actually a w a r d e d
m e n t ,
t e r m s
h u r r i c a n e
A t
traditionally,
a n d
p a y
p e r m i t
i n g
d e b a t e d :
r u l e
t h r o w n
W e
a u t o m o b i l e
h o t l y
t o
s i m p l y
t h a n
e x p e c t a t i o n
m o s t
g u e s s w o r k
h a v e
3 7 ) .
p r o b l e m s
d a t a
m o r e
t h a n
p r o b a b i l i t i e s t h e
t h a t
e x c e p t i o n
p r o b a b i l i t y
B u t
t h e
i r r e v o c a b l e
o f
t h e
o f
s h o w
f o r
cases
e x p e r t s '
s u c h
' g o o d . '
p .
lives,
o n
in
a r e
a
as
1980,
t h e
s t u d i e s
a c c i d e n t s
t h e
d e f i n e
p r o b a b i l i t y
is m o r e
t h e
rationally.
P y t h a g o r a s
m o n e t a r y
f r o m
t h i n g s
I n
b e t w e e n
e x p e r t s
p o t e n t i a l
n e i t h e r
t o
S o m e
t h e
p l a n t
t h a t
for
r e s o r t
t h a t
f o r m i d a b l e
u n i t s
n o v e l
t h a t
t h e
a c c i d e n t s .
substantial
m o r e
b u t
cases,
see
t h e
t h e
d o
see
( S c h n e i d e r m a n ,
e v e n
t o o
T h e
p s y c h o l o g i c a l
p r a c t i c e ,
s o m e
m o s t .
p o w e r
f o r
d i s a g r e e m e n t
o f
a c c i d e n t s .
a p p l y ,
I n
fear
e x a m p l e ,
exist,
a b o v e .
t o
s t u b b o r n
p r o d u c t
f e a r i n g
m u s t
w r o n g " e v e n
f o r
I n
t o
a n d / o r
t h e
t h e
a u t o m o b i l e
m e n t i o n e d
c o m p a r e .
( a n d
f o r
assessors
p r o b a b i l i t i e s
-
statistics
by.
world
s h o u l d
a u t o m o b i l e
c o m e
t o o
w e
risks,
difficult
as
is
as
a s s e s s m e n t .
s i n g u l a r l y
v a l u e
a n d
t h e i r
the
N u m e r o u s
criteria
f r e q u e n t
in
w h a t
v a l u e .
t r u s t w o r t h y
r u l e
d'etre
e x p e c t a t i o n ,
d i f f e r e n t
m o r e
p r o v e s
o v e r
o u t c o m e
t o
a c c i d e n t s , t h e
o f
its
u s e
disaster
i t s raison
l a y m e n
t e r m s
l a y m e n
t h e
I n d e e d ,
rule
w h e t h e r
p e r
fatal a c c i d e n t s
m i l l i o n
in a
w o r k -
h o u r s ) . statistics
a r e
t o o
o r
n e w
p r o b a b i l i t i e s . i g n o r a n c e ,
O n c e
t h e
i m p o s s i b l e a u n i q u e
c o m e
case, risk
r i d i c u l e d
e n t e r p r i s e
t o
h a s
b y J o h n
by,
b e c a u s e
assessors S t u a r t
r e g a i n e d
its
o f t e n
M i l l
as
r e s p e c t a -
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Numbers
bility w i t h b y
B .
d e
t h e
r i g o r o u s
F i n e t t i
b e c o m e
s u b j e c t i v e
o b j e c t i v e is m o r e
a n
p r o b a b i l i t i e s
t o
C o r p o r a t e
t w e e n
a
p o i n t
ability, 5 0 % , t o
o n
f o r
(e.g.
s c r u p u l o u s
n u c l e a r
p o w e r
( S e l v i d g e , W h y w h e r e
o r
s u b j e c t i v e
t e n t ;
t h e
( H o e r l
a n d
f o r
c e r t a i n t y
is
p r o b a b i l i t i e s o u r
d e e d
is
1 9 7 4 )
t h a t
-
w h o (Levi, f o r
c u l t u r e :
s u b j e c t i v e
t h i n k i n g
i m p l y -
a
o n l y b e a r e
t h a t
r e c e n t
in
t h e
b e t t e r
p .
n u m b e r s , p r e c i s i o n ,
o f
f o r
live
sense.
T h e all
u p
t o
o n l y
a r d u o u s
c o n -
d o e s
at p r a c t i c a l
s t a k e s
t h e s e
j u d g s u g -
a r e
h i g h
n u m b e r s
w h e n f o r
t o
w h e n
p r o f e s s i o n a l
n u m b e r s
t r u t h
n o t
b e t t i n g
a
a r e
t r a i n i n g
s e n s e
v o g u e t h a t
m a t t e r s
N o t
a n s w e r s
o f
w i t h
e m p i r i c a l
valor,
for
t h e
v a r i e t y
u p o n
p a r t
objectivity,
p r o b a b i l i t i e s
L l o y d s
t h e
0, a n d
a m o u n t
t h e
w i t h
4 4 1 ) . a n d
t h e
f u m b l e
p r e s s e d
like
p e r s u a d i n g
r a c e t r a c k
o f
p r o b -
e x a m p l e ,
b a d
It
e s t i m a t i n g
n e w
w h e n
finely.
t h o s e
f o r m a l
a r e
T h e
m a g n i t u d e
m a k e s
a n y
level.
a
o f
t h o s e
t h e
s t u d y
t h e y
h a r d e s t
1 9 8 0 ,
o f
u n t i l
for
d e s p i t e
p e o p l e
especially t h a t
o f
m a k e
o d d s
w e
c o n t i n u u m ,
f o r t h c o m i n g ?
e m p t y
h a b i t u a l l y
i n d e e d ,
w o u l d
v o g u e
q u a n t i f r e n i c i r o n i c
g o o d
analysts
a
n o t
is n i l -
b e -
shall
v a l u e s
a b o u t
e x e r c i s e
is
t h e
a r e
r a t h e r
m o r e
i n c l u d i n g
i n s u r a n c e
k i n d
t h e y
s u b j e c t i v e
f o r
something
t h e
a
s u b j e c -
c h o o s e
g i v e n
o r d e r s
p a r t i c u l a r l y
j u d g m e n t s
s i t u a t i o n s
g r e a t e s t
a n y
o f
difficulty
e x p e r i e n c e
t h a t
t o
a r o u n d
n o n e t h e l e s s
j u d g m e n t s , o f
f o r
e x p e r t s
m i n d ,
p r o b a b i l i t y
o u t
r e q u i r e d ,
as
t o m o r r o w ?
w i t h
a d v a n t a g e
k n o w s
a n d
p r o b a b i l i s t i c
j u d g m e n t risk
-
r a i n
t h e r e
j u d g m e n t .
u s i n g
o f
i n
s u b j e c t i v e
safety
a s k e d
crystallize
speciality
p e o p l e
d o e s
v e r y
Fallin,
s u s p e n d i n g h a z a r d
t h a t T h i s
a r e
s h e
o r
2 0 4 - 5 )
t o
s u c h
c o n t i n u u m
s t r a i g h t
is
is
5 0 %
t h e
p a r t i c u l a r
o r
disasters
m o s t
u n c e r t a i n
t h e y
a
u p
a r e
p e r s o n a l
t o
t h e
Still,
i n s o f a r
s t a t e
m o r e
a n c h o r e d
h u n c h e s
t r u e
it
o f
n u c l e a r
a l o t t e r y
full
t h a t
i n f o r m a t i o n
m i s t a k e s
i n
h e
p r o b a b i l i t y
s u g g e s t
t a k i n g
o n c e
m e c h a n i z e
" c o r r e c t "
will
for
t e n d
p r o b a b i l i t y
h a v e
l o n g e r
u s e
t o
assessor
-
d i v i d e
t r a i n i n g
w h e r e
p p .
n o
naturally.
g e s t s
in
cases
t h e
assessor
0 . 0 0 0 1 ) ,
p l a n t
s u c h
m e n t s
t h e
t h a n
" t h a t
a r e
fixing
t o
t h e
a n d
assessor's
t i c k e t
r e s p o n s e s
n u m b e r s
little
c o m e
a n d
1 9 7 5 ,
p u t
s t r o n g l y
a s k
in
t h e i r
t h e
o f
classical p r o b a b i l i s t s .
q u a n t i f y i n g
l o c a t e d ,
r e p e a t e d
assessor in
a
n o
a n d
q u e s t i o n
a n d
a r e
f o r e c a s t e r s ,
U s u a l l y
in
C o n s i d e r a b l e
u n c e r t a i n t y "
o f
p r o b a b i l i t i e s
0 . 0 0 1
e v e n t s .
a r t
m i r r o r
-
t h e y
t h e
p r o b a b i l i t i e s
r a t h e r
s m a l l
f o r
i n t e r p r e t a t i o n
classical p r o g r a m
t h e
is
t o
b u t
267
P r o b a b i l i t i e s
d e c i s i o n - m a k i n g
e v e n t
n a i v e
1 0 0 % ,
w e r e
w o r l d .
is t h e n
m o s t
c o n f u s e
r a r e
t h e
1 9 5 0 s .
belief,
w e a t h e r
a n d
t h e
s i m p l y
7 5 % ,
a p a r t
in
i n d i f f e r e n c e
d o
o f
t h e
this site?
p r o c e s s n o t
t h e
T h e s e
o f
oil at
o f
s a m e will
s t a t e b e t
drill f o r
i n
o f
c o n s i s t e n t
a n y
S a v a g e
r a t i o n a l i z e
p r o b a b i l i t i e s .
i n t e r n a l l y
a p e r s o n a l i s t
as t h e y
s c h o o l e d
world
o f
d e g r e e s
e c h o
the
revival
e x e c u t i v e s ,
a r e all b e i n g
t h a n
L.
e x p e r i e n c e ,
t h a n
tive
a n d
rule
t h e
u n -
s u b j e c t i v e s y m b o l i z e
fact.
v i r t u e s
It
is
o n l y
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int o
268
t h e
e x t e n t
t h e y
are
T o t o
that
t h e y
i n t e n d e d
t h e
a g r e e
t o
a m o n g n o
o u t
p s y c h o l o g i c a l a n d
lay
respectively, accidents,
m e n
t h e
t o
o v e r o f
fatal
as
M a s s i v e
T h e a n d
e x p e r t s
irrationality,
n u c l e a r
p o w e r
s o c i o l o g i s t s theless risk,
for
in
t e n d e n c y
u n d e r w e i g h t
t h e
t h e
"disaster
p o t e n t i a l "
t h e
v i v i d n e s s
G o v e r n m e n t s w h e n
large
relative
shifting
t h e
c u l a t i o n s
o f
t h e
w h e r e
o f life a n d
h a d
s o u g h t o f
f r o m
c o n s e n s u s .
l a y m e n
b e l i e v e d p r e t e n d
d e a t h "
a
t h e
sorts
is
B u t
t h e
Far f r o m r e s e n t e d
v a l u e s that
it
( q u o t e d
is
f o r m s
b o w i n g
s h o u l d best
t o
in D o u g l a s
t h e
o f
t o
c o u n t .
lay-
o f
t h e
1980, p.
nuclear
as m a s s
hysteria
o v e r
b e t w e e n
b u t
m i g h t s t u d y
w e r e
also
t o
w h e n risk
t o
distort
lay
subject.
d i s a p p o i n t e d t h e y
p r o b l e m
in
politics
t h e t o
v a u n t e d
objectivity
a b o u t
o f
rather
o f calt h a n
objectivity
i n t o
travesty
h a d
h o p e s
that
t h e
a
o f
the
f a n n e d
is
n o n e -
a n d
o p i n i o n
technical
o f
a n d
i n v o l u n t a r y
v a l u e
t o
m u c h
78).
the
e x p e c t a t i o n
that
a n d
p u z z l e d
d i s m i s s e d
irrational
e n e r g y ,
"It
a m o n g
a n d
s o l u t i o n
i n t r u s i o n
w a s
p s y c h o l o g i s t s
e x p e r t
a
v a l u e s
e x p e r t s '
t h e
-
States
t o
s t u d y
p r o p o r t i o n i n g
discipline
a s o l u t i o n
o f
o f
etc.
risk
o u t c o m e
d e p i c t e d
U n i t e d
r e a l m
t o
risks,
far g r e a t e r
part
v o l u n t a r y
t h e
b e t w e e n
associations
t u r n e d
b o r n
e s t i m a t e d
b e h a l f o f
r e c k o n i n g s
n e w
v a r i o u s
t h e
o n
t o
a u t o m o b i l e
( K a s p a r ,
historical
their citizens rejected
c o n t r o v e r s y .
t h e y t o
T h e y
o f
a n d
their
u n w a r r a n t e d
e v e n t
c r e a t e d
E u r o p e
d e c i s i o n
e x p e r t s ,
t h o u g h t
T h e y
t h e
t h e
they p e r c e i v e d
intuitive a n
b e
w h a t
for
w a s
e x p e r t s
o p p o s i t i o n .
w h a t
p u b l i c
e x p l o s i o n s ,
p u b l i c
T h e y
o f
accidents,
t o
f o r
o v e r w e i g h t
in
the
d a n g e r o u s "
b y
s u c h
"subjective"
o p p o s i t i o n
t h o u g h
p r e f e r e n c e
is large,
risk-benefits
a n d
d a m p e n e d
p r o b a b i l i t y
n u m b e r s
c o m m i s s i o n e d . t h e
in
a t o
w h i c h
v e h e m e n t
c o n d u c t e d
it
u s i n g
p s y c h o l o g i c a l
calculated
w e a p o n s .
-
N o
d e v a s t a t i n g
o v e r
able
disparities
p l a n t
that
w e r e
risk p e r c e p t i o n
s y s t e m a t i c
p u b l i c
t h e y
g e n e r a l
p o w e r
a n d
b u d g e
t h e
d a n g e r s
u n d e r s t a n d i n g
i n n a t e
w i t h
e x p e r i e n c e
risks
relative
s o m e t i m e s ,
t o
o f
1 9 8 2 ) .
T h e
v a r i o u s
t h e
t h e y
like
o f
w h e n
a n d
for
e x p l a i n e d
factors
p e r c e p t i o n s .
o n
e v e n
" o b j e c t i v e "
e v e n
w h a t
nuclear
h e l p
p e r s o n a l
p e r s u a d e
nuclear
their h e a d s
s y s t e m a t i c
a n
risk
t o
failed
a n d
c o u l d
as
plants,
and,
a n d
assessors,
Lichtenstein,
campaigns,
s h o o k
ineffable
discipline
t o
accidents.
S w e d e n ,
t h e
r e v e a l e d
probabilities
"insensitive,
in
that
analysts)
i n d i f f e r e n c e
e d u c a t i o n
i n d u s t r y
e d u c a t i o n
p o w e r
small
world
m a g n i t u d e
t h e w i d e s p r e a d
a u t o m o b i l e
e x p e r t s
t h e
(referred
a n d
n u c l e a r
p u b l i c
o n
risk
p r e g n a n c i e s ,
d i s c o v e r
a s t r o n o m i c a l l y
t h e
e x p a n d i n g
risk
f l o o d s ,
t o
o f
studies
v i e w s
Fischhoff,
r e q u i r e d
f r o m
o f
rapidly
b y
the
s u p p l a n t .
a m o u n t
suit. T h e
(Slovic,
d e r i v e d
t h e m s e l v e s
f o l l o w
e x p e r t
rule
d i s a p p o i n t m e n t
t e c h n i q u e s ,
o f
are
Numbers
o f
take
v a l u e - f r e e
d e c i s i o n s
in
a n d
W i l d a v s k y ,
1 9 8 2 , p.
7 3 ) .
a n
area
rational m a t t e r s A b o v e
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Numbers
all,
t h e y
t h a t
it
r e f u s e d
w a s
e x p e r t i s e a n d
t o
r a t h e r
a
c o l l i d e d
P o l l a k ,
a c c e p t
rule
t h e
q u e s t i o n
h e a d - o n
the
issue
t o
b e
w i t h
as
world
a
p r o b l e m
d e b a t e d .
t h o s e
269 t o
H e r e
b e
t h e
s o l v e d ,
ideals
o f p a r t i c i p a t o r y
i n s i s t i n g
o f
t e c h n i c a l
d e m o c r a c y
( N e l k i n
1 9 8 0 ) .
G a m b l i n g
T h e
v e r y
o l d e s t
c e r n s
g a m b l i n g ,
c l o s e r
t o g e t h e r .
p r o p o s i t i o n t o
i g n o r e
m u c h
d i v e r g e n c e a n d
c a l c u l a t i o n s
t h e m .
S i n c e
f i r s t h a n d m a d e
a
s t u d y
w e r e
fair:
o u t
o f
c a l c u l a t e d
t h e
o t h e r
p l a i n e d
b y
o f
b e e n
w h i c h
c h a n c e s .
F o r
a r e
e x a m p l e ,
o n
a n
w i n ,
s o
t h a t
y o u r
m o u n t s
v e r y
q u i c k l y ,
late
e v e n
n i n e t e e n t h
r e l e v a n t h o r s e m i z e
t h a n
u p
t o
t h e i r
o f
t o
in
Of
p r i m e
d u e
c h o i c e
Games
n e e d
t o
ticularly e v e n
a w a y 1 9 8 6 ) .
d i s t i n g u i s h h i g h l y
s o m e
a n d
t o
w h a t
t h e
o f
a
C a r l o .
t i m e s ,
o f y o u
t o
h a v e
e v e r y
K a r l
P e a r s o n
T h e
a v e r a g e s
b l a c k
T h e
t o
y o u r
capital
large-scale
a n d
t h e
y o u
b e c a m e
e v e n
o f
o n e
u n t i l
y o u
t h e
g o i n g
s t a k e
o v e r
b e t t i n g
i n
a m o u n t
o d d s
b e t
t h a t
r a c e t r a c k
total
c h a n g e
o r
a
a n y b e t
e x 1 3 4 ) .
o n
lose
is
b e
o n
s y s t e m s ,
b e t s
w i t h
p r o b l e m
f r o m
1 9 8 3 , p .
d o u b l i n g
t i m e
h a d
d e v i a t i o n s ,
M o o r e ,
b e g i n
l o s i n g
d e v i a t i n g
s t a n d a r d r e d
a n y
c o n t i n u e
p r o b a b i l i s t s
f r o m
c a l c u l a t i o n s
h o r s e s
t h e y
h a u n t e d
t h e v o n
r e v i v e d
t h e
in
t h e
case
o n
c o n s t a n t l y
less
a
g i v e n
t o
m i n i -
i n s u r a n c e .
