Experimental Test of a Theory of Decision

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AH EXPERIMENTAL TE$T ’DF :& THEORY OF DECISION

by L eon F e s t i n g e r

A d i s s e r t a t i o n s u b m itte d i n p a r t i a l f u l f i l l m e n t o f th e r e q u i r e m e n ts f o r t h e d e g re e o f D o c to r o f P h ilo s o p h y i n t h e D e p a rtm e n t o f C h ild W e lfa re , i n t h e G ra d u a te C o lle g e o f th© S t a t e U n i v e r s i t y o f Iowa l u l y , 1912

ProQuest Number: 10984100

All rights reserved INFORMATION TO ALL USERS The q u a lity of this re p ro d u c tio n is d e p e n d e n t u p o n the q u a lity of the co p y su b m itte d . In the unlikely e v e n t that the a u th o r did not send a c o m p le te m a n u scrip t and there are missing p a g e s, these will be n o te d . Also, if m a te ria l had to be re m o v e d , a n o te will in d ic a te the d e le tio n .

uest P roQ uest 10984100 Published by ProQuest LLC(2018). C o p y rig h t of the Dissertation is held by the A uthor. All rights reserved. This work is p ro te cte d a g a in s t u n a u th o rize d co p yin g under Title 17, United States C o d e M icroform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 0 6 - 1346

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ACSCJIOWL1CIXK-5I2KT The a u t h o r w is h e s t o e x p r e s s h i e a p p r e c i a t i o n to D r. K u rt Lew ln f o r h i a a i d and s u g g e s t i o n s i n d i r e c t i n g t h i s r e s e a r c h , a n d t o D r. D orw in C a r tw r i g h t f o r h i s h e lp an d c o lla b o ra tio n

in t h e d e v e lo p m e n t o f th e m a t e r i a l p r e s e n t e d

i n P a r t I a n d i n p l a n n i n g t h e e x p e rim e n t r e p o r t e d i n P a r t I I .

TABLE OF CONTENTS Part* I P r e s e n t a t i o n o f a T h e o ry o f D e c is io n C h a p te r I. II. III* IV . F.

P age In tro d u c tio n

1

M a th e m a tic a l S ta te m e n t o f t h e T h e o ry o f B e d e io n

II

D e riv a tio n *

2?

F i t t i n g t o E m p i r i c a l D a ta

37

R eview o f D a ta P e r t i n e n t t o t h e T h eo ry

UU

P a rt I I An E x p e r im e n ta l T e s t o f a T h e o ry o f D e c is io n F I.

F II. F ill.

IE . X.

P r o c e d u r e o f E x p e r i m e n t a t io n A p p a r a tu s C o n d u c t o f t h e E x p e r im e n t D e s c r i p t i o n o f th e S u b j e c t s D a ta R e c o rd e d

31 51 55 58 59

C o m p ariso n o f R e s u l t s w i t h P r e d i c t i o n s I n C h a p te r I I I

60

F i t t i n g o f th e T h e o r e t i c a l F u n c tio n s t o th e E m p i r i c a l D a ta 70 R e l a t i o n B etw een C o n fid e n c e a n d s t i m u l u s D iffe re n c e s 70 C u rv es o f D e c is io n -T im e and R e l a t i v e F re q u e n c y 67 F u r t h e r A n a l y s i s o f ’'C o n s ta n t E r r o r ” C o n d itio n UA R e le v a n c e to M easurem ent o f F o rc e s

117

Summary and C o n c lu s io n s

119

B i b li o g r a p h y

121

A p p e n d ix

123

TABLE «

PXCHJRES

F ig u r e J.. 2.