N e u m a n n
a n d
o f
g a m b l i n g
i n v e s t m e n t s
b e
r a t i o n a l
a n d
m a x i m i z a t i o n
p r e d i c a m e n t
i r r a t i o n a l
t o
c o n t r a d i c t i o n s
b e t w e e n
self-interest.
n e o - ( D a n i e l ) B e r n o u l l i a n
rationality
p h e n o m e n o n
T h e i r
b y
c o m p u t e
o f
b y J o h n
e c o n o m i c t h e
still
i m p a c t
w h i c h
s p e c u l a t i v e
f o r m s
u n i t .
b o o k m a k e r s
a r e
a d v a n c e d
o f
t h e
since
( 1 9 4 4 ) ,
c r i t e r i o n
L o p e s ,
o f
b e t
o f
as
in d i s t r u s t i n g g a m b l i n g
e x h a u s t i n g a d v e n t
t h e m
g a m b l e r s
a l t h o u g h
c o n -
losses.
g a m b l i n g
r a t i o n a l i z e
1 9 7 6 ;
t i m e ,
o n e
p r o b a b i l i t y
h o w e v e r ,
p a r t
r a t i o n a l
Theory a
is
t h e
c e n t u r y ,
race
is
e i t h e r
W i t h
p o t e n t i a l
w i d e s p r e a d
g a i n
f e w
5 7 ; also
M a r t i n g a l e , t h e
utility;
T h e
p r i n c i p l e
d o u b l i n g
k n o w l e d g e
E c o n o m i s t s ,
T h i s
n e t
1 8 9 7 , p .
o p i n i o n
g a m b l i n g
8 , 0 5 3
0 . 2 5 % .
lay
b r o u g h t
M o n t e
s w i t c h e s
t h e
t h e
at u p
u n a n i m o u s
o n
w i t h
c h a n c e ,
m a x i m u m .
[1894]
n o t
tables,
c a m e
m a n y
a l m o s t
o r v e r y
w h e e l s
o n l y
a n d
c o n d e m n
g a m i n g
r e d
b y
t o o
b a s e d
u n i t
c a s i n o
spins,
( P e a r s o n ,
h a v e
t h e
v a l u e
t o
C a r d a n o ,
r o u l e t t e
s u g g e s t e d
c h a n c e
P r o b a b i l i s t s m o s t
1 6 , 0 1 9
h a v e
e x p e c t a t i o n
at
t h e
e x p e c t e d
h a n d ,
c e n t u r i e s
G i r o l a m o
o f
p r o b a b i l i s t i c
c o n t i n u e o f
e x p e r i e n c e
o n c e
e x p e r t
t h r e e - o d d
P r o b a b i l i s t s
b y
t h e
o f
f o r c e d
g a m b l i n g w a s
f u r t h e r
f r o m like
E c o n o m i s t s
o f
M o r g e n s t e r n ' s
e x p e c t e d
e c o n o m i s t s ( I g n a t i n
a n d
c o m p l i c a t e d
r a t i o n a l
c o m m o d i t y g e n e r a l l y
O .
t h e o r y
v a l u e
literally S m i t h , b y
i n v e s t m e n t s , f u t u r e
a d m i t
t h e
as
t h e p a r -
t r a d i n g
o r
s t r u c t u r a l
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Numbers
270
similarity o f
b e t t i n g
p e r s p e c t i v e e m a t i c a l
m a i n t a i n t o
D o w
e x p e c t a t i o n ,
a n d for
b u y
that
syndicates sell
Industrial
( M o o r e ,
d o
o f
p.
fall
a n d
i m p a c t
o n
In
chapter,
this
these
t o o l s
values; d e e p
in
has
r e a s o n s
i n t o
battled.
O n
cations
o f
t h e r e ply
T h i s
Financial N e w
t h e
like
is n o
m i r r o r i n g
s i m p l e
act
o f
t h e
statistics
established also
part
certainty.
h a v e n e w
o f
t h e
T h u s
part
e x p a n d e d ,
steadily
retreated.
in
t h e
m a t h -
e c o n o m i c is
h a r d
p e r m i t t i n g L o n d o n
t o
i n v e s (or
t h e
o n
t h e
b e t t i n g
s h o w
h o w n e w o f
areas
t h e
t h e y
t o
b e
m a t t e r .
t h e s e are
m a n y
o f
w e
that
b u t
o b j e c t s
the
claim i n t o
rationality t o
s e e m i n g
p a r a d o x
chance's
t w i n
n e w
b e l i e v e that,
c u t
s o
t o
b e
t h e
as
u n c e r t a i n t y
c o i n e d claims
that t h e
w i t h
s i m t h e
attitudes
a n d
b e l i e v e
that
o f
t h e
t h e
appli-
m a r k .
T h e s e
n e w
values,
authority.
n u m b e r s
t o
o f
e v e n
t o
t o
appli-
H o w e v e r ,
seen,
e m p i r e
a p p e a r s
e m -
universally
s e n s e
c o l o r
f r o m
m o s t
a m b i t i o u s
fatalities. in
t h e
e v e r y w h e r e
r e v e r b e r a t i o n s
b e i n g ,
a n d
applications
c r e e d
strays
o f in
h a v e
c a n
g r o w i n g .
application
a l m o s t
traffic
A s
still
T h e i r
a n d
less
neutral,
life.
facts
are
are
o f
in
b o u n d
P y t h a g o r e a n
this
c r e e d
subtle,
that
a s s u m p t i o n s
far
a n d
g r e a t
as
o u r
w h e r e
statisticians
a
t h e
v e r y g u i d e a n d
registration
o f
o f
P y t h a g o r e a n
steadily
are
d e s c r i p t i o n ,
s t a n d a r d s
t h e
t h a n
d i s t i n c t i o n
o u t r i g h t
t h e
b e c a u s e
that
i n n o c u o u s
i n v o l v e s
called
f r o m
"useful
is e n o r m o u s
c o n s t r u e d ,
the
facts
m e r e l y
a
I n d e x
i.e.
s t u n n i n g
J u s t
t h e r e
a n d
s o
q u a n t i f i c a t i o n
applications
c h a n g e s ,
b r o a d l y
It
o f
t h o s e
say
interpretations.
cations
o n
t o
c o u n t i n g
is
sciences,
n o t
bare
is
as t h e
t h i n k i n g ,
a p p l i c a t i o n
-
b e c o m e
o f
census
rather
a s c h e m e
T i m e s
Y o r k )
i n d e e d
f o c u s e d
contrary,
the
s e r v e t h e
I n d e x ,
w a y s
statistics,
that
m o r a l
m a r k e t
C O N C L U S I O N
u n r e a s o n .
is
t h e
s t o c k
1 4 3 ) .
for
a n d
traditional
controversial.
accepted,
m a d e
t h e
H o w e v e r ,
t h e in
daily life, as w e l l h a v e
o n
o n
C o r a l
statistics h a v e
w e
b a c k
n o t .
7 . 5
P r o b a b i l i t y
world
b e t t i n g
t h e
I n d e x
1 9 8 3 ,
the
i n v e s t m e n t s
like
units
a n d
a n d
b e t w e e n
t h o s e
a n d
J o n e s
m a r k e t
at a c a s i n o
d i s t i n c t i o n
f u n c t i o n "
tors
o f
rule
o f
a n d It
c o m e s
c h a n c e
h a v e
is
just
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has as
II f a u t Blaise
parier.
Pascal
(1669)
8 o
>
T h e
8 . 1
e m p i r e
l e m s
s o m e
tual
c o n t i n e n t s .
p a r i s o n s
o f c h a n c e t h r e e
i m p o r t a n t
h u n d r e d
literary parts
o f
w e
listen
t o
tests, p u r s u e o r
e v e n I n
t h e s e
g r o w t h
this
applications. m e r e self
w i n
p l a y e d p r e t e d in
s o m e
b e
t h e y
w e
roles, o f
w a y ,
a n d
as
b e e n
ability,
t o
a n d
o f
as
c e n t u r y
t h e m ,
o f
c o u r s e
s h o w s .
a
o f
a n d
t h a n
t o
l e n g t h e n i n g
c o m -
e c o n o m i c s ,
e v e r y
wall.
b u y
a n d ,
I n s o f a r
u n d e r g o
statistics
a c q u i r e d w e n t
H e r e
m e d i c a l
insurance,
w a s
classical in
e x c l u d e
t h e
in
o n c e
c e n t u r y
w a s
intero r
applications, A
b e e n
shift t h e
t h e o r y t h e
i n t e r p r e t a t i o n s
applications.
it-
a n a l o g y
as a p r o p e n s i t y ,
p r o b a b i l i t y o u r
b u t
a n d
insurance.
h a d
as
d i v e r s e
sufficient
particular
life
that
o f
n o t
p r o b a b i l i t y
o f
t o
e v o l v e d
m o r e
i n t e r p r e t a t i o n
f r e q u e n c y ,
o r
e v e r
e x p l o s i v e
h a n d - i n - h a n d ,
W h e t h e r
list
its
e n c o m p a s s e s
occasionally
a n d
t e c h n i q u e
H o w e v e r ,
t o
statistical
also
polls,
c o n c e p -
subjects.
t i m e
applications
It
p r o b -
b e l o n g
o f living i n d e x ,
t h e o r y
e v i d e n c e
w h o l e
sciences
practical
plausibility
fate
o v e r
a l m o s t
s t e a d y
seen.
in g a m b l i n g
cliometrics,
a n d
its
s a m e
t h e
t h e
rather
-
as a relative
legal
discredit
a c c u m u l a t e w i t h
all t h e
t h e
d e t e r m i n e d
practice,
has
s t a n d a r d are
h a v e
certainty,
o f
n i n e t e e n t h
at
social
political
applications.
w e
c o u l d
early
w e
s p r a w l s
h u m a n i t i e s .
p o n d e r
t h e
f o o t h o l d
b r e a c h e d
m a t h e m a t i c a l
i n t e r p r e t a t i o n s probabilistic
has
p r o b a b i U t y
n e w
e v a l u a t i o n s
a n d
t h e
f o l l o w e d
as
n o w
industry,
d e v e l o p m e n t s
t h e o r y
a n d
in
reports,
a n e w
as a d e g r e e o t h e r
e v e n
aspect,
h a v e
I M P E R I A L I S M
c o n q u e s t s
m e d i c i n e ,
e m p i r e
o f
t h e
-
n e w s p a p e r ,
T h e s e
critical
t o
law,
disciplines
e x i s t e n c e
t o
style
a g o
b e e n
c h a n c e
a n u n s t e a d y
natural
sciences, p l o t
the
m a t h e m a t i c a l
h a v e
w e a t h e r
p a g e s
o f
t h e
statistical
t h e
read
years
o f
t h e r e
in its d e s c r i p t i v e as
b e g a n w i t h
A l l
a n d
o f
o f
P R O B A B I L I S T I C
T h e
territories,
i m p l i c a t i o n s
in
c o r e
in
the
t e n d e n c y o f
p r o b -
A l m o s t
e v e r y
271
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The
272
a p p l i c a t i o n f o r m ,
e v e r
a t t e m p t e d
h o w e v e r
T h e
d u b i o u s
e m p i r e
o f
i n t e r p r e t a t i o n s S e c o n d , o u s
as
a t i o n s
w e r e
t h a t
h a d
effectively
e c u m e n i c a l
a n o t h e r
c a t i o n s t h e s e
as w e l l
v a r i o u s
cation. o f
o r
e x a m p l e , b y
A n a l o g y m i g r a t e d
o f
w a s
f r o m
t h e
b r i d g e
o n e
o v e r
t r a n s p l a n t e d c o n t e x t c u r v e
o v e r
t h e
s c a t t e r i n g
o f
o f
w e l l
for, a n d
w h e n t o
t h e
cules en
masse
t h e
c o m e t ,
as
a
p r o d u c e d
inaccessible
a n a l o g i e s
i n t e r t w i n e d
5.5, a r e
t h e n
t o
o f
t o
as
q u i t e
t h e
a n
o f
a p p l i -
a n d
m e r i t s eclectic.
t h e i r
s u b j e c t s N e y m a n -
t h e
o f
a
o f
a n d
2.5). J a m e s t o
t h e
t h e
t h e
as
original
a p p l i e d statistics, as
for,
as
say, t h e
m e a n
as a
t h e s a m e
" t r u e " M a x -
a n a l o g i c a l
c h a i n
d i s t r i b u t i o n i n d i -
i n d i v i d u a l
m o l e -
t e m p e r a t u r e
t a k e n
M a x w e l l , t i g h t l y
h e
w e l l
u n p r e d i c t a b l e s o
t h e
C l e r k
n o r m a l
u n i f o r m
a p p l i e d
t e c h n i q u e
u n d e r s t a n d t h e
a n d
r e p e a t s
d i s t r i b u t i o n
v a l u e
masse,
h o w
o f
social
a r o u n d
l i n k
Q u e t e l e t ,
r e v e a l i n g
t e c h n i q u e
t r u e
(see
en
t h a t
Q u e t e l e t
n o r m a l
gas. J u s t
t a k e n
m a r k s
t o
n o r m a l
p s y c h o l o g y
i n t e r p r e t a t i o n
" e r r o r s "
ideal
t h e
statistics. A
m u s t
v e r s i o n
t o
t e c h n i q u e s
o f
p a t t e r n
t h e
m e a n ,
p r o d u c e d
cases
a
a n d
t h e
a n o t h e r
statistical
explicit,
m a t h e m a t i c a l
f o r m ;
o f a n a t i o n
in
o f
A d o l p h e
statisticians
n a t u r e ' s
o b s e r v a t i o n
p h y s i c s
a s t r o n o m y
t h e
regularities
I n
i n
t h e
a d d e d
m o l e c u l e s
5.6).
c e n t u r y
is
p r o b a b i l i s t i c
retains
u n d e r s t o o d
c o n d i t i o n
social
w h i c h
w a n d e r i n g s
t o
w h e n
e r r o r s
social o f
T h e
e x a m p l e
a n o t h e r
a r o u n d
social
p r a c t i c e
p a r -
a p p l i -
relative
F i s h e r i a n
p a r t i c u l a r
p r o b a b i l i t y
e x a m p l e ,
B o l t z m a n n t h e
o f
as w e l l
m o r a l
a p p l i e d
(see
F o r
s c a t t e r i n g
L u d w i g
velocities
v i d u a l s
d o m a i n
a s t r o n o m e r s
say, t h e
t h e y
h i s t o r y
o b s e r v a t i o n a l
I f
w h i c h
i n s t r u c t i v e
o b s e r v a t i o n s
a
d i s t r i b u t i o n v a l u e
o n e
s u b s t a n c e
t e c h n i q u e .
p o s i t i o n
t h e
a p p l i c a t i o n .
d e s c r i b i n g
t o o k t h e
o f
a l o n g
s o c i o l o g y
a n d
t o
in
c e n t u r i e s
c o n t e x t
t h e
this
b e c a m e
t w e n t i e t h
t h e
t h e
o f
o f
6.5).
t o
i n
f r o m
a c o m b i n a t i o n
result
d o m i n a t e d
t h e
in
d e g r e e
a s t r o n o m y
d r a m a t i c
t i m e s
t h e
in
b u t
i n t e r p r e t -
n i n e t e e n t h
h a d
least
n u m e r -
statistics
still d e b a t e
a n o t h e r .
b e y o n d s e v e r a l
b e n t
t o
f r o m
a
at
discipline
d i s t r i b u t i o n is
m e a n t
t o
t h e
a
o f t e n
a n a l o g y .
i n t e r p r e t a t i o n
a n d
d i s c u s s i o n s ,
a n a l y z e
6.4,
a n d
e i g h t e e n t h
via
s h e d d i n g
a n d
s o m e
a n d
m a n n e r
as
in
years.
lines
this
t h e o r y
coexist,
t o d a y
t e c h n i q u e s
Finally,
i n t e r p r e t a t i o n s ,
u s i n g
(see
use.
m e a n i n g
a p h i l o s o p h i c a l
t h e o r e m
in
f o r m a l ,
p r o b a b i l i t y
p e a c e f u l l y
p e r s o n a l i s t
m e t h o d s
t h e
w h a t
p s y c h o l o g i s t s
B a y e s '
P e a r s o n i a n
in
t o
First,
a p p l i e d
p r o b a b i l i t y
r e s p e c t
w e l l
disciplinary
t h e i r
p h i l o s o p h i c a l
m e a n i n g s
P r o b a b i l i s t s
r e a s o n
o f
b e
a n d
i n t e r v e n i n g
p h a s e s .
t r u l y
g u i d e d
W h e r e a s
v i e w
t o
is alive t h e
a c r o s s
b e c a m e
w i t h
chance
i n
t h r e e
c a m e
t h e y
as m o r e
f r e q u e n t i s t
F o r
in
f o r m a l i z a t i o n ,
a p p l i c a t i o n s .
o r
g r e w
originally
a n d
o n e
r e p u t a t i o n
t e c h n i q u e s
subjects,
of
a p r o b a b i l i s t
b o r r o w e d
e x p a n s i o n
ticular
b y
its
c h a n c e
t h e s e
d i f f e r e n t
implications
a n d
( a n d
c o n t e n t
B o l t z m a n n , s u g g e s t i v e l y )
c o u l d
b e .
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The
T h e r e across
are
n u m e r o u s
disciplinary
still s h o w
a n d
a c t i o n
-
o f
test
e.g.
leads
(see
reject
a h y p o t h e s i s
o f
h a v e
t h a t
o r
m i g h t
m e t h o d ,
p s y c h o l o g i c a l I n
s u c h
n i q u e s
m a y
m a y o f
c o m e
l i g h t
w i t h
a w a y
b e
t h e
o n l y
o n c e
d i s t r i b u t i o n
in
B u t
u s e r
n o r m a l
b e
b e
t o l d
a b o u t
t h e
(see
4.4,
t i e d
t o
T h e l a t i o n
field o f
s c r i p t i v e f e r v o r
7.2).
t h e i r
a
t o
o f
a r e
a
t h e
p a r t
o r
d e c i s i o n
e r r o r s .
w i t h
n o t
c u r r i c -
e x p e r i m e n t s
h y p o t h e s e s
k e e p i n g
o f
a c c e p t
d e m a n d
o f
a
c o u r s e
n e w
scientific
c o s t
B a y e s i a n
in
l i g h t
ideals
o f
t h e
o f
o f
t h e
e s t a b l i s h e d
t h e
practically
t e c h n i q u e s
b o t h
t h e w a s
o f
f o r
h i m
o f
a
a r e
m u l t i p u r p o s e
t o o l s .
h a s
facts;
n a m e l y ,
o f
a p p l i c a t i o n s
h a s
h o l d
in
o r d e r
is
for
n o r m a l l y t o d a y ' s
similar
t h a t s t o r y
analysis. h e r e d i t y ,
g e n e r a l
a
G a l t o n ' s
c o m m i t
f a c t o r
s o
b e c o m e
in
A
late
a c q u i r e d
F r a n c i s
a n d
n e w
F o r a n d
i n t e l l i g e n c e
a r e
n o
l o n g e r
a p p l i c a t i o n . o w e s
t h e
t h e
i n t e r p r e t a t i o n s
a n d
t h a t
discipline.
e v e r y t h i n g
w i d e s p r e a d ,
statistics
o f
T r o j a n
d e b u t
b i o l o g i c a l
t h e o r y
m a t h e m a t i c a l
statisticians
its
t e c h n i q u e .
d e s c r i b e d
a
s u c h
o f
specific t h e
t e c h -
c o n s e q u e n c e s
o f
e n t h u s i a s m
c o r r e l a t i o n
m e a n
t e c h n i q u e s
c o n t e x t s
n o r
fit
i n d e e d
m u s t
t h a t
o f
o f
h a s
s o m e t h i n g
h i s t o r y
g a t e s
S i n c e
it
t h e
t h e
n o t
d i s t r i b u t i o n
t h a t
v e r y
t o
t h e i r
v a r i e t y
c o n d i t i o n s
t h e
m a y
t h e
o r i g i n s .
c o n d i t i o n s
early
o r
a n d
c o n v i c t i o n
t h a n
i n t e r p r e t a t i o n
a n d
w i t h i n
n o r m a l
c e r t a i n
t o
a n d
m a y
a n d
m o r e
c o m p a r e d
a s s u m p t i o n s
disciplines
s u r e ,
t h e s e
t h a t
p a r t i c u l a r
m a n y
b e
c o n t e n t
n u m b e r
t h e o r y ,
analysis
o r i g i n a l o f
t h e i r
t o w a r d s
N o w
s u c h
f o r
s o m e
a d e c i s i o n
m i g r a t i o n ,
a l r e a d y
s h e e r
d i s t r i b u t i o n o f
f a c t o r
a r e
t h e
p a r c e l
S p e a r m a n ' s
p s y c h o l o g y e d u c a t i o n ,
a d o p t
w h i c h
t h e
c o u l d
a n d
a p p l i c a b l e ,
n e i t h e r
r e g r e s s i o n
t h e y
b e
a n d
G a l t o n ,
t h e s e
s o
p a r t
m i g h t
explicit,
o f
T o
t o
d i s t r i b u t e d .
w e r e
o f
a b o u t
B u t
e r r o r
l i n g e r s i n
t h e
t o
m a k e s
r e a s o n s
t e c h n i q u e s
t h e
m a r k s
t e c h n i q u e .
o f
o r
later,
agricultural
in
a n d
c o n c e r n i n g
usually
( a n d
t h r o u g h
a g r i c u l t u r e
a l t h o u g h
i n t e r d i s c i p l i n a r y
T h e
h o w e v e r
t h e
e n t h u s i a s m
historical
m a d e
a p p l i c a t i o n s
" m e r e "
in
in
F i s h e r i a n
r a n
c o n s e q u e n c e s
m o r e
chaining,
A p p l i c a t i o n s
p r o b a b i l i t i e s
a s s u m p t i o n s
e i g h t e e n t h - c e n t u r y m a n y
o f
a p p l i c a t i o n .
E v e n t u a l l y w o r e
cases
n o t
c o n t e x t t o
r o u t e
fertilizer
e s t i m a t i o n
revise
f o r
t h e
d e c i s i o n
c e r t a i n
c o n s i d e r e d
b u t
i m p o r t e d .
p a c k e d
o r
o r i g i n s :
practical
analogical
p s y c h o l o g y
e x p e r i m e n t ,
t h e
b e
t o
273
p r a c t i c e .
early
a r e
h o r s e ,
p e r m i t
s u c h
social scientist
e a c h
successively
e v i d e n c e
a
t h e
i m m e d i a t e
t h a t
scientific
after
t o o k
y e s - n o
u s e
Similarly,
n o
s o r t
m e t h o d s n e w
6.3).
o f
a d m i n i s t r a t i o n .
a
t o
chance
e x a m p l e ,
practical
t o
w h e t h e r
u l u m
usually
F o r
statistics
t h e s e
of
e x a m p l e s
e d u c a t i o n a l
t r a c e s
significance
o t h e r
b o u n d a r i e s .
N e y m a n - P e a r s o n i a n ) t r e a t m e n t s
implications
It
n i n e t e e n t h
m a t h e m a t i c a l
its
e x i s t e n c e
j o i n e d
c e n t u r y
t o
t o g e t h e r p u l l e d
p r o b a b i l i t y
t h e w h a t
a s u n d e r
t h e o r y
a n d
a c c u m u t h e in
d e t h e i r
e m p i r i c a l
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274
The
statistics.
T e c h n i q u e s
e n o r m o u s l y statistics a t i o n s
o f
a p p l y
t h e
s a m p l i n g
p r o d u c t s
t u r n e d
r e p r o d u c t i o n . as t h e s e t e s t i n g
o u t
T h e
n e w
t h e r a p y
traffic.
n o t h i n g .
A l t h o u g h
h u r t ,
h e r e
in
k n i g h t s
e r r a n t
8 . 2
T h e
W
o f
H
i n t e r p r e t a t i o n s
c a t i o n s
a r e
a
d i s t i n c t i o n t h e
b e t w e e n
r e c e i v e d
c o n c e p t ,
w i t h
i d e n t i f i e d
t h e s e
spectively, h a v e
a n d
b e e n
years, basis
c o n s e n s u s
I a n
H a c k i n g s ( H a c k i n g ,
p r o b a b i l i t y
in
c o n s i d e r a b l y
h o p e b e g i n T h e J a k o b s e n s e s ( o r
o t h e r s
1 9 7 5 ) .
will
d o
T h e s e
t h a t
o f
o f
its
little
this
m o r e
c o m p l e t e
a n d
in
as
it
are w e r e ,
m y r i a d
c e l e b r a t e d it
is a
a p p l i -
h a s
b e e n
J a n u s - f a c e d
C a r n a p
( 1 9 4 5 )
relative
f r e q u e n c i e s , A l t h o u g h c a m p s
T h e
in
r e -
t h e r e r e c e n t
d u a l i s m
is
t h e
e x p l o r a t i o n
o f
t h e
origins
o f
close
o f
t h e
h i s t o r y
o f
s i t u a t i o n
is
s t u d y
r e v e a l s
p o i n t
b r i n g
in-
r e a s o n
1 8 3 7 ,
s u b j e c t i v e
s i m p l e
t h a n
n o t
R u d o l f
o p i n i o n .
a p p l i c a t i o n s
t h a n
d o
P o i s s o n ' s
i r r e d u c i b l e .
a
e l e v a t o r s
t h a t
t h e s e
t o
H o w e v e r ,
a n d
M E A N ?
a n d
s t i m u l a t i n g
a n d
are,
b e l i e f
C a r n a p ' s
a b o u t
e v e r y t h i n g
p r o b a b i l i t y
a n d
w o r r i e d
3.7).
sides.
f r e q u e n t i s t
i n
v e r y
e x p e r t s
" c h a n c e "
b e
o r g a n i s m s
r e s e a r c h e r s
t h a t
b e h i n d
t h a t
o f
m e d i c a l
a b o u t
S i m e o n - D e n i s a n d
q u a l i t y
u b i q u i t o u s
r e g i m e n s
(see
lie
t h e
b u i l d i n g
f o r
t e c h n i q u e s
a n d
t e c h n i q u e s
a n d
c h a n c e
d u a l i s m
r e c e n t
b y
e x p e r t s
s u b j e c t i v e
t h e
c o m p l e x c a n
flexible
a n d
c o n s i d e r -
s a m e
o f
h a v e
t h a t
t h e
b i n a r y
o p p o s i t i o n
w o u l d
t o
c o m p l e x i t y ,
in
t h e
e n u m e r a t i o n
w e
o r d e r
t h a t t o
t h e
h e r e . first
g e n e r a t i o n
B e r n o u l l i , t h a t
d e g r e e s
m i n d s ,
w e
-
specific
g e n e s
as
u p o n
p r o b a b i l i t y
P R O B A B I L I T Y
f a v o r e d
c o n t e x t
m o r e
H e r e ,
t h a t
t h e
o f
d e g r e e s
b o t h
is
m e d i c a l
p r o b a b i l i s t s
t h e
h a s
p r o b a b i l i t y
s u g g e s t .
w i t h
in
rests
c r o i r e "
a n d
b e l i e v e d
m i l i t a n t s
t h e o f
sides
w i t h
S i n c e
d e
a m o n g
o b j e c t i v e
t h e
office
s e n s e
m a t t e r
lot.
" r a i s o n
w i s d o m
a
p r o b a b i l i t y
m u l t i f a r i o u s
a n d
a n
in
f o r
e l e c t o r a t e ,
o f
D O E S
o f
a n
a r c h i t e c t s a r e
i n f e r e n c e
T h e
c o n s u l t e d
e m p i r e
T
line,
a p p l i c a t i o n .
t h e
A
s e c o n d a r y . o f
a n d
w h e r e
b e
e x p e r t i s e
i n
p o i n t
t o
s u b j e c t
g e n e r a l
t h e
statistician
e x p e r i e n c e
t o
c o n c r e t e
b r e a t h t a k i n g l y t h e
l o n g
s a m p l i n g ,
o p i n i o n s
is as l i k e l y
as b y
c l a i m
t o
a s s e m b l y
Statisticians
t h e i r
a n y
a n
a n d
chance
a p p l i c a t i o n s
s e e m
political
b y
o f
c e n t u r y ,
m a t h e m a t i c a l
e l e v a t o r
c a n ' t
d o m a i n
c o n t e n t
t h e
t e c h n i q u e s , a
t h e
a n d
of
m e a s u r e m e n t ,
t w e n t i e t h
c o n t e x t
t o
for
e x p a n d e d
i n
implications
f o r
p r o b a t i v e
a l r e a d y
p e r t a i n e d
t o
o f p r o b a t i v e t h e y
w e i g h t
o f
w e r e o f
p r o b a b i l i s t i c
i n t e r p r e t e d d i f f e r e n t w e i g h t )
f r o m
p r o b a b i l i t y
k i n d s w e r e
i n t e r s u b j e c t i v e ,
this w i t n e s s '
w o r k s ,
o f
subjects.
states o f if
t e s t i m o n y
i n
n o t o r
m i n d
a
H u y g e n s v a r i e t y
D e g r e e s -
o r
o f o f
(see o f
d i s t i n c t c e r t a i n t y
r a t h e r ,
o b j e c t i v e t h a t p i e c e
t h r o u g h
states
1.3).
o f
T h e
c i r c u m s t a n t i a l
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The
e v i d e n c e f o r e
w a s
has
a s s u m e d
closer
K e y n e s '
logical b e
physical n o t
v a r i o u s
m o r t a l
r e s e m b l e
rather
q u i t e
as
close
l o n g t h e y
dictions
o f
strongly s u c h
in
T h e r e h a v e
o f
n o
a r g u m e n t
years J u s t
w a s
his
solar
a n a l o g y
balls,
o f
w i t h
17
a
p o i n t e d a
" F "
D e
insisted
c o u l d
a n
n o t
e q u a l b e
o r
b y
t h e
at
t h e
t i m e ,
18
Bernoulli's that
b e c a u s e
n u m b e r
ascribed
t o
o f
t h e
w e r e
inp r e -
D u r i n g
a n d
o f
this
is
still
probability,
s o
u n r e m a r k e d
" f r e q u e n t i s t " 1 7 1 0 in
w a s
o f
18
o f
a n
" M . "
u r n
w o m e n
c h a n c e " .
T h a t
o f
t h e
o b s e r v e d : 17
o v e r b y
p r o m a n y
c h a n c e . r e c o n -
probability,
d e s p i t e
"F."
filled
N i c h o l a s
p e r f e c t l y 3 5
m a d e
Y e t
s e r v e d
A s
w i t h
( D ' A l e m b e r t
discrepancy
enlist
c o m f o r t a b l y
a n d
a r g u m e n t . )
t o
c o n c e r n i n g
g o v e r n e d
b e
t o
" p r o -
service
t h e
as
o r
a t t e m p t
t h e
that
ratio
c a n n o t
birth
a n d
also
century,
field,
statistics w e r e
m e n
" m e r e
t h e
p r o c e s s
p l a n e t a r y
d e c a y
w e r e
statistics.
t h e
m a r k e d
p r o -
o b j e c t s
similar a r g u m e n t
a r g u e d
in
say,
t o
m a r r i a g e
will
instances
" M "
-
h u m a n
collectives,
n u c l e u s
m a r k e d
m e c h a n i s m a n d
like
i n t e r p r e t a t i o n s
d i e
b u t
P o p p e r ' s
applications
statistics
" c h a n c e "
p r o p e n s i t y
o r
o f
K a r l
t h e
o f
susceptibility
i n d i v i d u a l
A r b u t h n o t ' s
A r b u t h n o t
if
t o
f r o m
label
births
if
Probabilities
o f p r o b a b i l i t y
Bernoulli's
h u m a n
m e a n t
o u t
D a n i e l
i n s u r i n g
s y s t e m .
t w o - s i d e d
criticisms o f M o i v r e )
D a n i e l
n o t
drift.
e m p i r i c a l
i m p r o b a b l e
c h a n c e
m a r k e d
a n d
f e m a l e
f r e q u e n c y
B e r n o u l l i
e x a m p l e , J o h n
m a y
classic
as
n i n e t e e n t h
a n d
g e n e t i c
t w e n t i e t h - c e n t u r y f o r
t o
p h i l o s o p h y
t h e
c r i m e
mortality
t h e
o t h e r s
i n t e r p r e t a t i o n s
o f
m a l e
all
r a n d o m
p r o b a b i l i t y
t h e
d r o v e
t o
original
o f
are
a t o m i c
t h e
in
p s y c h o -
p r e d i c a t e d
w r i t e s
objects.
n o t i o n .
basis
t h e
w h i c h
a v e r a g e s
that a n
collectives;
f r o m
t o w a r d
t o
physical
statistics
p e r s o n a l
facility,
r e s p e c t
o f
current o f
A r b u t h n o t
w i t h
patible
t h e o r y
e x t r e m e l y
w h a t
ciled
in
d e s i g n , o r
o f
w i t h
a p p l y
the
Savage's
d e v i c e s
a p p l i e d
d e s c r i p t i v e
f r o m
o r i g i n s
o f
s o m e t i m e s
facility
o n
M a y n a r d
subjects,
as f r e q u e n c i e s
l o n g e v i t y
c o n v e n i e n t
m a t h e m a t i c a l
p o r t i o n
m e m b e r s
C o n s i d e r ,
single
original
i n t e r p r e t a t i o n
t h e
t o
b u t
t h e r e -
c o n t i n u o u s .
g a m b l i n g
t h e p r o b a b i l i t y
t h e
are still o t h e r
pensity."
t h e
t o
r e p r e s e n t e d
as
o f
individual
f r e q u e n t i s t
ideal)
d e g r e e s
B e r n o u l l i
facilities,
u n d e r s t o o d
are
h e y d a y
t o
a n d
J o h n
d i s t i n g u i s h e d
p r o p e n s i t i e s
t h a n
i n t e r p r e t a t i o n
early a n d
t h e
physical
t o
L e o n a r d
b e
o f
judges,
c e n t u r y
n u m e r i c a l l y
s y m m e t r i c
o r
all c o m p e t e n t
t o
also
275
d i s e a s e s . Q u e t e l e t's " p e n c h a n t s "
moyeri\
c o m e s
t h a n
s p o k e
J a k o b
chance
t w e n t i e t h
e v e n
also
facilities
t h e s e
"I'homme
sofar
e x a m p l e ;
s u c h
t h e
f o r
(as o p p o s e d
o r
probabilists
sole
h a d
p e n s i t y
real
of
s a m e
s h o u l d
objects: physically
t h e
b o d i e s
o f
c o n s i s t e n t ,
early
in
latter
probabilities
T h e
t h e
probabilities
T h e s e
internally
b e
affinities
logical
probabilities.
t o
implications
c o m -
identical a n a l o g o u s
A r b u t h n o t
a p u r p o s e ,
o f
m a r r i a g e a b l e
is,
a n
e v e n t
( a n d
n a m e l y age,
c a n n o t
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it b e
276
The
i d e n t i f i e d
as
o r
(see
d e s i g n
s e n s e
o f
a
c h a n c e 1.7).
c h a n c e : like
d e s i g n .
s e n s e
o n
T h i s
" c h a n c e "
t h e
w e r e
i n
m e n t w h i c h
t o
in
d o
T h i s
s h o r t
f r o m
t o
cast
w i t h
w a s
i n
a l o n e .
o n
a n c e
t h e
a n d
in
a n d
h i s t o r y ,
(1)
s e e m s
a r e
later
n a t u r a l
a b s e n c e
t h e i r
t h e i r
o f
e m p h a s i s
u s e f u l n e s s
t h a t
a n
t h e
for
a
t o
o f
1.2),
a n d
a r e
e v e n t
t h e y
a r e
first
familiar o f
will
t o
p e r s o n a l o n l y
s u b j e c t i v e
will o r
p a r t
t h e
s u r f a c e
n e i t h e r
i n d i s s o l u b l e
o f
a r e
s y s t e m
T h e y
j u d g -
e x p e c t a t i o n s ,
b a c k b o n e
p r o b a b i l i t i e s
a n
p r o b a b i l i t i e s
c o m b i n e d
s o r t s
S a v a g e ' s
b e t t i n g .
w i t h
t h e
f o l l o w
a n d
list,
n o t
o f
a
o r
t w i s t s
o n
i n
in t h a t
n o t
c o m e
i n t e r s u b j e c t i v e ,
o f
t h e
d e t e r m i n i s m ,
c a n
d e f y
b o t h
e x p e c t a t i o n
a n y
w e
o f
in
real a
t h e
m u s t
a n d
t h e o r y
a n d
s i m p l e
as
at
a
variability
s u r v e y
t h e
t w o
statistics
o r
o f
o f
r e l a t i o n s h i p s
e n o u g h
o n l y
a n o t h e r
p r o b a b i l i t y
m e a s u r e
f o r m
is
g e n e r a l i z a t i o n . o n e
f u n d a m e n t a l
first
m e a s u r e
it is still
i n t e r p r e t a t i o n
u n d e r s t o o d
t o
t w o ,
m a s t e r s
w h i c h
s u g g e s t
t u r n s
B u t
m e a n
u n c o m p r o m i s i n g
e v e n
t h o u g h t
t a x o n o m y .