3*

4*

Pag© A T o p o lo g i c a l R e p r e s e n t a t io n o f a D e c is io n I n ­ v o l v i n g tw o A l t e r n a ti v e ©

3

The P henom enal F i e l d a n d th e F i e l d o f A c tio n when t h e V a r i a b l e S tim u lu s I s C l e a r l y L o n g er t h a n t h e S ta n d a r d

5

The P henom enal F i e l d and t h e F i e l d o f A c tio n t h e n t h e V a r i a b l e S tim u lu s l a C l e a r l y S h o r t e r t h a n t h e S ta n d a r d

6

A T o p o lo g ic a l R e p r e s e n t a t i o n o f a S i t u a t i o n When t h e S tim u lu s I s P e r c e i v e d a s F a l l i n g on t h e B o rd e r B etw een C a t e g o r i e s

8

5*

E xam ple o f a Z* D i s t r i b u t i o n

19

6*

T h e o r e t i c a l R e l a t i v e F re q u e n c y C u rv e s f o r I n ­ d i c a t e d V a lu e s o f R e s t r a i n i n g F o rc e

23

T h e o r e t i c a l D e c is io n -T im e C u rv e s f o r I n d i c a t e d V a lu e s o f R e s t r a i n i n g F o rc e

24

Maximum D e c is io n -T im e a s a F u n c tio n o f Re­ s t r a i n i n g F o rc e

31

P r e c i s i o n o f R e l a t i v e F re q u e n c y O give a s a F u n c t io n o f R e s t r a i n i n g F o rc e

34

?• 8. 9* 10.

T h e o r e t i c a l D e c is io n -T im e C u rv e s F i t t e d t o D a ta fro m One S u b je c t U nder T h re e C o n d itio n s o f Ju d g m en t

■ 45

l i f t . Time E ' D a rin g t h e R e s o l u ti o n o f C o n f l i c t B etw een A l t e r n a t i v e s S e p a r a te d b y D i f f e r e n t " D is ta n c e s " i n th e P re fe re n c e S e r ie s 49 lib .

12.

Time E la p s i n g f o r E s t h e t i c Ju d g m e n ts B etw een A l t e r n a t i v e s S e p a r a t e d by D i f f e r e n t " D is ­ ta n c e s " in th e P re fe re n c e S e r ie s

49

E l e c t r i c a l C i r c u i t Used f o r P r e s e n t a t i o n o f S t i m u l i a n d M easurem ent o f Decl s i on-Time

53

mBLE OF FIGURES ( C o n t . ) F ig u re 13 a*

P age H a l a t i o n B etw een C o n fid e n c e a n d P h y s i c a l S t i a u l u a - D i f f e r e n o e U n ite f o r S u b j e c t H .S . u n d e r " U s u a l" I n s t r u c t i o n s

71

13b ,

K e l a t i o n B etw een C o n fid e n c e and P h y s i c a l S tim ­ u l u s U n i t e f o r S u b j e c t H* S . u n d e r " A c c u ra c y " In s tru c tio n s 71

13o.

R e l a t i o n B etw een C o n fid e n c e and P h y s i c a l S tim ­ u l u s - D i f f e r e n c e U n i t s f o r S u b j e c t H. S . u n d e r "S p e e d " I n s t r u c t i o n s 72

134.

R e l a t i o n B etw een C o n fid e n c e and P h y s i c a l S tim ­ u l u s - D if f e r ® n e e U n i t s f o r S u b j e c t H* S* u n d e r " C o n s ta n t E r r o r " I n s t r u c t i o n s 72

lift,

R e l a t i o n B etw een C o n fid e n c e and P h y s i c a l S tim ­ u l u s - D i f f e r e n c e U n i t s f o r S u b j e c t B.W. u n d e r " U s u a l" I n s t r u c t i o n s

73

H b.

R e l a t i o n B etw een C o n fid e n c e and P h y s i c a l S tim ­ u l u s - D i f f e r e n c e U n i t s f o r S u u b je c t E.?f. u n d e r " A c c u ra c y " I n s t r u c t i o n s 73

14a *

R e l a t i o n B etw een C o n fid e n c e a n d P h y s i c a l S t i 4 u l u s - D l f f e r e n e e U n i t s f o r S u b j e c t B. w* u n d e r "S p e ed " I n s t r u c t i o n s 74

H d.