also
m e a s u r e
a n d
b e e n
p r o b a b i l i t y
s e r v e d
m o s t
as
a
h a s
p r o b a b i l i t y
P r o b a b i l i t y
t h e
w o r l d ,
t h e
p r o b a b i l i t y
h a v e
a s c e n d a n t .
o f
i g n o r -
d e t e r m i n i s m ; c o u l d
a d m i t
stochasticity. b e t w e e n s e v e r a l
I n
p r o b -
p o s s i b l e
d e t e r m i n i s m .
u s e f u l
t o
m e t a p h y s i c a l
entific
w i t h
p u r p o s e
A r i s t o t e l i a n
F o r
w h i c h
t h e
(see
a n d
c e r t a i n t y ,
t h a t
8 . 3
It
like
d e p e n d i n g
t o
o f
w e r e
p r a c t i c a l
i n d e t e r m i n i s m
r a n d o m n e s s
b r a n d s
a g e n t s ,
c o n v i c t i o n o f
in
T h e s e
p r o b a b i l i t y
it is a
statistics
t h e
t h e o r y
o l d
s i m p l y
b y
called
v a l u e .
r e l a t i o n s h i p s
u n d e r s t o o d
ability
m e a n t
D a r w i n i a n s ,
s i t u a t i o n
o f
a c t i o n ,
v i e w
p r o b a b i l i t y
t o
t h e
n a m e ,
T h e y
a n d
t h e
h a r m o n i z e d
o r d e r
still
t h e
cause.
o c c a s i o n e d
F i n e t t i ' s
t h i n g s
historical
t h e i r
t h e n
t h e i r
d e g r e e s
list o f
T h e
d e
i n d i v i d u a l ' s
d e t e r m i n i s m
p o i n t
t o
e x h a u s t i v e ,
P r o b a b i l i t y
n o t
t o
o f
arise.
d o u b t
t h i n g s .
t h e
o u t c o m e
c o n c r e t e
s t a n d
t h e y
a n d
f r o m
u n l i k e
t h e y
w h i c h
far
a n
since
m a t h e m a t i c a l
call f o r
b u t
b y
c o n s i d e r a t i o n s
o r
p r o b a b i l i t i e s "
p r e f e r e n c e s
T r u e
e x p r e s s
o r d e r ,
c h a n c e
t h o s e
" p r a c t i c a l
p r o b a b i l i s t s
pass,
n o r
t h e
o f
p r o b a b i l i t i e s .
t h e y
i.e.
invisible,
c o n c e r n
t h a t
Paley,
o f
p e r t a i n e d
p u r p o s e ,
p r e s e r v e d
p r o b a b i l i t i e s
f o r m u l a t i o n s
cases
also
effect
t o d a y ' s
o f
-
chance
i n d e p e n d e n t l y p r o b a b i l i t y
W i l l i a m w a s
of
(4.3).
w e r e
o f
H e r e ,
v a r i a t i o n s
o r g a n i s m
T h e r e
e v e n t
a b s e n c e
t h e o l o g i a n s
implications
u s
t o
d i s t i n g u i s h
d e t e r m i n i s m ,
d e t e r m i n i s m ,
(4)
D E T E R M I N I S M
(2)
at
least
five
v e r s i o n s
e p i s t e m o l o g i c a l
m e t h o d o l o g i c a l
o f
d e t e r m i n i s m :
d e t e r m i n i s m ,
d e t e r m i n i s m ,
a n d
(5)
(3)
sci-
e f f e c t i v e
d e t e r m i n i s m .
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The
(1) t h e
Metaphysical
for
f u t u r e .
a
f u t u r e
h a s
t o
C l a u d e
B e r n o u l l i
i n
W r i g h t
d i d
n a t u r e ,
like
(2)
m a t i o n . ciple,
( o r
c a n t h e
n o
p a s t )
possibility
e q u a l
since
it
s t r e n g t h ,
e v e r
p r a c t i c e .
I n
this
sense,
h a r d l y
e p i s t e m o l o g i c a l t h a t
t h e
(3)
also
T h e
s o m e w h a t
r e t r o d i c t i o n ) :
p h e n o m e n a ,
Scientific f e a t u r e s o f
t h e
t h e s e
f e a t u r e s
t h e o r i e s
o f
t h e i r
b e
t o
b y
trivially
l a w s
a n d
as
w h i c h called t h a t (ii)
o b t a i n e d
for
o r
t h e
b e
classes is
p r i n t o t h a t
is
o n l y
t h e r e
is
p r i n c i p l e "
m o r e
s u c h
o p e n in
t h a n
a n
d e t e r m i n i s m ,
w i t h o u t
it c o m e s
a n d
l e a v e s
( o r
p h e n o m e n a
n o
m a k i n g
as n o
as t h a t
s u r p r i s e
L a p l a c e
a n d
o p p o n e n t s
o f
B i c h a t . b e t w e e n
m e t a p h y s i c a l
u n s a t i s f a c t o r y . m e a n s
e m b e d d e d
in
if t h e y
u n i q u e l y l a w s
f u t u r e
T h i s
w o r l d
o f
scientific
specify
(i)
a
a n d
w h i c h
p a s t )
is ( o r
o b s e r -
t h e o r i e s .
set
all o b s e r v a b l e f r o m
a n d
s i t u a t i o n
o f p r e d i c t i o n
usually
( o r
it
a r g u e ,
o f
t h e
f u t u r e
i n
s e e m
t h a t
clause
g o v e r n i n g
n e c e s s a r y
i n f o r -
p r e d i c t a b i l i t y
r u l e s
d e t e r m i n e
specify
m e t a p h y s i c a l
m e t a p h y s i c a l
p o t e n t i a l
d e t e r m i n i s t i c
t h e
t h a n
e s c a p e
d e t e r m i n s m ,
t o
e x t e n d e d
w o u l d
o f
in
4.2).
least
b e
w o u l d
d e t e r m i n i s m ,
d o e s
it
w e l l
s h o r t
false. H e n c e ,
c o u r s e ,
o n
a r e
" i n
d i s t i n c t i o n
is, o f
l a w s
o f
(see
at
c a n
d e t e r m i n i s m
q u a l i f i c a t i o n
f o c u s i n g
g e n e r a l
m a y
S e w a l l
p o t e n t i a l
that,
it,
v a r i a t i o n
ability
o r
c l a i m s
it
J a k o b
o p p o s e d
a b o u t
o u r
sight,
c e r t a i n
several)
latter,
o f
p h i l o s o p h e r s
p r e d i c t
effective
o b j e c t s
objects, c a n
t h e
t h e a n
a r e
B u t
like
e v o l u t i o n i s t
p o s i t i o n first
g i v e n
p h y s i o l o g i s t
h a v e
B i c h a t
c l a i m
" i n p r i n c i p l e "
a m o n g
d e t e r m i n i s m
m i t i g a t e d
s o m e
e p i s t e m o l o g i c a l
o f
A t
latter.
T h e
t h e
a c t u a l
s t r o n g e r
m e t a p h y s i c a l
reject
lack
e p i s t e m o l o g i c a l
v a b l e
o f
t h e this
e p i s t e m o l o g i c a l
d r o p
o u r
" d e t e r m i n a t i o n "
a b l e
o n e
also s u p p o r t
f o r m e r
o f
d e t e r m i n i s m
p r o t a g o n i s t s
B e r n a r d ,
b e
( p o s s i b l y
c a n
as
i n p r i n c i p l e .
will
w e
m a k e s
p r o v i d e d ,
w e
A g a i n ,
t h e
as
a
i.e.
d e t e r m i n i s m
t h e
O t h e r s
o t h e r
t i m e ,
t h a t
p r o b a b i l i s t s
is i n d e p e n d e n t o f
I n
t o
M e t a p h y s i c a l
1.4).
n o w
d e t e r m i n e d
effect
like
g i v e n
affairs
r e s p e c t
t h e
p h y s i o l o g i s t
basis
o f
a b o u t .
c o n s i d e r a t i o n s
m a k e s
i m p l i e s
w h e t h e r
since
t h e
r e t r o d i c t i o n .
e x p l i c a t i o n
r e t r o d i c t a b i l i t y )
e x p l i c a t i o n
t h e
d e t e r m i n i s m
m e a n i n g f u l
b y
that,
u n i q u e l y
w i t h
t o
p h e n o m e n a ,
f u t u r e .
o f
(see
state
a n d
past.
c l a i m
c o m e
p r o m i n e n t
L a p l a c e
determinism t h e
thesis
t h e
o r
t o
single
less specific
o n
e v e n t
s y m m e t r i c a l
w i t h
d e t e r m i n i s m
p r e d i c t
d e t e r m i n i s m ,
it
p r o p o u n d e d
t h e
e p i s t e m o l o g i c a l
f o r
b y
a n t i - p r o b a b i l i s t s
p r o b a b i l i s t i c
Epistemological
w e
i n c l u d e
o f
d e
M e t a p h y s i c a l
a
d e t e r m i n e d
S i m o n
277
b o u n d
a d d i t i o n a l
s h a r e
4.5), o r
t h o s e
f u t u r e
a n
m a d e
4.2)
o f
a n y
o n l y
scientists;
P i e r r e
(see
is
u n i q u e l y
(see
v i e w
w o r l d ,
is
chance
c h a r a c t e r i z e d
necessarily
c l a i m
a m o n g
o r
w h e t h e r
t h e
o n e
B e r n a r d
t h e
t h e r e
c o m p r i s e
o n l y
c o m m o n
o f
p a s t
of
is
w a s
g i v e n
S o m e t i m e s
u n d e r s t o o d
t h e
h i s t o r y
c o n s i d e r a t i o n
w o r d s :
is
determinism
a n t e c e d e n t
u n d e r
implications
o f
basic
p r o p e r t i e s t h e s e
t i m e s ,
o n c e
basic t h e y
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278
The
are
k n o w n
b e
ascertained
Scientific t h e
at a g i v e n t o
t i m e .
a n y
determinism,
claim
t h e o r i e s initial
can
t h e
b e
t o
desirable
o f
its
as
p o s i t i o n
credible
o r
n o t
N e w t o n
himself,
b e l i e v e d
their
faithful
their
b e
w i t h o u t
P l a n c k
c o n t r a s t e d
w i t h
t h o s e
the
scientist
d e l a y
E v e n
scientific
t h o u g h ,
a c c o u n t
b y
o f
l o o k
o f
n o t
c o m p l e t e l y
in
m o r e t o u s it
an
alike
c i r c u m s t a n c e
v e r s i o n
o f
e x i s t e n c e
o f
primarily
always
b e t t e r
b e
t o
scientific
(or
w h e r e
p r a g m a t i c )
d e t e r m i n i s m
is o n l y
s u p p o r t e d
i n d e t e r m i n i s t i c logical t o
e v o l u t i o n ,
causes,
m a c r o s c r o p i c d e t e r m i n i s m
t h e
a n d
S e w a l l
d e t e r m i n i s m , drift
t o
b e
c i r c u m s t a n c e s . rationally
is
s o
o f
c h a n g e s
b y
o f
o r
t o
T h e y
t o
t o
t h e
adjust
t h e o r i e s c o m e ,
in-
p h i l o s o p h e r -
c o u l d
reads:
b e
true
w a y s ,
o f
in
c o u r s e ,
that
it
is a n
t o
m i g h t
o p t i o n ,
s u p p o r t e d .
d e v e l o p m e n t
4.5),
since
all
d e t e r m i n e d O t h e r s
c o m p e l l i n g
s e e m that
b e
n o
t o
h a v e
t h e y
e.g.
i n t o
m a y
c o n t i n g e n t
t o
yet T h e o n e
in
b e
o f
that
w i t h
it
is
i n c o m M e t h o d -
(theoretical) t r o u b l e -
is
o n l y p o s i -
c o n f i r m e d
drift
b u t
f o u n d
c l u n g
as
acceptance
w h e n
b y
that
u b i q u i -
t h e
t h e
p r o b l e m
a
o n
r a n d o m
m u t a t i o n s
b y
as
empirically
o f
is
v i e w e d
d e t e r m i n i s m
o f
s a w
a n
attainable.
It g e t s
p r o t a g o n i s t
b u t
difference.
b u t
e v e n
e n -
p o s i t i o n
for
satisfied
b e
denial o f scientific
is g r e a t l y
o u t
relies
rest
scien-
situations
c o n s i d e r a t i o n s ,
t h a n
o f
false,
t w o
t h e
c i r c u m s t a n c e s ;
k n o w l e d g e
o r
w a t c h for
available
b a c k i n g
T h i s
W h e n e v e r
m a y ,
(see
actually
its acceptability
practical
t h e
t h e
c o g n i t i v e
r e s p o n s i b l e
p o o r l y
W r i g h t
5.8).
scientific
determinism.
that
q u e s t i o n s
T h u s ,
(see
o f
5.6)
t h o u g h
c o n f o r m
o u t l o o k m o r e
m a k e
physicists
w i l l i n g
t h e
d e t e r m i n i s m
t h e
w h o
(see
d i f f e r e n t
that
actual
theories.
m e t h o d o l o g i c a l
h a v e
b y
-
s o m e n o t
clear
t o
N e w t o n ,
d i d
fact,
o f
sufficient
w e r e
m o d e s t ,
d e t e r m i n i s m
if scientific i n d e t e r m i n i s m tively
in
f u r t h e r
a b s e n c e
E i n s t e i n
c o m p a s s
w o r l d ,
d i f f e r e n t i a t i n g
f u r t h e r
A l b e r t
n a r r o w
w h i c h
m o t i v a t e d
ask
k n o w l e d g e
ological
s u c h
w o r k
historical
(5.3).
d e t e r m i n i s m
theoretical
o w n
b y
d e t e r m i n i s t i c
o f
o f
c a n
c o m p l e t e n e s s .
o f
d e t e r m i n i s m ;
M a x w e l l
assertion
d e v e l o p
b e e n
t h e y
characterized
t h e
f o l l o w e r s
methodological
b e h a v i o r
p l u s
usually
M a n y
called
w i t h
m e t h o d o l o g i c a l
m a y
p l e t e
it
p o i n t
a n t i c i p a t i o n
the
b e
is
I n
a n d
c o m p l e x
o n l y
b y
c o g n i t i v e
u n d i s c o v e r e d belief
can
that
w i s h .
p r o g r a m
that
a n d
t e r m s
their
C l e r k
s u c h
in
c h a n g i n g
P e i r c e
o u r
v i e w
probabilists
t h e in
g i v e n
c o m b i n i n g
characterized m a x i m
e v e n
S a n d e r s
tific d e t e r m i n i s m h a n c e d
o r
t o
physicist J a m e s
C h a r l e s
(4)
beliefs
b e
w o r l d
h a v e
a l t h o u g h
m u s t
accuracy
scientific
M a x
m u c h
c l u d i n g
in
as
p h i l o s o p h i c a l
o f
w e
acceptable.
it,
s u c h
t h e as
t o
creed,
s h o u l d
o f
e x p a n s i o n
this
r e m a i n e d
features
is a p h i l o s o p h i c a l
d e s c r i p t i v e
f u r t h e r
chance
d e g r e e
c o m p l e t e
this
of
basic
d e s c r i p t i o n
m a d e
successes
obstacles
T h e
t h e n ,
that
implications
in
b i o -
s u b s c r i b i n g s u p p o s e d
t o
identifiable
m e t h o d o l o g i c a l
it d e s p i t e
a d v e r s e
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The theoretical that
it
d e v e l o p m e n t s ;
is
s o m e t i m e s
determinism Planck,
inspires
[1926]
1938, p p . (5)
T o
M a x
explicate
effective
several levels o f scientific versus
3, pp.
18).
that
o f
situation
at the second
level. F o r
well-defined
genetic
e n v i r o n m e n t ,
is,
the
change the
by
an
versa
1936,
pp.
( c o m p a r e 43ff.,
distinction
o f
the
that
to predict
certain
organisms
w e
have
or p r o d u c e
level
o f
occur
remain
restricted
by o u r
plant w i t h specific properties, w e w i t h
n o
c o m m i t m e n t
Effective the
to
determinism
p h e n o m e n a ;
or
the
o f
to a d o p t
claiming
cogni-
scientific
a deterministic
d e t e r m i n i s m
m a y b e local, referring t o a specified
global,
that,
in
spite
o f
in
general.
level or area
certain
in
the
w h e r e a s
p o s t - q u a n t u m
Nevertheless level
o f
strict
causal
mechanical
they n e e d
not,
macroevolution.
regardless
o f
the
for
c o m p l e t e
expansion
d e t e r m i n i s m
o f
the
each
m u t a t i o n
m a y
n o
this reason, a b a n d o n
o f
each
determinism
o f
chance
a n d
will
d e p e n d
d o
so.
at
the
r a n d o m ,
mutation.
n e e d
it h a s
b e e n
n o t
necessarily
taken
to, shake
against scientific d e t e r m i n i s m .
has only been affected
d e t e r m i n i s m
4.3),
the p r e c e d i n g distinctions a n d examples
It may,
primarily directed
(see
be
s i o n o f it, w h i l e l e a v i n g o t h e r s intact. I n g e n e r a l , t h e a d v a n c e o f has b e e n
D a r w i n
longer
m a y
o f
remain
d e t e r m i n i s m
m a c r o e v o l u t i o n
m i c r o d e t e r m i n a t i o n
e m p i r e
in general.
o f
evolutionists
Conversely
I n g e n e r a l , it is clear f r o m the
d e t e r m i n a t i o n
o n
the
indirectly. T h e c o m p l e t e
o f
that
subvert o n e
ver-
probability
Methodological
prospects
pattern
o f
violations
f o r all p r a c t i c a l i n t e n t s a n d p u r p o s e s . T h u s , C h a r l e s
believed
for
diverse
effective scientific
theories a n d techniques in various areas o f application, a n d hence again influenced
only
determinism, w h a t
counts
at
o n e
h o w e v e r , for
a n d
o f
against
theories.
structure
the
to
extent.
Also
removes.
it. W e
philosophical w o r l d
scientific
appear
t w o
T h e
fate
r e m a i n s o p e n , as l o n g as w e
w h a t
certain slack b e t w e e n t e r m s
or
A t
history
epistemological
any
m u s t
n o t
thinking
as defined
be
metaphysical specify to
exactly
observe
their articulations
discrepancies
o f probabilistic
o f
p r e p a r e d
views a n d
rate,
determinism,
b e
d o
a
stance,
scientific d e t e r m i n i s m , all a p p l i c a t i o n s o f scientific k n o w l e d g e will deterministic
the
p r a c t i c a l goals, say, o f b r e e d i n g
are free
truth
a
spon-
t a n e o u s l y a n d in a n u n p r e d i c t a b l e way. N e v e r t h e l e s s , as l o n g as o u r tive ambitions
a
situation
alterations
molecular
with
b e t w e e n
indeterministic
be able
help at
vice
a
s h o w s
methodological
conceivable
m a y
m u t a t i o n s
or
n e e d
level, b u t
the
attitude
as t h e level o f living
then,
first
His
w h e t h e r
[1929]
w e
example, w e
w h e r e a s
a n d
theorizing, such
at
example.
determinism,
1 6 5 - 6 ,
It
279
decide
determinism,
molecules.
deterministic
is a n
to
metaphysical
a n d
of chance
Planck
difficult
1958, vol.
1 2 - 1 4 ,
implications
b e t w e e n to
a
a in
t h e m
remarkable
above, w o u l d
s e e m
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280
The
t o
d e p e n d
ceived. t h e
o n
t h e
T h u s ,
w i t h i n
s e v e n t e e n t h
c o m p l e t e
t h e
for
t h e
p r o b a b i l i s t i c s t i m u l a t e d
t h e o f
t h e
real
t h e
w o r l d .
w h e r e a s
science
p r o b a b i l i s t i c
w o r l d
v i e w .
r e m a r k a b l e
f o r c e
t e m o l o g i c a l
d e t e r m i n i s m
o w e s
t o
sense,
p o s s e s s
as
b e
this
s t r o n g
e v e r y w i t h
a
r u l e
w i t h o u t
g i v e n
t h e
t h e
t o
n e a t
o t h e r . issue
T h e a n d
H o w t h a t
a
d o
a r o u n d
1 8 0 0 ?
t e c t i v e
b e l t
h i g h e r
t h e
e d g e , less
s t a b l e
t h e
in
for
p e r f e c t
K a n t :
u n i t y
a n d
a n d
w e it
a
epis-
t h e o r i e s
b e
k n o w n
in
o f
t o w a r d
c a n
c o m p o s i n g
a n t e c e d e n t
-
w o u l d
t o
t h e
in
a
said
t o
c o u l d
a n d
t i m e ,
n o t
p h i l o s it l e d
t o
c o u l d
n o t
h a v e
w e r e
n o t
e a c h
c o n d i t i o n s
in
h a v e
c o n v i n c i n g
g e t
I n
this
a c c o r d -
L a p l a c e ' s
o f
a n s w e r
h a r d
c o r e
o f
a n d
s o m e
a n d
m e r g e d
c e n t u r y
t o
a n d
t h e
t h e o r e t i c a l s u b s i d i a r y
s t a n d a r d s
a c c e p t a b l e .
p e r h a p s
e v e n
stabilized
a r e
for
a
e a c h live
t h i n k i n g flourishing
as a k i n d
o f
p r o -
p r o g r a m .
T h e
g e n u i n e
n e e d e d
W h e r e v e r
u n d e s i r a b l e ,
his
t o d a y .
scientific
s t a n d a r d s
w i t h
certainly
s e r v e d
d e t e r m i n i s t i c
g r o w i n g
m e t a p h y s i c a l ,
p r o b a b i l i s t i c
w a s
is t h a t p r o b a b i l i t y
t h e
r e m a i n e d
u n t i l
t h e
scientific
d e m o n
a n d
h a s
o p t i o n
r e l a t e
a n d
s e t t i n g ,
e s p e c -
C o n v e r s e l y ,
i n t o
f a m o u s
d e t e r m i n i s m
scientifically
l a c k i n g
ideals
i n t e l l e c t u a l
beliefs
t h e o r i e s ,
s y s t e m .
e n t r e n c h e d
d e t e r m i n i s m
b e e n
m e c h a n i c a l
p l a n e t a r y
d e e p l y
w i t n e s s
s e v e n t e e n t h
s h o r t
n o t
e p i s t e m o l o g i c a l
p h i l o s o p h i c o - s c i e n t i f i c
u r g e n t l y
a r e
t o
v e r s i o n
k n o w l e d g e
c o m p l e t e n e s s
b y
t h e
s c i e n c e
h a s
c u r r e n t
k n o w l e d g e
t h i n g
m o d e r n
b y
d e t e r m i n i s t i c
o f
p o w e r .
e p i s t e m o l o g i c a l
m o r e
o f
scientific
t h e
t h e
m a d e
a n d
m e t h o d s
s o m e o n e t h e
p r o b -
b e t w e e n
t u r n e d
causal p r o c e s s e s
this v i e w
d e t e r m i n i s t i c
T h e
t o
o f
p h e n o m e n a
a p p l i c a t i o n
w o r l d
r e s u l t i n g
e m e r g e d
t h a t
b o u n d
t h e
s e r i o u s
t h a t
rise
t h o s e
t h e
s u p p o r t
a n d
t h e
n e c e s s i t a t e d
a s s u m e
p r e d i c t i v e
e p i s t e m o l o g i c a l
A r i s t o t l e :
o f
t h e
o p i n i o n s
in
o f
t h e
also
t h u s
m e t a p h y s i c a l
c o n c e p t
o f
law.
w a s
o f
in
w i t h
like
if
o f
p e r -
t h a t
h e n c e
t h e o r y
b e l i e v e d
p r o b a b i l i s t i c
specialized
c l a i m s
a
o f
t h i n k
a n d
i n e v i t a b l y
p h i l o s o p h i c a l
c o i n c i d e n c e
it
v i e w
u n l i m i t e d
w a s
successful
a c h i e v e m e n t s , scientific
o r
parellel
t h e i r
e r a
say,
W h e n ,
t h e m
w e r e
are
d i s c r e p a n c y
e r g o d i c
p e r s i s t e n c e
a n
t o
m e t a p h y s i c a l
P e i r c e ,
if it is e s t a b l i s h e d
n a t u r e
o f
It is p l a u s i b l e
o f
o n l y
o f
o n e
in
f o u n d ,
d e t e r m i n i s t i c
a n d
ially
is
c o n c e p t i o n
k n o w l e d g e
a n c e
it
o t h e r w i s e .
a n y
a n d
t h e
o f
like
p r a c t i c e d ,
c a m e
m a t h e m a t i c s ,
d e t e r m i n i s t i c
w h o ,
t h e y
f r a m e w o r k
e x p l a n a t i o n ,
C o n v e r s e l y ,
t r a d i t i o n a l
k n o w l e d g e
p o s s i b l y o p h y ,
t h e
o f
w h e t h e r
e p i s t e m o l o g i c a l
o n l y
d e v e l o p m e n t
as
a n d
p r o b a b i l i s t s is t h e
a n d
t h o s e
a n d
m u c h
a n d
applicability
m e t a p h y s i c s
strict
n a t u r e
i m p r e s s i v e
chance
d i s c r e p a n c i e s ,
early
scientific practice
t h e o r y ,
T h e
s u c h
of
m e t a p h y s i c a l
d e t e r m i n a t i o n
t o
c h a o s
o f
c e n t u r y ,
p r e s u p p o s i t i o n , ability,
k i n d
implications
a
f o r
k n o w l m a k i n g
c e r t a i n t y
a n d
w e l l - r e a s o n e d
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The
a n d
q u a n t i t a t i v e
d i s p e n s a b l e , science.
as
s o o n
light
o f
p r o b a b i l i t y a
a n d
e p i s t e m i c
r a n d o m t h e
t h e
e r r o r s
r e l e v a n t A s
a
m a t t e r o f
t h e
level o f
l a w
o f
m o l e c u l e s , t h e
o f
b e c a m e n e e d e d .
n e w
a n
r e m o v e d ,
n o t i o n s
indefinitely,
d e a l s w i t h
t h a t
l a w l i k e
o f
causal
case
i n c l u d i n g
a
o r
are
at
least
a p p l i e d
t o
b e in
this
h o w e v e r ,
it
i n v o l v e d . p o i n t .
w o u l d
d i s t r i b u t i o n , t h e
n o t h i n g
h y p o t h e s e s ) ,
m a y
t h e y
a b o u t
t h e m
o f
is
T h e
G r a n t e d
s e e m
e.g.
t o
b e
a c c o r d i n g
n a t u r e
o f
h u m a n
o b s e r v e r
at
Q u e t e l e t ' s
s u c h
c a n
said
tific
d e t e r m i n i s m .
t h a t
in
a p p l i e d
t h e
a
h i g h e r
a
t o
p h i l o s o p h e r s
as
m a t e r i a l
basis o f
as
as
its
a
w h e t h e r
t h e
C h a r l e s t h e
S.
o n l y
statistics
a n d
t o
n a t u r e
b a s e d e x i s t
o f
physicists
a
a n d F r a n z
l o w e r vari-
b i o l o g y ,
tries t o
o n o r
n o t
t h e n o t ,
validity
H a n s E x n e r
T h i s
m a k e
It
o f
it
w e r e
statistics.
ino n l y
p r e s u p will
m a t h e m a t i c a l
u n i v e r s a l
P e i r c e
at
c u r v e
a s s u m p t i o n s . is
w i t h
O n c e
e r r o r
right, a n d
t h e y
d o
o f
c o n c e r n s
e v e n t s
in e v o l u t i o n a r y
it
o f
p a t t e r n
goes.
t h e
b e i n g
d i s t r i b u t i o n s
m a t h e m a t i c a l
o w n
v e r y
m o r a l
t h e
t h e
will as o n e
r e g u l a r i t y
theory
o b j e c t s ;
t h e
free
o f
f r o m
n o t h i n g
t h e
p r o b a b i l i s t i c
o f
i n c l u d i n g
h a s
the s t u d y
far
v e l o c i t y
b e s i d e s
t h e i r
o f
w h i l e
e m e r g e d ,
u n d e r m i n e
scientists,
o f
o n e
a l a w l i k e
only,
as
d i s t r i b u t i o n s
in
t h e
A g a i n ,
far
t h u s
p r o d u c e s
t o
is
h u m a n
o b v i o u s l y
o b j e c t
this s e n s e
s u c h
listed
l a w
b e c a m e
p o s i t i o n
r e g u l a r i t i e s
level
d e t e r m i n a t i o n s , I n
h e
t h e
s h a p e
d i s t r i b u t i o n s t h e
e v e n t u a l l y
s u p e r p o s i t i o n
d e t e r m i n a t i o n s
tics
s o m e
v i e w s .
s t u d y
o n
e r r o r s
k n o w l e d g e .
o t h e r
its c o n c l u s i o n s . b e
o f
i m p o r t a n t
field
f u r t h e r
also
b e
a
o f
d e t e r m i n i s m ,
a p p l i c a t i o n s ,
is
o f
as e x p r e s s i n g
a s p e c t s
e x a c t
t r e a t m e n t
scientific
m i g h t
fact
t h e
a n
in-
h y p o t h e s e s .
-
e r r o r s
t h e i r
l a w
w h o s e
o u r
a p p e a r s
t h a t
n e g l e c t s
a n d
o r
o t h e r
( p o s s i b l y
u n d e t e r m i n e d ,
f r o m
p o s i t i o n
M a x w e l l
b e c o m e
A
t h e
w h o s e
o f
a n d
f e r e n c e s
S o m e
I n
i n t o
a s s e s s m e n t
t r u s t w o r t h i n e s s
o b j e c t i v e
s e t u p
d i s t r i b u t i o n s
clear
discipline
affect
Y e t ,
society, e x p r e s s e d
r e m a i n h a d
fact,
c a u s e s
e r r o r s .
probabilities
a t i o n
t h e
it is clear, h o w e v e r ,
d e s c r i p t i o n
level
a n
t h e
p r o b a b i l i s t i c
r e d u c e d
i n d e t e r m i n i s t i c
a c c i d e n t a l t h e
is
t o
scientific
t h a t
b e c o m e s
t u r n e d
bill, f r o m
a s s t r i c t l y epistemic
o b s e r v a t i o n a l
e x p e r i m e n t a l
u n a m b i g u o u s ;
o n
f o r
is
beliefs
t h e
e p i s t e m o l o g i c a l
e p i s t e m i c .
c u r v e ,
fit
e p i s t e m o l o g i c a l ,
(e.g.
b e
s e c u r i n g
p a r t ) .
s o u r c e s
t h e
o f
m i g h t
p u r e l y
t h e
c e r t a i n t y
W h e r e
t h o u g h
281
a n d
d a t a
u n o b j e c t i o n a b l e .
e v e n
t o
k n o w l e d g e
entities
is
n o r m a l
object,
o f
o u r
chance
i n v e s t i g a t i o n
statistical
i n t e r p r e t e d
d i s t r i b u t i o n
s o m e t h i n g t o
o r
o f
o f
a p p e a r e d
indefinitum.
i n t e r p r e t a t i o n
t h a t
b e
ad
q u e s t i o n a b l e ,
b r a n c h
d e g r e e s
r e s t r i c t i o n
p u r e l y
a
of
f o r m u l a t i n g
m e t a p h y s i c a l ,
is t o
d i m i n i s h e d
o f
t h e o r y
e r r o r s
r e l a t i o n s h i p s
b u t
as
P r o b a b i l i t y
o b s e r v a t i o n a l
I n
m e t h o d
implications
n o t
statisscien-
R e i c h e n b a c h , a n d
M a r i a n
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282
The
v o n
S m o l u c h o w s k i
g o n e
a
step
precision ation
further.
o f o u r
as
the
variation
a n d
implications
the
Since
as the
o f
w e
the
result o f
chance
mathematician discover
observation,
result
of
variation
they a r g u e d
m u t u a l
the
Richard
s u m m a t i o n
Mises, have
w h e r e v e r
that w e
cancellation
v o n
should
o f
o f m a n y
w e
force
v i e w
variations
e v e n the
d e t e r m i n -
rather
than
i n d e p e n d e n t
d e t e r m i n -
uncontrollable
variations
ations. T h e in
connection
nature
place
for
J a m e s ,
easily
b e t w e e n
associates
Peirce's
follower
a r g u m e n t
o f those w h o
h a d
o f physics, such
that
is
a n d
the
natural
friend,
presented
d e t e r m i n i s m
(James,
1884).
praised
in a question let
by
vincing
instantiation
the
as that
action
say
a n d
completely
identifiable
the
least.
m o t i v e s
freedom.
T h e
Decisions
reasons, role o f
all.
obtain
or
actions
hardly will in
a
con-
the
his-
in accordance
w i t h
one's
metaphysical
issue
remains
unresolved,
sumably T r u e ,
b e c o m e
there
scientific f r o m
the
w h a t e v e r T h e
ever
is
d e t e r m i n i s m
an
a n d
ideas.
m o r e
other
o f
i m p a c t
recent
with
be
o f
to
f o r all o t h e r
m a n y
like
triggered
o n
this
is w h a t
o f
the
o f
h u m a n
determinism
probabilistic
1986, for
first
theory
a n d
observable
w e
will
a n d
theories, freedom.
influences
W h a t e v e r
the
a recent and that was
applications,
genetic
material.
a small scale. W e
Since
such
the truth
careful
universally
indeterministic including
devices
tech-
natural can
be
d e t e r m i n i s m is v i o l a t e d , a t l e a s t may, h o w e v e r ,
o f
resulted
by a t o m i c o r s u b a t o m i c processes, a n d
o f
a b o u t
d e v e l o p m e n t
scientific
therefore
p r e -
observe.
t h o u g h t
strongly
o f determinism.
the
will
d e t e r m i n i s m
indeterministic
(see E a r m a n , was
d e t e r m i n i s m
with
erosion
conceptions
f o r m s
this
metaphysical
that interferes
built a n d such processes exist, effective suitable cases a n d
rate,
o f
effective
significant
as
scientific
any
strand
mechanics
m u t a t i o n s
A t
scientific
irreducibly
nological devices processes
o u r
l o n g
w i t h
f u n d a m e n t a l
theories o f physics
to
respect
m o r e
o n
fate
assessment), q u a n t u m recognized
loose.
i n d e t e r m i n i s m
e m e r g e n c e their
m o r e
the
as
correlation
i m p o r t a n t
B u t
present prospects a b o u t
the
b u t
to
to
will p e r h a p s accept or reject metaphysical d e t e r m i n i s m freedom,
a m b i g u o u s
c o n n e c -
as o p p o s e d
are
free
But,
O n e
o f
r e m a i n e d
after
possibly
inexplicable,
or
s o m e
physics
will, the
m i g h t
a
this day.
conception
has, therefore,
it
as
theories
q u a n t u m
f r e e d o m
a
W i l l i a m
Conversely,
o f free
s u p p o r t
to
o f h u m a n
tory o f d e t e r m i n i s m
securing
Peirce. free
indeterministic
as d e e p
alone
accidental
d e t e r m i n e d
in
the spell o f successful deterministic
controversial,
actions
than
h u m a n
to save the possibility o f h u m a n
arbitrary,
interest
less a case in p o i n t
as Pascual J o r d a n ,
indeterminism,
it, are
a n d
b e e n u n d e r
as is t o b e e x p e c t e d with
w i t h
is n o
against
b e c a u s e it s e e m e d
f r o m
itself
free will. M a x w e l l
forceful
tion
i n d e t e r m i n i s m
plausibly claim
in
that
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The
it is still p r e s e r v e d electric s h o c k s that
is
d r a w
s u m a b l y
t h e
b e
m e n t s .
t o
as
b y
t h e n ,
theory,
it
u n d e t e r m i n e d
as
far
affects
as
t h e
w i t h
d o
m a d e o f
drifting
g e n e
sufficiently
scientific validity
n o t
in
t h e
o r d e r
t o
theory.
p o o l s
c a n
selective
effective
b y
t h o u g h
n e w
i n d e t e r m i n i s m
o f
kill cats
e v e n t s ,
clear
character
r a n d o m l y
c o n t a c t
w e
q u a n t u m
S c h r o d i n g e r
"paradoxical" o f
283
F o r , ordinarily,
E r w i n
d e v e l o p m e n t
s u m ,
of chance
scale.
single
t h e
d e t e r m i n e d
In
q u a n t u m
b y
possible,
a t t e n t i o n
M o r e o v e r ,
a larger
t r i g g e r e d
certainly
o u r
o n
implications
p r e -
e n v i r o n -
is
b a s e d
d e t e r m i n i s m
o n o n l y
marginally. B y is
implication,
h a r d l y
t h e
i m p a i r e d
p r o c e s s e s .