R e l a t i o n B etw een C o n fid e n c e an d P h y s i c a l S tim u l u s - D l f f e r e n e e U n its f o r S u b j e c t B. w* u n d e r " C o n s ta n t B r r o r " I n s t r u c t i o n s 74

15a,

R e l a t i o n B etw een C o n fid e n c e and P h y s i c a l S tim u l u a - B i f f e r e n e e U n i t s f o r S u b j e c t U .S . u n d e r " U s u a l" I n s t r u c t i o n s

75

R e l a t i o n B etw een C o n fid e n c e and P h y s i c a l s t i m u l u s - D i f f e r e n o e U n its f o r S u b j e c t U .S . u n d e r "A c c u ra c y " I n s t r u c t i o n s

75

R e l a t i o n B etw een C o n fid e n c e and P h y s i c a l S tim u l u s - D i f f e r e n c e U n i t s f o r S u b j e c t U .S . u n d e r "S p e e d " I n s t r u c t i o n s

76

R e l a t i o n B etw een C o n fid e n c e a n d P h y s i c a l S tim u lu s - D if f e r e n c © U n i t s f o r S u b j e c t U .S . u n d e r " C o n s ta n t E r r o r " I n s t r u c t i o n s

76

15b.

15d .

15d .

TABLE Of f x a m m F ig u re

(C ont.) Page

16a*

H a l a t i o n B etw een C o n fid e n c e a n d P h y s i c a l S tim u l u a - D if f © r o n e a U n i t s f o r S u b j e c t tT.B. u n d e r " U s u a l” I n s t r u c t i o n s 77

16b*

H a l a t i o n B etw een C o n fid e n c e a n d P h y s i c a l S tim u l u a - D i f f e r e n o e U n i t s f o r S u b j e c t «T*B* u n d e r "A e o u ra o y " I n s t r u c t i o n s 77

16c.

H a l a t i o n B etw een C o n fid e n c e an d P h y s i c a l S tim u lu s - D lf f e r e n e e U n its f o r S u b je c t I .B . u n d er "S p e e d " I n s t r u c t i o n s 78

164

.

R e l a t i o n B etw een C o n fid e n c e a n d P h y s i c a l S tim u lu a - D if f e r e n o e U n its f o r S u b je c t I .B . u n d er " C o n s ta n t E r r o r ” I n s t r u c t i o n s 78

17a .

H a l a t i o n B etw een C o n fid e n c e a n d P h y s i c a l S tim u l u s - D i f f e r e n o e U n its f o r S u b j e c t N .P . u n d e r " U s u a l” I n s t r u c t i o n s 79

17*.

R e l a t i o n B etw een C o n fid e n c e an d P h y s i c a l S tim u l u a - D i f f e r e n o e U n its f o r S u b j e c t N .P . u n d e r " A c c u ra c y " I n s t r u c t i o n s 79

17s#

R e l a t i o n B etw een C o n fid e n c e an d P h y s i c a l s t i m u lu s - D if f e r e n c © U n i t s f o r S u b j e c t N .P . u n d e r "S peed" I n s t r u c t i o n s 80

174.

R e l a t i o n B etw een C o n fid e n c e and P h y s i c a l S tim u l u s - D i f f e r e n e e U n i t s f o r S u b j e c t N .P . u n d e r " C o n s ta n t E rror* I n s t r u c t i o n s 80

18 a .

T h e o r e t i c a l D e c is io n -T im e and R e l a t i v e F re q u e n ­ c y C u rv e s F i t t e d t o th e D a ta f o r S u b j e c t H.S* u n d e r " U s u a l" I n s t r u c t i o n s 89

18b*

T h e o r e t i c a l D e c is io n -T im e an d R e l a t i v e F r e ­ q u e n cy 0 r v e s F i t t e d t o t h e D a ta f o r S u b je c t H.S* u n d e r " A c c u ra c y " I n s t r u c t i o n s 90

18c.

T h e o r e t i c a l D e c i s i o n - f i a e an d R e l a t i v e F r e ­ q u en cy C urves F i t t e d to th e D a ta f o r S u b j e c t H.S* u n d e r " S p e e d " I n s t r u c t i o n s 91

IS d .

T h e o r e t i c a l D e c is io n -T im e a n d R e l a t i v e F r e ­ q u e n cy C u rv e s F i t t e d to th e D a ta f o r S u b j e c t H .S . u n d e r " C o n s ta n t B r r o r " I n s t r u c t i o n s 92

VI

TABLE OF FKHJEE5 (C o n t.) Flgtuw 19*o

19be

29e>

19d*

20a•

20b#

20c#

Page T h e o r e t i c a l D e o ia io n -T im e and R e l a t i v e i ’r e q u e a s y C u rv e s F i t t e d to th© B a ta f o r S u b je c t B*We u n d e r ’’U s u a l” I n s t r u c t i o n s

93

t h e o r e t i c a l D e o ia io n-Tim® and R e l a t i v e F r e ­ q u e n cy C u rv e s F i t t e d to t h e B a ta f o r S u b j e c t B*w. u n d e r " A c c u ra c y " I n s t r u c t i o n ®

94

t h e o r e t i c a l D e cisio n -T im © a n d R e l a t i v e F r e ­ q u e n cy C u rv e s F i t t e d t o t h e D a ta f o r S u b j e c t B.We u n d e r " S p e e d " I n s t r u c t i o n s

95

T h e o r e t i c a l D e c is io n -T im e and R e l a t i v e F r e ­ q u en cy C u rv e s F i t t e d t o th e D a ta f o r S u b je c t B#W. u n d e r " C o n s ta n t E r r o r " I n s t r u c t i o n s

9b

t h e o r e t i c a l D e c isio n -T im © a n d R e l a t i v e F r e ­ q u en cy C u rv e s F i t t e d t o th e D a ta f o r S u b je c t U .S . u n d e r " U s u a l" I n s t r u c t i o n s

97

T h e o r e t i c a l D e c !s io n -T im e and R e l a t i v e F r e ­ q u e n cy C u rv e s F i t t e d to t h e B a ta f o r S u b je c t G.S* u n d e r "A c c u ra c y " I n s t r u c t i o n s

9#

T h e o r e t i c a l D e c is io n -T im e and R e l a t i v e F re ­ q u en cy C u rv e s F i t t e d t o th e D a ta f o r S u b je c t Gr«3# u n d e r "S p e e d " I n s t r u c t i o n s

99

20d.

T h e o r e t i c a l D e c is io n -T im e an d R e l a t i v e F r e ­ q u e n cy C u rv es F i t t e d t o t h e D a ta f o r S u b j e c t U .S . u n d e r " C o n s ta n t E r r o r " I n s t r u c t i o n s 100

21a#

T h e o r e t i c a l B e c is io n -T im e and R e l a t i v e F r e ­ q u en cy C u rv e s F i t t e d to th e D a ta f o r S u b je c t J# B* u n d e r " U s u a l" I n s t r u c t i o n s 101

21b#

T h e o r e t i c a l D e c is io n -T im e and R e l a t i v e F re ­ q u e n cy C urves F i t t e d t o t h e D ata f o r S u b j e c t y .B . u n d e r " A c c u ra c y " I n s t r u c t i o n s 102

21c#

T h e o r e t i c a l D e c isio n - T im © and R e l a t i v e F r e ­ q u e n c y C u r v e s F i t t e d t o t h e D a ta f o r S u b j e c t J , 13. u n d e r " S p e e d " I n s t r u c t i o n s 103

21d.

T h e o r e t i c a l D ecisio n -T im © and R e l a t i v e F r e ­ qu en cy C urves F i t t e d t o t h e D ata f o r S u b je c t y.B # u n d e r " C o n s ta n t E r r o r " I n s t r u c t i o n s 104

v ii

TABLE OF FIGURES (G o a t* ) F ig u r e

Pag©

22a .

T h e o r e t i c a l D e e ls io n -T ira e a n d R e l a t i v e F r e ­ quency C u rv a e F i t t e d t o t h e B a ta f o r S u b j e c t ft.P # u n d e r " U s u a l" I n s t r u c t i o n s 105

22b .

T h e o r e t i c a l D e c is io n -T im e a n d R e l a t i v e F r e ­ q u e n cy C urves F i t t e d t o t h e B a ta f o r S u b j e c t N .P , u n d e r " A c c u ra c y " I n s t r u c t i o n s 106

220 •

T h e o r e t i c a l D ecisio n -T im © and R e l a t i v e F r e ­ q u e n cy C u rv e s F i t t e d t o th e D a ta f o r S u b je c t N .P . u n d e r " S p e e d " I n s t r u c t i o n s 107

2 2d .