O n are
t h e o r i e s
s o m e
b y
deterministic. finding
s u c h
t h e
as
o n
t h e
t h r e a t e n e d
physical
stricted
a l t h o u g h A t
this
part,
o f
T h a t
O f
t h e y
h a d
are
radically
t h e o r i e s
c a n u n d e r m i n e
o f
figuration, f r o m
N o t
t h e
is
a n d
q u a n t u m
in
t h e
a d d i t i o n c o n f i d e n c e
e p i s t e m o l o g i c a l
insights
o r
reactions
w o r k d a y
related
t h e
strikes
also
o r
a
a n d
p r a g m a t i c
t o
q u a n t u m
physicists
(cf.
m e t h o d o l o g y
o n t o l o g i c a l
b l o w
t h e
clearly
practical
a l m o s t
o f
r e f u t e d .
i m p o r t
has
o f v i e w
m a i n l y
t r u t h
o t h e r w i s e
s i t u a t i o n
distinct
are
p u z z l e s
o f
rare n o t
like
m e t a -
q u a n t u m
this
as
theory,
in
t h e
v i o l a t i o n
occasions.
c h a n g e d
the q u e s t i o n
a n d
against
Y e t ,
case is
I n
re-
o t h e r
dramatically,
is o n e
o f
e p i s t e m o l o g i c a l
indistinguishable
is
q u a n t u m
o f
m o r e
i n d i s t i n g u i s h a b l e t i m e
as
principle.
d e t e r m i n i s m
c o m p a n i o n s
s y s t e m s , initial
a n o t h e r
also
m a d e
s y s t e m s t h e
in
b u t
as has b e e n
s u c h
c o m p l e x
l i m i t e d
r e v e a l e d
m e c h a n i c s ,
c o m p l e x
c o m p l e x i t y ,
radically w i t h i n
also
d e t e r m i n i s m ,
m e c h a n i c s
a l o n e
(practically)
d i v e r g e
o n l y
m o d e r a t e let
a n d
c u r r e n t
E u r o p e a n
a n d
e l e m e n t a r y
in
t h e
less
i m -
d e t e r m i n i s m .
w a y .
s y s t e m s
spirit
m e t a p h y s i c a l
b e c o m e
p o r t a n t
o f
o n
t h e
a n d
g r a n t e d
w a s
e p i s t e m i c
classical
v e l o p m e n t s
c o u r s e ,
c o n t r i v e d
t h e r e f o r e ,
t h e y
d e p e n d
g e n e r a l
m e t h o d o l o g i c a l
that
interest
c o m p a r i n g
m e c h a n i c s
a metaphysical p o i n t
p o i n t ,
after
h e y d a y
overall
f r o m
b y
o f
t h e o r y
t h e
A m e r i c a n
d e t e r m i n i s m
specially
t h e
b e t t e r
in
single
r e p l a c i n g
m e t h o d o l o g i c a l
p r a g m a t i c
i n d e t e r m i n i s m ,
t o
w o r d s :
s h o w n o f
o f
likely t o
o n
o f
p r o s p e c t s
c i r c u m s t a n c e s ,
t h a n
r e a l m
t h o s e
o r
d e t e r m i n i s m
duality.
d e t e r m i n i s m .
effective
as
i n d e t e r m i n i s m
q u a n t u m
e p i s t e m o l o g i c a l o f
true
b y
w a v e - p a r t i c l e C o n v e r s e l y ,
a
v e r y t h e
b a d
are m o r e
part
1 9 8 7 ) ,
t h e
g o o d
t h e s e
b e
m e t h o d o l o g i c a l
level, as
equally
c a n
o f in
o r
inclinations
C a r t w r i g h t , hardly
as g o o d
a t h e o r y
I n d e e d ,
m e c h a n i c s
except basic
U n d e r
m e t a p h y s i c a l n e e d s .
-
that
d e t e r m i n i s m
in
a d e q u a c y
a n d
classical clear
c h a o s
(classical!) c a n
b e
spans. T h e
physical
b y r e c e n t theory.
t h r e e - b o d y
unstable,
c o n d i t i o n s
n o
a n d
d e t e r m i n i s t i c
that
is,
d e E v e n c o n start
n e v e r t h e l e s s s t r u c t u r e
o f
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284
The
t h e
t h e o r y
s y s t e m s ,
d o e s
like
e x c e p t i o n s . c a n c e , t h e y
like
a r e
n o t
o u r
w e
a r e
l e d
t h a t
o f
t h o s e t h e y
t o
b y
t h o s e
t h e o r i e s all
p s y c h o l o g y
a r e
t h e o r i e s , t h a t
t h a n
o n
w i l l i n g
is
m u c h
interpretandum.
e n a b l e
u s
t o
c o n c e i v a b l e
n o t
h a v e
a
j u d g i n g t o
is
t h e
m o r e
will
d e p e n d
a d d i t i o n a l t h e
ties
a p p r o x i m a t i o n s
r e -
t h e m s e l v e s , as a m a t t e r is
n o
t h e n
o f
less
fact,
t r u e
for
b e h a v i o r ,
o r
m a x i m s
m e t a p h y s i c a l
o f
scientific
w a s
o n
w e
m e n -
i n c l u d e
if t h a t
p r o p e r t i e s
o f
in
m e t a p h y s i c a l
It
o n
h o w
just
i n t e r p r e t a t i o n
solely
its o b j e c t s ,
o b s e r v a b l e
as
d e t e r m i n i s m .
d e t e r m i n i s m t o
o f
s o m e t i m e s
will d e p e n d
b e t w e e n
case
u n a m b i g u o u s . d e t e r m i n i s m
a r e
d e f i n e d
t h e
t i m e
b y
for It
is
i n d e t e r m i n i s m ,
h a s
less
a
o f t e n
r e m a i n
is
t h e
c e r t a i n l y
m a t h e m a t -
s t r u c t u r e
t h e s e
d o e s
o b j e c t s
t h a n
n o t
i n
a n y
o f
those
w a v e
states
d e s c r i b e
it d o e s
n o t
p o s i t i o n a
u n i t e
a n d
d i f f e r e n t
this
p r e c i s e
v a l u e s
m o m e n t u m n a t u r e .
state
o f
H e n c e
I f
f e a t u r e
t h e
f u n c t i o n
t o
m i s g u i d e d
o n t o l o g i c a l
is
m a x i m a l
o f
t h e
a
c l a i m
for
T h e o r
states o f
i n
o f
a
m a x i m a l d e t e r -
s o
v i e w
t h a t o f
it t h e
c h a r a c t e r i s -
m i c r o - r e a l i t y
a g a i n s t
t h e
s p e c i f i c a t i o n
state,
as i n d e t e r m i n a t e
particle.
t h a t
c e r t a i n l y
o f all m a c r o s c o p i c a l l y a
m e c h a n i c s ,
r e m a r k e d
c o m p l e t e .
S c h r o d i n g e r
d e v e l o p m e n t
q u a n t u m
b e e n
a n
o f
o n e
a s s u m p t i o n s
b e
b e
I f
also,
t o
s i m p l y
m e t a -
a p p l i c a t i o n s
resistant,
d e t e r m i n i s m
o u r
assigns
p a r a d i g m
i n t e r p r e t e d
like
o f
p h e n o m e n a .
e c o n o m i c
m a y
tics,
m e c h a n i c s
e x c e p t i o n
t h e o r i e s
a realistic i n t e r p r e t a t i o n ,
t h a t
p r i n c i p l e ,
q u a n t u m
a n d
u n d e r
fact
i m p l y
d e t e r m i n i s t i c
o f i m p o r t a n t
m i n i s t i c . M o r e o v e r ,
b e
a r e
t h e o r y
s e v e r e d
b a s e
a t h e o r y
t h e
o f
specification,
w o u l d
t h a t
a p p l i c a t i o n .
m i c r o s y s t e m
b e
signifi-
n o t
o f
realistic i n t e r p r e t a t i o n
It
o f
d e t e r m i n i s m ,
d e t e r m i n e
e n t i r e l y
b r e a k d o w n
o u t .
w e
for
t h a t
C o n v e r s e l y , is
c a r r i e d
P i c k w i c k i a n
ical s t r u c t u r e
y e t
T h i s
o f m e t a p h y s i c a l
A f t e r
o n l y
s o m e w h a t
a d o p t
b e l t
t h e
criteria
t o
t h e
e p i s t e m o l o g i c a l
d o e s
m a t t e r
t h e
o f
r a r e
a s s u m p t i o n
explicitly.
h o w e v e r ,
o f
a n d
a
as i n d e t e r m i n i s t i c ;
t h e
are,
t h e o r y .
u n s t a b l e
t h e
t h e y
physics.
a s s e s s m e n t
h o w
a n d
o f
e l e m e n t s
d e t e r m i n i s m , a r e
p a r t s
b i o l o g y ,
w i t h
a s s u m p t i o n s
c o n s i d e r e d
t h e
p r i m a r i l y
r a n g e
c o m p l e x
as
as
q u a s i - s t a b l e
practical
d e t e r m i n i s m
p r e d i c t i o n s ,
w i d e
a d d i t i o n a l
b e
f o r
I f w e t h e
t o
o n
d e t e r m i n i s t i c
n o t
o r
w h a t
o f g r e a t
s y s t e m s ,
is
t h e
stable
f o r
e v e n
scientific
it
r a t h e r
p o p u l a t i o n
i n t e r p r e t a t i o n
t i o n e d , t h e
t o
fully
d e t e r m i n i s m ,
p r o b a b i l i s t i c
M e t a p h y s i c a l s t u b b o r n .
t h e
a
C h a o t i c
a p p l i c a t i o n s
c o n t a i n
e v o l u t i o n a r y
b u t
r e c o g n i z e d
c h a o t i c ,
b e
t h a t
o f
c o n t r a r y ,
t o
cliche,
t h e o r i e s
c o u n t
n o w
l o n g - t e r m
f o r m s
p h y s i c a l
w i l l i n g
q u i r e d
all
t h e
d e t e r m i n i s m ,
classical
is
D e s p i t e
u n d e r m i n e s
p h y s i c a l
a n d
t h e
p h e n o m e n a
c o n c l u d e
p r e c i s e
chance
o f t e n
b y
d e t e r m i n i s m .
p e r m i t
n e v e r t h e l e s s .
a r e
p r o v e
c o v e r e d t o
of
cases; o n
s y s t e m ,
w e a t h e r ,
e p i s t e m o l o g i c a l n o t
s u c h
p h e n o m e n a ,
a d e q u a t e l y
T h u s
d o
solar
M a n y t h e
b a r
implications
m a y
d e t e r m i n i s m
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The
s h o u l d
b e
n a t u r e
c o n d i t i o n a l
o f
t h e
W h a t
t w e e n
m i c r o s t a t e s
still
I n
v i e w
a d h e r e
q u a n t u m
t o
a n d
t o
t h e i r
a n d
t h e
o f
(see
h a s
t h e
w i t h
t h e
t h e
t h e
m e t h o d ,
o f
o f
t h e
e r o s i o n
b e
t h e
sciences
g r a d u a l l y
t h e
t h e
p r o p o s i t i o n s ,
m e n t s
T h e
a n d
ideal
n e w
p h e n o m e n a ,
o r
t o
t h e
b e u s e
T h e
rise
r u l e
o f
d e r s . tice
f u r t h e r .
m a d e :
T h e r e
scientific
r e t r e a t
h a d
w a s
a n d
b e
v e r y
t h e o r y , t o
t h e
b e
t h e
w h i c h
flexible
in
t h e
o n e
c o n d i t i o n s
v e r s i o n
t h e n u m -
o f
laws,
s o m e
t h e
r u l e o f
c h o i c e
a n d
e x -
b u t
n o t
e x p e r i -
s o r t
o f
A
t o
t h e
c h o i c e
n u m b e r s ,
d e t e r m i n a t i o n .
w a s
t o
in
w e a k e n e d
necessary.
a t least
this
d e m o n s t r a t e d
sciences
o r d e r
B u t
o f
recalcitrant
i d e a
h a n d ,
o f
b y
d e t e r m i n i s t i c ,
t o
1.4).
m a t h e m a t i c a l
Scientific
w i t h
set
f r o m
o b j e c t s
t h e
b e c a m e
b e
s u g -
d e t e r m i n a t i o n .
n a t u r a l
d e t e r m i n i s m , o n
a
m a t h e m a t i c s
t o
s e c t i o n ,
a r t i c u l a t i o n
m u s t
b e
n u m b e r s
( s e c t i o n
s t r o n g e s t
t o
t h a t
p r e s u p -
n a t u r a l
t h e
a n d
this
n a t u r e
s u c h
o f
t h e
i n d i s p e n s a b l e
c e n t u r i e s ,
clearly
m o r e
d i s s o l v e d
science
t o
o f
o f
m o r a l
d e t a c h e d
c o n v i n c -
m o d e r n
m a t h e m a t i c s .
a p p l y
m o r e
o f
p o w e r f u l
f r o m
limits h a d
b e
t h e
m e t h o d
d e t e r m i n i s m
b e t w e e n
c o n t e n t
t o
o n e .
n o n - e p i s t e m i c
r u l e
in
b e g i n n i n g
c o n f r o n t a t i o n
t o
f r o m
r e n d e r e d
in p h i l o s o p h i c a l
t h e
k n o w l e d g e
t h e
o r d e r
m a r k s
t r a d e - o f f
m e t h o d
b o t h
t o
d e s c r i b e d
less
claim,
a g o .
still u n d e r s t o o d
n a r r o w
p r o b a b i l i t y
is a
in
t h e
c e n t u r i e s
n i n e t e e n t h
in
o r
is a h a r d
h a s
t h e
o f
w h i c h
t w o
e x p r e s s i o n
as
for
d e t e r m i n i s m
c h a r a c t e r i z a t i o n
just
t h e o r i e s
m a y
case
scientific
m o s t
t h e m s e l v e s
t h e
o f
c o r e
e v e r
o f
b e -
q u a n t u m
m o r e
n a t u r e
t h e m s e l v e s
e x p a n s i o n
t h e
o f
t h e i r
this
t o
f o u n d
a n d
scientific
scientific
t o
belt:
s e e m e d
w e r e
w e r e
I n
e i t h e r
n u m b e r s
if n o t
a
o f n u m b e r s o f
t h e
d e t e r m i n i s t s
p r o t e c t i v e
scientific
A t
n i n e t e e n t h - c e n t u r y
t h a t
h a d
t h a t
o b s e r v a t i o n s still
o f
d o w n
h i s t o r y ,
d e t e r m i n i s m
a n d
ideal
necessary.
several
p e r f e c t
m a t h e m a t i c a l l y ,
its
b e
assimilate
p h i l o s o p h i c a l
lost
c a n
classical s y s t e m s ,
n a r r o w e d
k n o w l e d g e
t h e
d e t e r m i n i s t i c
p r e s s e d
o f
a c c o r d i n g
p r o p e r t i e s
i n d e e d ,
c h a o t i c
g l o r i o u s
n a t u r e
d e t a c h e d -
o r
e n o r m o u s
o f
that,
m e t a p h y s i c a l
m a y ,
t h e
g e n e r a l i z a t i o n :
fact
o b s e r v a b l e
s u g g e s t e d
o f
e i g h t e e n t h
o f
t o
o f
a r g u m e n t s
t o
b e
a n d
applicability
d u r i n g
f o r m
clarification
c o r r e s p o n d e n c e
e p i s t e m o l o g i c a l
c o r r e s p o n d i n g l y
s e e m e d
t o
g r a d u a l l y
d e t e r m i n a t i o n o f
u n d i s p u t e d
T h e y
D u e
p i c t u r e
m a t h e m a t i c a l
b e r s
h a v e
p r o b a b i l i t y
f o l l o w i n g
p o s i t i o n
285
o n t o l o g i c a l
r e s o l u t e
u n s t a b l e
its l o n g
c o m b i n a t i o n
c o m p l e t e
A s
also
m e t a p h y s i c a l ,
8.1)
g e s t s
o f
d e v e l o p m e n t
c h a r a c t e r i z e d T h e
s i t u a t i o n ,
c o r e .
o f
t h e
d e t e r m i n a t e
t h a t
o f
it
i n t e r p r e t a t i o n s
f u s i o n
t o
w e i g h t
is
p r i n c i p l e s .
c l a i m s
N e v e r t h e l e s s ,
ingly,
chance
p r e v i o u s
m a c r o s c o p i c a l l y
this
o n t o l o g i c a l t h e
n o
a n d
o f
p h y s i c s
d e t e r m i n i s t i c elusive
a
h o w e v e r ,
m e c h a n i c s ,
s y s t e m s .
u p o n
of
m i c r o w o r l d .
r e m a i n s ,
q u a n t u m
implications
m a d e
e x t e n d
i n
o f p r o g r e s s
its
scientific
t h e
-
t h e b o r p r a c -
a d a p t a t i o n o n
t h e
o f
o t h e r .