T h e o r e t i c a l D e c is io n -T im e and R e l a t i v e F r e ­ q u e n cy G u rv es F i t t e d t o th© D ata f o r S u b j e c t N .P . u n d e r " C o n s ta n t E r r o r " I n s t r u c t i o n s 100

v iii

TABUS Of TABLES T a b le

P age

1*

T h e o r e t i c a l V a lu e s o f R e l a t i v e f r e q u e n c y

25

2*

T h e o r e t i c a l V a lu e s o f D e c is io n Time

26

3*

S t a n d a r d D e v i a t io n and P r e c i s i o n o f t h e R e la ­ t i v e f r e q u e n c y O g iv e a s a f u n c t i o n o f th e M a g n itu d e o f th e Mean R e s t r a i n i n g f o r c e

33

D i f f e r e n c e s B etw een Maximum D e o ls lo n -T im e an d 50% R e l a t i v e f r e q u e n c y

61

D i f f e r e n c e s i n S e c o n d s B etw een H ig h e s t a n d L ow est P o i n t s o f t h e D e c is io n -T im e C urve

64

Means and S ta n d a r d D e v i a t i o n s I n S tim u lu s U n its o f th e R e l a t i v e f r e q u e n c y O give

68

S ta n d a r d D e v i a t i o n s o f t h e C o n fid e n c e f u n c t i o n

84

4* 5* 6* 7#

I n A p p e n d ix : 8a . O r i g i n a l

D a ta f o r S u b j e c t H. S .

123

8b . O r i g i n a l

D a ta f o r S u b j e c t B. W.

124

8e . O rig in a l

D a ta f o r S u b j e c t 0 . S .

125

6d . O r ig in a l

D a ta f o r S u b j e c t iT. B.

126

Be.

D a ta f o r S u b j e c t N . P .

127

O rig in a l

1

Part I Presentation o f a Theory of Decision

-La

C h a p te r X imTOTOGTlOR P r o b a b ly t h e mark; o f m a t u r i t y o f & s o la n c e i s

extent

th e

t o w h ic h I t u s e e m a th e m a tic s ; th e e x t e n t t o w h ic h i t

c a n s t a t e i t s la w s anti f u n c t i o n a l r e l a t i o n s h i p s i n p r e c i s e m a th e m a tic a l te r m in o lo g y * have s t i l l

to

The f u l l r e s o u r c e s o f M a th e m a tic s

be a p p r o p r i a t e d by p s y c h o l o g i s t s #

t e c h n i q u e s , © s p e c i a l l y t h o s e e m p lo y in g th©

S ta tis tic a l

h e o r i e s o f p ro b a ­ Same g e o ­

b i l i t y , h a v e fo u n d w id e a p p l i c a t i o n i n P s y c h o lo g y .

m e t r i c a l c o n c e p t s , p a r t i c u l a r l y t h o s e o f to p o lo g y h a v e a l s o b een u se d a lt h o u g h som ew hat l e s s w i d e ly . h o w e v e r, h a s

R a re ly , i f e v e r ,

h e r e b een a th o ro u g h and f r u i t f u l a p p l i c a t i o n

o f b o th ty p e s o f mat h e m t i e s ! m t e r i a l to th© same s e t o f d a ta # R e c e n tly i n p s y c h o p h y s ic s , w here t h e v e ry c a n c e r o f s t a t i s t i c a l a c t i v i t y h a s been l o c a t e d fro m i t s

e a rlie s t

b e g in n i n g s , a n a t t e s t h a s been m ade to u t i l i z e g e o m e tr i c a l c o n c e p ts i n t h e c o n s t r u c t i o n o f a th e o r y w hich b r i n g s p sy c h o ­ p h y s i c s and " m o ti v a ti o n p s y c h o lo g y " c l o s e r t o g e t h e r .