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The
286
8 . 4
T h r o u g h o u t v e r s u s
t h e
u n c e r t a i n t y
relationships: the t o
ability also
t h e o r y
n o
cations h e r e
a
certain
t h o s e
w h o
a n
o f
o n
a b o u t
ations
t o
t o
in
a n d
i n f e r e n c e s
a b o u t
S i n c e s u c h
as
d r a w i n g
his
ence. s o u g h t t h e m
T h e
m o d e l b y
t h e
o f
t o
w h e n
s o u n d
w e
t h e
these o f
t o
a
b a d
h a v e
b e e n
T h e
f r o m
o f
b e l i e f
h a v e
h a v e
s e e n
a r m e d
t h e
m u d d l e - h e a d e d w i t h
in chapter
his
since w e
d r e a m a
T h e r e
t h e o f
t h e r e f o r e , i n f e r e n c e
k i n d s as
all o f
o f
situ-
t h e
h u m a n
t o
i n v e s t -
Bayesian, t h e m
d r a w
shall d e s i g n a t e
t h e m
theirs t h a n
o f
f o r m s
t o
o f
b e
o f
r i g h t - t h i n k i n g ,
o f
1, w h e n
sure,
e v e n
p r o b a b i l i t y
o r d e r t h e
t h e
a
f o r m
o f
for
inferP o i s s o n
t o
m a k e
e n l i g h t e n e d
c o m p l e x i t y )
as a
a c o n c e p t i o n
w a s
C h a r -
i m p o r t a n t
t h r o u g h in
o f B u t
t e c h n i q u e s
o f s u r p a s s i n g
uncertainty, itself
(or
it is t o d a y .
m e c h a n i z e d
B e r n o u l l i
m a s s e s
a calculus
a U n i v e r s a l
battery are,
J a k o b
a p r o b l e m
t h i n k i n g
e l i m i n a t e
i n c l u d i n g
s t r o n g e r
w i t h
c o n c e i v e d
u n d e r
for
sciences
m a k i n g
m o d e r n
f r o m o f
o f
b e e n
realize
a n d
rules
inference.
d r e a m e d
t o
classical
that
B u t
uncertainty
a n d
T h e
t h e
c o n -
u n c e r t a i n t y
v a r i e d
vary,
m e t h o d s .
uncertainty.
is, t h e y
also
past e x p e r i e n c e ,
n o w
c o n f r o n t e d
as
appli-
t h e
m e c h a n i z e
o p i n i o n .
t e s t i n g in
rules
t h e
that
irrelevant
o r
c a n n o t
t o
are
t h e o r y
s u c h
has,
p r o b -
certainty
p r o v i d i n g
o n e
a i m
a p p l i e d
i n d u c t i v e
able
are
i n f e r e n c e
T h e y
standardize)
b y
e l i m i n a t e
i n f o r m a t i o n
m a d e
it is
in
t h e o r y
T h e s e
frailty
accept
rules
d o
( a n d
i n t u i t i o n s
t h e
t h e s e
h y p o t h e s i s
issue.
u n c e r t a i n t y ;
b u s i n e s s
t h e y
p r o b a b i l i t y
H o w e v e r ,
h u m a n
their
d e t e r m i n i s m
p r o b a b i l i t y
applications
p u r s u e .
probabilists
t h e
u s e d
v e r s u s
g o v e r n e d
belief in
o f
certainty
d e t e r m i n i s m
w o r l d .
u n d e r f r o m
that has n e v e r
u n d e r
aid. T h a t
f u r t h e r
lation. A s
s t e m s
o f
i n d e t e r m i n i s m
applications
w h a t
f r o m
n e v e r
successors
available
a m e c h a n i c a l
a c t i o n
f u t u r e
b e t w e e n
their
uncertain
situation,
rules
w a s
c o d i f y
t h e m s e l v e s
w e i g h
a d r e a m
classical
t o
an
o f
traditionally
p h e n o m e n a
A l t h o u g h
business.
i n f e r e n c e s
d i f f e r e n c e s
b e s t
probabilists
L e i b n i z
acteristic,
the
t e c h n i q u e s
inferences,
o p p o s i t i o n
that
a d m i t t e d
N e y m a n - P e a r s o n i a n
Leibniz,
w h e r e a s
effect,
t o
t h e
t o
u p
d e c i s i o n
In
r a n g i n g
Fisherian,
o f
a n d
t h e
s u c h
d e c i s i o n s
w h o
s o m e
t o
o f
g i v e
t h e
d e t e r m i n i s m / i n d e t e r m i n i s m
rationalize
itself,
collectively
in
c o n d u c t .
h o w
w h i c h
c o n d i t i o n m e n t
a n d
c o u r s e
t h e r e b y
t o
u n c e r t a i n t y
intrinsic
w h a t
t h o s e
i n f e r e n c e
m a k e
a b o u t
a s h a d o w
r e f u s e d
m e a s u r e
w o r l d .
belief
like
I N F E R E N C E
t h e o r y ,
u n p r e d i c t a b l e
t h e
that
a n d
chance
c o m p l e m e n t a r i t y
a p p e a r a n c e
the
g i v e n ,
o p i n i o n
a n d
certain
w h e t h e r
u n c e r t a i n t y
a n d
a
deal w i t h
rational
c l u n g
A
s t a n d
struction
o f p r o b a b i l i t y
u n c e r t a i n t y ;
m a k e s
t a k e
as
h a s
face o f variable m e a s u r e
of
M E C H A N I Z E D
h i s t o r y
indetermi'nism.
implications
as
m a t h e m a t i c a l
m a d e
plausible
implicit
calcu-
results o f probability
t h e o r y
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The
w e r e
at o d d s
first
tried
w a s
t o
eye:
a
t h e
w i t h
t o
t h e i n t u i t i o n s
c o r r e c t
n a t i v e g o o d
i m m u n e
i n t o
e x t e n s i o n
A l t h o u g h t h e t o
t h e
t h e
i n t u i t i o n s
o f
universality,
n o t a b l y
m o s t
c o m m a n d :
e v e n
is
social
that
g a v e
in disciplines
their
r e a s o n i n g .
h o w e v e r ,
a b o u t
t h e o r i e s
a b o u t
m e t h o d s ,
case o n
o f t h e
a n d
that
physicists
t h o s e
p s y c h o l o g y , e r r o n e o u s
that
its
w a r r i n g
this
i n f e r e n c e
is a
t h e
relative
m e t h o d s .
w a s
silenced
precisely
T h e y t h e o f
that
w e r e
n o t
c o u r t r o o m rival
f o r m s
o f
statistical
sensus,
neutrality,
are m o r e
W h i l e
a d m i x t u r e
o f
cisions
are
o f
p r o b l e m s
statistics
t h e o f
t h e
t o
o f
t h e
o n
allure
In
s u c h
t h e
F i s h e r
e x p e r t s
t h e y
rather
t h a n
m e d i c a l
data.)
that
s e e m
F o r o f
r e a s o n s
statistical
a n
o c c a s i o n a l
c o n t e x t s
w h o
a r g u e
t h e
lean that
n o n e t h e n o
m e a n s
i n f e r e n c e
s t a n d i n g
utility-based
b e t t e r
e n -
geneticist.
o f statistical
B a y e s i a n
c o n -
a
It is b y
revises
in
d e -
biologists
p r e c e p t s
C o n v e r s e l y ,
o f t e n t h a n
practical
a f o r m
o n e
e v i d e n c e .
tests
o w n
rational
w a s
w i t h
B a y e s i a n
their
statistics
practical
o f
p s y c h o l o g i s t s
d e f y
c h o o s e
sort
h i m s e l f
ears.
b l a n d i s h m e n t s
Certainly,
m o r e
m o s t
t h e
i n f e r e n c e
their
s c h o o l s
statistics, in
a n d
p r e c i o u s .
v a r i o u s
rests
Fisherian,
c l o s e d
illusion
it
t h e
i n t o
statistical
t o
in
m o n o l i t h i c ,
B a y e s i a n
m o r e
c o n s e n s u s
d i v i d e d
m o m e n t o u s
t h e
is e v e n
always
n e w
o f
their
c o n s e n s u s
since
are
Bayesian,
a p p l y i n g
Fisherian
i n t e r p r e t
N e y m a n - P e a r s o n
e v a l u a t i n g
o f
in
s h o w s
w a s
statisticians
balance,
( C u r i o u s l y ,
d e c i s i o n s basis
i n f e r e n c e
t o
i n f e r e n c e
for
6
b e e n
difficult
n o t
p r e t e n s e s ,
p s y c h o l o g i s t s
b e c a u s e
b e c a u s e
c h a p t e r
false
areas o f application.
scientists s h o u l d
o n
A s
claims
h a v e
t h e
settled
c o r r e c t
u p o n
b u t
attain
as
disposal,
t o
is m o s t
theories,
are just as d e a f
a n s w e r s
p r e f e r
irrational
t o y e s - n o
h y p o t h e s e s
t h e
N e y m a n - P e a r s o n ,
Fisherian
that leads
office
p r e s u m e
e m b r a c e d
instead
m e r i t s
b e n t
w h o
n e v e r
fact,
t h e
statistics
m e t h o d s .
I n
s u b s t a n t i v e ,
b y
a n s w e r .
t e c h n i q u e s
u n d e r
strife,
in
t h a n
specialized
B a y e s i a n
o b v i o u s w h y
h a n g
s a m e
n a k e d
i n t r o d u c e d
T h e s e
statistical
inference.
u n i q u e
scientists
subjects
less u s e
a n d
Fisherian
social
t o w a r d
m a y
historical
h a v e
c o u n t e r e d
their
lives
e m o t i o n
c o n s e n s u s
a n d
since
d o c t o r ' s
o r
their
t h e
at e v e r y o n e ' s
still rests
c o u l d
B u t
E x p e r t s
t h e
w h e r e
i n f e r e n c e
alone.
o r
cisions
that
it
that
u n i q u e .
N e y m a n - P e a r s o n i a n
basic
a p p e a l
statistics.
c o n s e n s u s
w e r e
o v e r
in
a c h i e v e d ,
a s s u m p t i o n
a n s w e r s
c a m p s
o f
principles
s a m e
at
t h e o r y
t h e
physicists,
p r o b a b i l i t y
scientists,
P r o b a b i l i t y t o
t h e
w h e r e
n o t
m a t h e m a t i c i a n s
spectacles w e r e
it w a s
u n i q u e n e s s .
scientists,
t h e
statistical i n f e r e n c e
e n l i g h t e n e d , a n d
m e n ,
i m a g i n a t i o n
statistics. Physicists a c c e p t e d Social
o r
a l o n g
always o f
287
intuitions.
m e c h a n i c a l ,
f o r m s
neutrality,
successful
it
a n d
t h e
t h e
d e s i g n e d
d i s t o r t i o n s
m o d e r n
n o t
a t e l e s c o p e
it w a s
j u d g m e n t s ,
of chance
o f r e a s o n a b l e
m o d e l ,
w h a t
b e c a u s e
t o
intuitive
their
s e n s e
m e c h a n i c a l
original. J u s t
w a s
implications
s u i t e d
m e t h o d s .
t o
o f d e t h e
A c c i d e n t
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288
The
c r e a t e d in
a
t h e
a s s o c i a t i o n s
single,
t h e m
i n
T h e o n c e
s t e a d y
is
a
O f
t a k e
n o n s t a t i s t i c a l
f u n c t i o n
o f r u l e s is t o
a m b i g u o u s statistics, areas
c o u r s e ,
o f
t h e
sciences
tive
a s s o c i a t i o n s
O u r
c o n t e m p o r a r y
t h e s e
a s p i r e ter.
is
t o
this
d e p e n d
cation.
O n c e
o r
t h e
set
t h e
n o t i o n o w e s
c a n o f
a l t e r n a t i v e
t h e o r i e s
t h e
will
t o
b e l i e v e
u n c e r t a i n t y
s o l u t i o n s
w i t h
It
false
h o p e s ,
t h e
d e a l
t o
f r o z e
s h o u l d
t o
r e p l a c e
f r o m
h a s
b e e n in
t h e
Fisherian
i n f e r e n c e .
u n c e r t a i n t y i n f e r e n c e
N o
are
statistical
i n f e r e n c e ,
a n d
a b o v e
responsibilities
t h a t
e v e r y
u n j u s t
a l t h o u g h
f a s c i n a t i o n for
w i t h
t o
s o m e
b y
b l a m e o f
u n a n i m i t y
in
t h e
t h e i r
m e c h a n i z e d t i m e s
t h e all
t h e
largely o f
b y
o n
a
a b s e n c e
n o r m a t i v e
infer-
statis-
objectivity. A l l
t o
i n f e r e n c e
g u i d e
m u s t
testing,
a p p l i -
i n t e r v e n e
t h e
a l t h o u g h
r e d u c t i o n
o f
h a v e
i n f e r e n c e
s t e m s
o f
a n d
just
o f
t h e
for
o f
h o p e
f r o m
legero f
t h e g r e a t
e x i s t e n c e
o f
c a l c u l a t e d
o b j e c t i v i t y
t o
a v o i d i n g
t h e
j u d g m e n t
e n -
statisticians s h a r e d
p r i o r
s u c h
o f
o f
p e r s o n a l
m a t h e m a t i c a l
t h e
m u c h
c o n f l a t i o n
t h e
o r
t h e o r y ,
m a t h e m a t i c a l
f r o m
t e c h -
t h e i r
N e y m a n - P e a r s o n
o f
t h a t
c h a r a c -
j u d g m e n t ,
o f
i g n o r a n c e
n u m b e r
t h e
t e c h n i q u e s
j u d g m e n t o f
s u b j e c t i v e .
m e c h a n i z e d
illusion.
e x e r c i s e
strife,
a n d
d e s c r i b e
b y
j u d g m e n t
p e j o r a -
n a m e
b y
o f
i n
its
s t e m s
b y
p r e c i s e l y
w i t h
certainty,
f e d
w a s
t h e o r y
d i s c r e t i o n ,
a m o u n t
i n t o
t h e
r i d d i n g
h y p o t h e s i s
t e c h n i q u e s
e x p e c t a t i o n s
it
t o
j u d g m e n t
null
r u l e s a r e
o f
t o
case
t h e
t a s k
t a k e n
is a n
B u t
p r o b a b i l i t y
statistical
t h e
p e r p l e x i t y
t h e
d e c i d e d ,
c o n s e n s u s ,
b e
in
g o o d
c r i t e r i o n , in
it,
p r o b a b i l i t y
m e t h o d .
b u r d e n
d r e a m
a i m e d
j u d g m e n t o f
t h e
s u i t e d
t h e
h a v e
o n c e
for
S i n c e
t h a t
t h e
j u d g m e n t
i n
m a t h e m a t i c a l
d e f i n e d
t h a t
u s
D e s c a r t e s '
idiosyncratic,
objectivity,
w h e r e
g u i d e
called
ideally
o n e s ,
w o u l d
y e a r n i n g s
s e e m e d
t h e o r y
t o
a n d
g r e a t e s t
u n i q u e
i n t e r s u b j e c t i v e
o f
areas
m a t h e m a t i c a l
u n c e r t a i n t y .
w a s
m o d i c u m
o f
o f
s i t u a t i o n s
o f
in
r u l e s
a m b i g u i t y ,
g r e a t
B a y e s i a n
T h e s e
t h e
s u r p r i s i n g
e s c a p e
statistical
tails.
a
a i m s
t r a n s f o r m
o p p r e s s i v e
case
i n f e r e n c e
d e c i s i o n
in
as in
o f
n o t
a
h i s t o r y for
arbitrary,
significance
e x p e c t a t i o n s .
t h e
a n d
u n d e r
m e t h o d s
daily life o f p e r s o n a l
applicability
p r o b a b i l i t i e s
a p p e a l
t h e
o n
level o f
d e m a i n
o f
n o w
n i q u e s
t o
r u l e s
p r o b a b i l i t y
c o u r s e ,
a g a i n
i n f e r e n c e
t h e
U n c e r t a i n
t h e n
m e c h a n i z e
i n f e r e n c e
O f
a n d
t h e r e f o r e
W h e r e a s
tical
m e t h o d ,
y e a r n i n g
e l i m i n a t e
all.
e l e m e n t s ,
It
t h e
f o r m s ,
statistical
t h e
e n c e .
for
o f
u n c e r t a i n t y
first
o f
chance
a n d
statistical
m a t h e m a t i c s
w h e r e
h e a v i e s t ,
o f
l e i t m o t i v
c a n
w a s
field
m e t h o d
a d v a n c e
statistics.
t h o s e
of
place.
a n d
a n d
b e t w e e n
u n e q u i v o c a l
p r e v a i l e d
least
implications
t h e m .
m o r e
c e r t a i n t y
f o r
t h e s e
R a t h e r ,
w i d e s p r e a d in
u n c e r t a i n
c i r c u m s t a n c e s .
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The
8 . 5
T h e s e
a n d
statistics
a n d
t h e
m a t h e m a t i c s
c o m e
is
w h e t h e r
b o t h
t r a n s f o r m e d
t o o t h e y w e
w e
risk
a n d
o v e r
a r g u e
o u r
p o i n t s ,
m u c h
a
a n d
life
c e n t u r y ,
t h e
J o h n
m a n ;
F e l l o w
o f
t h e
R o y a l
diarist.
p a g e s
pre-statistical w h e r e v e r t h e
c a t h e d r a l a n d
e r e c t e d
in
9 0 7
m e n
7 5
k e e n l y
o f
t h e
o f
n u m e r i c a l ,
b u t
P e o p l e
E v e l y n e n d o r
c o u l d
in
t h e
a n d
t h e
a n d
basis
w e
a
t h e i r
o u t -
v i e w s
h a v e
o f
c o n a r e
w o r l d ;
w h a t
Weltanschauung.
Y e t
h a r d l y
m a k e
n o t i c e
u p
w a y
for
w a s
o u r
o f
for
its
m i n d s ,
life
is
t o o
c o s t
t r a v e l o g u e
" p o p u l o u s "
o b j e c t s
are
p u r c h a s e d
a n d
t i m e .
o f
c a n
h e h e
feats
h a v e
m a t t e r
y e t a n d
T h e y
a
for
n u m b e r s
h i g h ,
3 2
o b e l i s k a n d
e v e n
a n d
D u t c h
c e n s u s e s
feet
l a b o r
m o r e t o
o f i m -
t h e
in-
a l t h o u g h
h e
rivals,
t h e
o f
recently
t h e
n u m b e r
e n t e r e d
y e t
feet
i n n u m e r a b l e
o f
m o d e r n
bell
a r e
visited,
E n g l a n d ' s t h e i r
o f
fix
s h a r p - e y e d
g r e a t
c r o w n s h a d
a n
t h e
E g y p t i a n
b e
f r o m
n o t
n e i t h e r
t o
r e v i e w
p r o g r e s s i v e
a
a v i d
13
late
h o r t i c u l t u r e ,
t h a t is
t h e
a n d
a
t h r o u g h
a n d
o f f "
cities
s u b j e c t
fire
b e n t ,
t h e
not
t o
p u r p o s e s ,
3 7 , 9 7 5
n u m b e r s
w a s
scientific
e x a m p l e ,
t h a t
c o m m i t m e n t s
r e t u r n
E v e l y n
r e c o r d e d
t a l k ' d
its
still y o u n g ,
o u r
life
b e e n ,
briefly
o f
factual
p r o s p e r i t y
t h e
h a s
u s
d e v o t e
a n d
R o m e
t h e
b u t
d o u b t
statistics
t h e
statistical
t h e o r y
see
p o u n d s ; in
o f
w o r l d ,
a n d
L e t
learn,
m u n d a n e
at
b e
" s o m u c h
p r o d u c t s
h a v e
a
p r o d u c t i v i t y
o f his life in L o n d o n , p r o b a b i l i s t i c
o f
E v e l y n ' s
w o n d r o u s n o t
w a s
B u t
n u m e r o u s
i n d u s t r y
d i m e n s i o n s
indices.
in
i n t e r e s t e d
t h e i r
w e
S q u a r e
n o
for
t r a n s f o r m a t i o n s
c h a n c e
( 1 6 2 0 - 1 7 0 6 ) .
d i a r y
D a m e
o u r
a t t i t u d e s
a r r o w
a n d
o f o n
p r e c o n d i t i o n s
a n d
a n e w
o f
s o c i e t y
i n t e r a c t i o n s ,
T h e s e
O u r
f o r t u n a t e l y
h a d :
h o r s e s .
c o u l d
relief.