©

s h a l l h e r e a tte m p t t o b r in g s t a t i s t i c a l and g e o m e tr i c a l con­ c e p t s t o g e t h e r i n a q u a n t i t a t i v e th e o r y o f d e c i s i o n . C a r tw r ig h t (5 ) i n u r e c e n t a r t i c l e p r e s e n t s a th e o r y o f d e c i s i o n - t i m e i n t o p o l o g i c a l and v e c t o r i a l i»erms w h ic h l e a d s t o th© g r o s s p r e d i c t i o n

t h a t d e c i s i o n tim e a p p ro a c h e s

a maximum a s t h e r e l a t i v e f r e q u e n c y o f a g iv e n r e s p o n s e

2 ap p ro a ch e s f i f t y p e r c e n t.

n th

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o t h e r w i s e u n r e l a t e d and a p p a r e n t l y i n c o n s i s t e n t p s y c h o p h y s l o a l d a t a became c o n g r u e n t u n d e r o n e t h e o r y o f d e c i s i o n t i m e . Mow w© can male© a r e f i n e m e n t and f u r t h e r q u a n t i f i c a t i o n o f th© t h e o r y oo thn t t h e p r e c i s e s h a p e and a b s o l u t e value© o f b o t h d e d a l c m - t i n a an d r e l a t i v e f r e q u e n c y n a y he p r e d i c t e d f o r ape o I f l e d c o n d i t i o n s . '.?h© d i s c u s s i o n o f t h o s e r e f i n e r , e a t s w i l l ho f a c i l i ­ t a t e d by a b r i e f summary o f a.he e a r l i e r s t a t e m e n t o f ;>he t h e ­ ory*

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fcini© i n a p r>yohoph y s i o n 1 e x p e r i m e n t o p e r a t e I n e s s e n t i a l l y th© same way a s t h o s e d o t © m i n i n g any s o r t o f d e c i s i o n .

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to p o lo g ic al re p re se n ta tio n o f n ty p ic a l decision s itu a tio n a nd t h e f o r c e s which d e t e r m i n e I t s outcome a r e r e p r o d u c e d i n Figure 1.

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th e d a ta f o r r e l a t i v e frequency a r e p re s e n te d only f o r the c o n d i t i o n o f u s u a l i n s t r u c t i o n s , a nd t h e n n o t i n a fo rm c o n ­ venient fo r our purposes.

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10

g i v e s t h e t h e o r e t i c a l c u r v e s drawn t o

t h e e m p i r i c a l d a t a f o r d e c i s i o n t im e f o r one o f J o h n s o n ’ s s u b j e c t s under the t h r e e c o n d itio n s d e s c rib e d above.

The

c o n v e r s i o n o f c o n f i d e n c e to t h e z s c a l e a l o n g t h e a b s c i s s a i s co nstan t under a l l th ree c o n d itio n s. t h i s conversion I s C s 32s,

The e q u a t i o n f o r

The c o n s t a n t f o r t h e c o n v e r s i o n

o f t h e t h e o r e t i c a l d e c i s i o n time c u r v e s i n t o u n i t s o f s e c o n d s i s a l s o t h e same f o r a l l t h r e e c o n d i t i o n s . c o n s t a n t i s 11.3*

T his

The b a s e c o n s t a n t i s d i f f e r e n t f o r t h e

t h r e e c o n d i t i o n s a s s h o u l d be e x p e c t e d i f t h e c h an g e i n a t t i t u d e a f f e c t s r e a c t i o n tim e.

I t i s i n te r e s ti n g to n o te,

h o w e v e r , t h a t t h e b a s e c o n s t a n t s a r e a b o u t t h e sarae f o r t h e a c c u r a c y and u s u a l i n s t r u c t i o n s . T here i s t e n t a t i v e c o r r o b o r a t i o n o f t h e t h e o r y i n t h a t w h i l e f o r t h e u s u a l i n s t r u c t i o n s th e r e s t r a i n i n g f o r c e is .8 8

. 4 0 , u n d e r c o n d i t i o n s e m p h a s i z i n g a c c u r a c y i t g o e s up t o and w ith i n s t r u c t i o n s em phasizing speed i t drops to . 1 0 .

How w e l l t h e t h e o r e t i c a l c u r v e s f i t

t h e e m p i r i c a l d a t a may

b e j u d g e d by t h e r e a d e r f o r h i m s e l f . T h ere i s a d d i t i o n a l e v i d e n c e f r o m o t h e r s o u r c e s t h a t d e g r e e o f c o n f l c e n c e i n o n e ’ s judgm ent i s a f a c t o r r e l a t e d to d e c is io n tim e.

Oe o rg e ( 1 0 ) c o n c l u d e d from h i s e x p e r i m e n t

th at decision-tim e

i n c r e a s e s w ith i n c r e a s in g doubt concern­

ing th e judgm ents.

T h i s e x p e r i m e n t was a g a i n a p s y c h o p h y s i ­

c a l one c o m p a r i n g l o u d n e s s o f n o i s e s .

Ifive c a t e g o r i e s of

r e s p o n s e w e re a l l o w e d a n d t h o s e c a t e g o r i e s w h i c h i n d i c a t e d u n c e r t a i n t y on t h e p a r t o f the s u b j e c t showed th e h i g h e s t a v e r a g e judgment t i m e s .

Ilennon ( 1 2 ) r e p o r t s a p sy c h o p h y ­

s i c a l e x p e r i m e n t on c o m p a r i s o n o f l e n g t h o f l i n e s

i n w h ic h

t h e s u b j e c t was a s k e d t o r a t e h i s ju d g m e n t c o n f i d e n c e i n one of fo u r c a t e g o r i e s : little

p e r f e c tly c o n fid e n t, f a i r l y con fid en t,

c o n f i d e n c e , an d d o u b t f u l .

The a v e r a g e t i m e o f j u d g ­

ment f o r t h e s e c a t e g o r i e s i n c r e a s e s r e g u l a r l y a s t h e c o n f i ­ dence d e c r e a s e s . T h e r e i s a l s o d a t a s h o w in g t h a t t h e r e l a t i o n s h i p s d e r i v e d from th e th e o ry h o ld a l s o in a r e a s o u t s i d e o f psycho­ p h y s ic a l judgm ents.

D a s h i e l l ( 6 ) i n an e x p e r i m e n t on a f f e c ­

t i v e judgments found r e s u l t s c o n s i s t e n t w ith the t h e o r y . T h e s u b j e c t s made j u d g m e n t s a s t o w h i c h o f a p a i r o f c o l o r s they p r e f e r r e d .

Dach c o l o r u s e d was compared w i t h e v e r y

o t h e r c o l o r and t h e r a n k o r d e r o f p r e f e r e n c e e s t a b l i s h e d on t h e b a s i s o f th e number o f t i n e s e a c h c o l o r was c h o s e n . 1 hen

t h e jud g m e n t t i m e s a r e a r r a n g e d a c c o r d i n g t o t h e num­

b e r o f s t e p s o f s e p a r a t i o n i n t h e p r e f e r e n c e s e r i e s be tw ee n

t h e two o o l o r s ' p r e s e n t e d , t h e d a t a i n .Figure l i b i s o b t a i n e d . A l t h o u g h we uo n o t know t h e r e l a t i o n s h i p b e tw e e n t h e a b s c i s ­ s a on t h i s g r a p h a nd t h e a b s c i s s a o f o u r t h e o r e t i c a l c u r v e s , it

i s c l e a r t h a t t h e same t y p o o f f u n c t i o n o b t a i n s .

course,

{Of

t h e r e i s no v a l u e f o r a e r o p r e f e r e n c e s c a l e s e p a r a ­

t i o n , s i n c e t h e s m a l l e s t s e p a r a t i o n , c o u l d be

1

: c o m p a r is o n

b e tw e e n a d j a c e n t members o f t h e p r e f e r e n c e s c r i e s . d in g to th e t h e o r e t i c a l f u n c tio n ,

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t h i s curve should l e v e l

o u t somewhat b e t w e e n 0 and I . ) T h e r e i s a l s o r e l e v a n t d a t a a v a i l a b l e from e x p e r ­ i m e n t s i n v o l v i n g c o n f l i c t betw een d i f f e r e n t g o a l s .

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ells

c o n d u c t e d an e x p e r i m e n t i n which c h o i c e s had t o be

made b e tw e e n d r i n k i n g l i q u i d s r a n g i n g i n t a s t e fro m d e s i r ­ ab le to u n d e sira b le .