E s q .
4 0 , 0 0 0
P e t e r ' s
N o w h e r e
h a b i t a n t s
i n f e r
N o t r e
w e i g h s
S t
b e
p a r s e
t h e
i m p a c t
eye.
Society,
his
n e w
p i c t u r e
e m p i r e
p r o b a b i l i t y
E v e l y n
c o u l d
o f
a n d
p r e s s i v e .
is
eyes.
t h e y
a r o u n d ,
o f
b r e d
sciences,
t h a n
fellows.
w h a t
a n d ,
t h e
c o h e r e n t
w e
t h e
i n t o
E v e l y n ,
tourist,
t h e
o u r
w h e n
i n d e f a t i g a b l e I n
j u d g e
s p r i n g
in
b e y o n d .
t h e
w a y
it w i t h
s e v e n t e e n t h o f
i n t o
c a t c h
a
o f
causal
t h e s e
t h e
i m p a c t
P r o b a b i l i t y
Lebensgefuhl
t h e
t o
c o n t r a s t
i n t o
a n e w
b o r n
a n d
c o n s e q u e n c e s
d a y s
s u m
u s ; o v e r
o f
if w e
t o
age.
w o r l d
w e r e
T h e
t a n g l e d
r e a s o n i n g
w i d e
t h e
m a t h e m a t i c s
q u e s t i o n .
statistical
a n d
t h e
b e e n
d o m i n i o n
B u t
a
289
d i s t i n g u i s h
f r o m
a t t i t u d e s
H o w e v e r
in
is m o r e
h a v e
w a y
in
v a s t
c o n s t i t u t e w h o
live
t h e
i d e a s a n d
i l l - p o s e d
e x p l a n a t i o n
a n d
v a r i e d
a n
it is t o
s o c i e t y
W h e t h e r
t h e s e
is
o n
chance
L E B E N S G E F U H L
difficult
t h e o r y
d i r e c t i o n s .
clear:
t i n g e n c y
h o w
p r o b a b i l i t y .
ideas, o r
in
s h o w
p r o b a b i l i t y
a n d
p o i n t s
of
S T A T I S T I C A L
c o n s i d e r a t i o n s
statistics
implications
h e
m u s t
canals. r e a l m
a n d
o f
T h e t h e
e c o n o m i c
c o u n t a b l e . e v e n
life
i n s u r a n c e
these
e n t e r p r i s e s
w e r e
e i t h e r
b a s e d
h a d o n
t o w a r d s a n y flat
t h e
statistical rates,
o r
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290
a
The
m e t i c u l o u s
s u r e d .
e x a m i n a t i o n
P a s s i o n a t e
frost,
d r o u g h t ,
f u r t h e r
t h a n
w o r l d ,
w i t h
m a n y
c o u n t e r f e i t
D u r i n g
t h e
h e e d
o f
a n y t o
c o n s t a n t ,
fitted
t h e
first
W h e n
it
t o
his
i n d i v i d u a l
in
e v e n
h a v e
b e e n
table,
r e c o r d e d
t h e
d e a t h s
n u m e r o u s
w a s
t h e
o t h e r
biblical
o f
G r a u n t ' s
o r
r e g a r d
s u c h
a v e r a g e s .
H a d
o f
a n n u i t i e s
p u r c h a s e ) I n d e e d , d w e l t
at
a g e
t h e
o f
t h e
T h a m e s
o n e
f l a m e
b r i g h t
n e r s
as o f
a m a z e tual
t h e just
p e r s p e c t i v e
o f
a n d
t h e
as w e l l
as T h e
a n d
all
specificity
t o
h e
y o u n g
a n d
o f
n o
his
b a b y
m o r e
t h e
causes,
b u t
t h e i r b e
t h e
c o l l e a g u e s
since
t o
m e r e
o u t
p r o b a b l y
o r
c o n -
i n v e s t i g a t e d
-
p a i d
b u t
i g n o r e
o f
it
t h e y
it in
t h e
m o r e t h e
t h e
singular.
H i s
t h e
rare,
t h e
a n d
streets
o f b e
o f
lifespan. II,
l o n g e v i t y
e x p e c t a n c i e s
B r i t i s h
in his
dis-
g o v e r n m e n t ' s
p r i c e
L o n d o n . b u t
t o
( s e v e n
years'
t h e
t h e y
e v e n t
is
t h e
u p
o n
c a n t o
is
t h e
t h e i r
l u c u l e n t
t a b l e
m a n a n d
d i f f e r e n t
fac-
full
o f
i n d i -
p a r t i c u l a r s .
p r o b a b l y
o b s e r v e d
t h o u s a n d s
a
f r o z e n
a s t o n i s h
is g r a n u l a r , in
w i t h
a n a t o m i c a l
e x q u i s i t e
s p e a k
w h i c h
c r a m m e d
" e m i t t e d
Statistics
w h a t
t h e
e m p i r i c i s m ,
set
t h a t
w o r l d
i n d i v i d u a l
o f
s h o p s
a p p r e c i a t e d
t h a n
S o c i e t y
C h a r l e s
typical
s t r i k i n g :
c a n d l e " ;
E v e l y n ' s
closely
life
d i a r y
a g e m s t o n e
t o
a g e d
s o m e
p r e s e n t e d
n a t u r a l
n o t
s a m e
t h e
w a x
sizes
R o y a l
t h e o f
t h e
a n t h r o -
2 0 .
i n s t a n c e ,
h e a v i l y
t o
t h e
a v e r a g e
w a s
b r a n d
s m a l l
t o
E v e l y n
w a i s t c o a t
H a l l e y
a n
years,
E v e l y n ' s
w i n t e r ;
i s o l a t e d
o f
m e a s u r e
p a i d
t o
E d m u n d
g r a n d s o n ,
his
h a v e
t o
t h a n
a n d
c l o t h i n g
n o t i o n
tables.
L e y d e n ;
as a
w e i g h t
i n
his
a t t e n d e d
w h e n
h a d
m a n
n o v e l ,
e v e n t s
a r o l e
filter
b r e e c h e s
r a t h e r
s u b s c r i b e d
f o r e i g n
t e x t u r e
c o r r e s p o n d s
t e n d e n c y
o f
a m b a s s a d o r
t h e
t h e y
s t a n d a r d i z e
p r e s e n t
w o u l d
b i t t e r
large
M o r o c c a n
h u m a n its
w e r e
u n u s u a l l y
o b j e c t s
a
U n i v e r s i t y
sensibilities.
v i d u a l
as
n o
e v e n t s
t o
w e r e
H i s
r e g u l a r l y
H a l l e y ' s
h e
p a r t i c u l a r
d e s c r i p t i o n s
t h e a t e r
1 6 9 4 ,
7 4
a v e r a g e s
u p o n
v i v i d
in
e x t e n d e d
c o u l d
a n d
b e f o r e
t h e y
t h r e e - s c o r e - a n d - t e n
f r o m
issue
t o
h e
c o m p u t e d for
as
o f
S o c i e t y
E v e l y n
w o r l d .
c o n t e m p o r a r i e s ,
ideal
h o w
i n d e e d ,
s e a s o n s
n a t u r a l
a t t e m p t e d
d i m e n s i o n s ,
E v e l y n
life
a n d
-
t o
R o y a l
scientists
E v e l y n ' s
e m p i r i c a l
h e
t h e
in-
c h a n c e
m o m e n t o u s
n e v e r
c h a n c e
s e r v e d
A l t h o u g h
m a y
t o
d u e
case
n o t e d
b a s e l i n e
f o r
o t h e r
e a c h
causes.
f i g u r e
later. a n d
a t t r i b u t e
t h a t
b u t
b e
c o m e :
F e l l o w ,
n a t u r a l
n o t
c e n t u r i e s
t o
p h e n o m e n a
o f
d u l y
t o g r a n t
systematically.
d i d
a v e r a g e s
sessions
o f
l o a t h e
a n d
as
s u r r o u n d i n g
E v e l y n
i n d e e d
t h i n g s
u n i f o r m
p o m e t r i c
w a s
effects,
g r o u p
w a s ,
m i g h t
c h a n c e
chance
m e t e o r o l o g i c a l
p r i n c e s
variability
t h a n
A v e r a g e s w e r e
o f
h e his
t e n u r e
s u b t l e
as r e l u c t a n t
s t u d y
o f
his
effects
r e c o g n i z e d
w e r e
d e a t h s
o f
of
c i r c u m s t a n c e s
H e
c o m e t s
signs
a n d
b u t
m e m o r y .
t h a t
t h e
e l u s i v e
t h e t h a t
s t o r m ,
d i v i n e
c o i n c i d e n c e ?
m o r e
a n d
a d m i t t i n g
n e c t i o n
o f
g a r d e n e r
his o w n
n o n e t h e l e s s
implications
o f
t h e o r
H i s
u n i v e r s a l
r e p o r t e d
faceless
in
cases
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The
s u m m e d h a v e o n
u p
in
statistics.
B u t
t o
t h i n k
a r g u e
l e a r n e d
t h e m
t h e y
b u t
for
t h e
f u n d a m e n t a l t h e
b e l i e v e t h e
in a n d
t o
t h e
It
is
a n d
p u r p o s e s
w e t o
t o
d i f f e r e n t
a
o f
t i m e s ,
tyrannically. m i n d s a n d
o r
statistics
w e
tics o f
T h i s
infallible, o f
r e a c h e d , as
a r e
t h a t
e x i s t e n c e .
m a r g i n
w e
it
m u s t
T h e s e -
d e e p
-
t o
t h u s
g r e a t e r
t h a n
t o
at
w e
c o n f e r t h e
e x p e r i e n c e t h a t
o n e ,
int h a n
-
w a s
w e o f
collectively
t h e
i m p r e s s i o n
t h e
a c c i d e n t
l a n g u a g e
statistics traffic
s h a p e s
r e s e a r c h ,
o u r
n o t
beast,
o u r
a
a n d
t h i n g s ,
a n d
t o n g u e .
e m o t i o n .
u s u a l l y f o r
t h a t
safety.
n a t i v e
p u b l i c
b u t
o f
a u t o m o b i l e
c o n c e r n i n g
is
still
d o
I n
c l i n g
c e r t a i n
t o
p u b l i c
d e e p - f e l t
i m p r e s s i o n s
t o
n u m b e r s .
S i n c e
D i c k e n s '
( 1 8 5 4 ) ,
h a v e ,
t o
settle
d i s p u t e s
a
s h o r t
t o o l s
all.
a b s o l u t e
w a s
o f
f o r
F r o m
o r
g e n e r a t i n g
s a m e
all s u c h
p e r s o n a l possibility
t o
b u r d e n
at
local
o u t s e t , f o r g e
is
t h e
t h e
w o r s t ,
m e l d
m a n y
t h e
i m p e r s o n a l
a
t r u l y
n e i t h e r
w h e n
h o p e i n t o
injustice
o f
t h e
h o n e s t l y
a n d
fear,
p u b l i c in
social
u n i v e r s a l
B e c a u s e
least
o f
I n
a
P r o b a b i l i t y
f o r
e x p e r i e n c e o f
m i s t a k e n
fiat.
civic p a s s i o n s .
decisions,
t h e
it
a n d
t o
i n
o n e :
f o r c e
f o r
alive
c o n v i c t i o n .
i n d i s p e n s a b l e will,
t h e
t h e
a n d
irenically;
p u b l i c
w a s
a n d
h o w e v e r ,
at
e x e r c i s e d
s h o u l d e r
all t h a t
n o n e
g e n e r a l
s u b m e r g e
f r o m
T h e y
c a r r i e d
t h e
w a r m - h e a r t e d
for
t h o u g h t
u p
t h e
a shift
f u n c t i o n
t h e
cast
a r e
f r o m
w e r e
e d g e s
i n t u i t i o n s
c o u n t
a v e r a g e s ,
s t o p p i n g
s u m m o n s
t o
t o
t o
i n v o k e d
R o u s s e a u ' s
a n d
i n
m a y
l e a r n e d
i n d i v i d u a l s
versatile
s t o m a c h
is
if it
s t r a n g e
h a v e
a v e r a g e s ,
a n n u a l
e v e n
e m o t i o n s
t h e i r
w e
u n t u t o r e d
t h e
v i s i o n
a l t e r n a t i v e
t h a t
h o n o r
d e c i s i o n s ,
this w a s
P e a r s o n
collectively
l e a n i n g s ,
i n d i v i d u a l
w r o t e
d i s c o u r s e
all e m o t i o n s .
w e r e
m o s t
n o t
collectively
g l o b a l
s h a r e d
i n t o
K a r l
b u t
o f
n o v e l
cases,
t o
o u r
Times
f u n c t i o n s
t h e
is
f r o m
t h a t
u n c e r t a i n t y
m u s t
a n d
all
if
t h a t
f r o m
f e a r e d
o n e
E v e l y n
o u r
pointillist
a b s e n c e
o p i n i o n s
k n o w l e d g e
n o r
I n
s i n g u l a r
o b s e r v a t i o n s
Hard
t h e s e
t h e
r e c o m m e n d a t i o n s
n o v e l
n o
-
a n d
p u b l i c
is
statistics
w h e n
a n d
less a t t e n t i v e
n a t u r e
g a z e
p e r h a p s
a n d
c o n s e n s u s b e s t
h a v e
frigid
a n d
p r o b a b i l i t y
o f
p r o b a b i l i t i e s ,
t e n d e r - m i n d e d
t h e i r p a r t s
l e a v e , it is t h e
a n d
a n d
anti-statistical
h u m a n
m a y
p a r t s
o u r
a v e r a g e s ,
n o
h o w e v e r
Lebensgefuhl
shift
p s y c h o l o g i c a l
w a s
E v e n
rationalizes
E v e l y n ' s
o f
c o i n c i d e n c e s ,
o u r
a r g u m e n t t h a t
o u r
o f
since
ineffable.
m u s i n g s like
c e r t a i n t i e s
f o r
f r i e n d
statistical
s o m e t h i n g
y e a r s
E v e l y n ,
d e e p e s t
-
291
reality.
p r o b a b i l i t y :
o f
p r i v a t e
b i t t e r
o f
a close
t h e
O u r
test
t h e
l a n g u a g e
p r o b e s
o u r
o f
o f
chance
t e r m s
s u m
E v e l y n
h u n d r e d
a n d
s t u f f
a
u n i t
in
t h e
i n d i v i d u a l
e v e n
t h o s e
statistics a c c i d e n t
t h e
t h r e e
invisible
closer
a r e
h i m ,
of
w h a t e v e r
t h a n
s u m m a r i z e .
w e ,
I n
a n d
a reality g r e a t e r
d i v i d u a l s
implications
t h e
just
statisn a m e
justice. s h a r e d
e m o t i o n s
t r a n s f o r m
a n d
i n d i v i d u a l s
risks i n t o
a n d
a b o v e
citizens
o f
all a w a r e n e s s a c e r t a i n
k i n d
t h a t
t h e y
are
o f polity.
O f
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292
The
c o u r s e , t o
n e i t h e r
p r o b a b i l i t y
a n d
s o l u t i o n
t o
e r n m e n t
p o l i c y a
-
regularities. s u r p r i s e u p o n
t h a t
e x p e r i e n c e d e x p e r i e n c e d
c a b i n e t
o f
n o
spin
o f
o f
u p o n
c u r i o s i t i e s . Pace
e n e m y
c a t i o n
s a m e
a frisson
o f
w o n d e r .
s u r p r i s e ,
h e r
w h e e l
statistics is o n e
h a s
n o n e t h e l e s s
c a n
m a k e
o f
b e e n
a
T h e
o f
statistician's
u s w i t h
n u m b e r
b e o f
fact
l e t t e r s
o f
t h e
w a s
w o r l d
u p s i d e
d o m e s t i c a t i o n full
t h a t
o f it
o f
o f
s a l a m a n d e r t h e
d o w n .
T h e
c o n t i n u e
t h e t o
b e
o n l y
p a r -
statistics Q u e t e l e t ,
e a c h
year,
in
a n
as
n o t h a t
Italian Lebensgefuhl
p e r s o n i f i -
u n p r e d i c t a b l e
s t o r y
u n p r e d i c t a b l e a n d
a n d
v e r y
e a c h
is
m a c r o s c o p i c
statistical t h e
g o v -
o d d
just as i n t e n s e
w o n d e r ;
w o n d e r s ,
will
a n d
o n e
t o g e t h e r
E v e l y n ' s
astray
t r a d i t i o n a l l y
c o m p a n i o n
life
o f
s i n g u l a r i t y ;
w e n t
p e t r i f i e d
G r a d g r i n d ,
m a t t e r
L a p l a c e
v i e w i n g
a
-
r e l a t i o n
r e p r e s e n t
a
a v e r a g e s
R e a d e r s
o f
it o u r
u n s u s p e c t e d
regularity.
D i c k e n s '
is
p r i c e
k i n d
n e c e s s a r y
statistics
a s t o n i s h m e n t
s t o r y
c e r t a i n t y
a n d
a n y
o f p l e a s a n t
b o o n
t h e
b e a r
m a y h e m ,
o n e
F o r t u n a
t u r n i n g
a n d
w i t h
t h a t
w i t h o u t
t h e
s u r p r i s e
t h e
p r o b a b i l i t y
f o r e g o -
chance
e m o t i o n
r e s e a r c h .
u n s u s p e c t e d
E v e l y n
is
t o
k i n d
P a r t i c u l a r s
u s w i t h
b u t
scientific
a n o t h e r
l e a r n i n g
d o u b t
o r
of
civic
d i f f e r e n c e s
w i l l i n g n e s s
for
n o r
statistics,
s e t t l i n g
s o m e t i m e s ticulars
c i t i z e n s h i p
implications
o f
p r o b a b i l i t y
F o r t u n a .
B u t
p r e d i c t i o n
it w e
so.
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