Although th e d a ta i s not p r e s e n t e d

i n a fo rm c o n v e n i e n t f o r t h e p r e s e n t c o m p a r i s o n , t h e r e s u l t s a r e i n l i n e w i t h o u r t h e o r y i n t h a t th e a v e r a g e d e c i s i o n t i m e f o r c h o i c e s b e tw e e n s i n l i a r t a s t e s i s g r m m r t h a n f o r d issim ilar ta s te s,

s i m i l a r i t y a g a in b e in g d e fin e d i n terms

of s i m i l a r i t y in d e g re e o f p r e f e r e n c e . b a r k e r (1 ) r e p o r t s a stu d y o f s i m i l a r n a t u r e , haven l i q u i d s :

pineapple ju ic e,

orange j u ic e ,

tomato j u i c e ,

w a t e r , lem o n j u i c e , s a l t w a t e r , and v i n e g a r , we re p r e s e n t e d in p a i r s fo r choice.

Each l i q u i d was p a i r e d w i t h e v e r y

o t h e r l i q u i d a n d the p r e f e r e n c e r a n k i n g s d e t e r m i n e d I n a manner s i m i l a r t o t h a t use d lr> k a s h r e l l w ere e m p lo y ed ;

{b ) .

ivo v a r i a t i o n s

I n t h e ’’r e a l ” c h o i c e s i t u a t i o n t h e s u b j e c t s

a c t u a l l y had t o d r i n k some o f t h e l i q u i d

they chose; in the

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F i g u r e 11a ( T o p ) . Time F l a p s i n g D u rin g t h e R e s o l d t i o n o f C o n f l i c t Between A l t e r n a t i v e s S e p a r a t e d by D i f f e r e n t " D ista n c e s" i n the P re fe re n c e Series# (From r i a r k e r , 1) F i g u r e l i b ( B o t t o m ) . Time E l a p s i n g f o r E s t h e t i c J u d g m e n t s Between i l l t e r n a t i v e s S e p a r a t e d by D i f f e r ­ e n t " D i s t a n c e s " i n t h e P r e f e r e n c e S e r i e s (From D ashiell, 6 )

" h y p o t h e t i c a l ” c h o i c e s i t u t i o n t h e y w ere r e q u i r e d t o c h o o se t h e l i q u i d he w o u ld p r e f e r t o d r i n k I f r e q u i r e d t o do s o .

It

i s c l e a r t h a t t h e r e s t r a i n i n g f o r c e s a g a i n s t m aking a d e c i ­ s i o n a r e s t r o n g e r in th e " r e a l " c h o ic e s i t u a t i o n th an in th e " h y p o t h e t i c a l" c h o ic e s i t u a t i o n .

The d a t a f o r t h e s e two

g r o u p s a r e r e p r o d u c e d i n F i g u r e 11a* g rap h o f F ig u re l i b ,

As i n t h e c a s e o f th e

t h e r e l a t i o n b e tw ee n t h i s e m p i r i c a l

a b s o i s s a a n d o u r t h e o r e t i c a l a b s c i s s a i s unknown.

A g a in ,

h o w e v e r, i t i s o b v io u s t h a t t h e c u r v e s o b t a i n e d a r e o f t h e same g e n e r a l t y p e a s t h e t h e o r e t i c a l c u r v e s . l i n e w ith th e th e o ry ,

In a d d itio n , in

th e c u rv e o f t h e " h y p o th e tic a l" c h o ic e

s i t u a t i o n shows a lo w e r maximum d e c i s i o n tim e a n d l e s s s t e e p e lo p e th a n th e c u rv e f o r th e " r e a l " c h o ic e s i t u a t i o n .

(We

may a s s u m e t h a t t h e r e s t r a i n i n g f o r c e i n t h e " h y p o t h e t i c a l " s i t u a t i o n i s w e ak e r t h a n i n t h e " r e a l " s i t u a t i o n . ) The e v i d e n c e a l r e a d y e x i s t i n g fro m d i f f e r e n t a r e a s o f c h o io e s i t u a t i o n s l e n d s some w e i g h t t o o u r b e l i e f t h a t th e t h e o r e t i c a l a n a l y s i s p r e s e n te d here h o ld s f o r a l l ty p es o f s i t u a t i o n s i n w hich a c h o i c e b e tw ee n two a l t e r n a t i v e s m u st be m ade.

I t seem s s u f f i c i e n t t o w a r r a n t a more p r e c i s e

t e s t o f th e th e o ry .

SI

P a r t XI An E x p e r i m e n t a l T e s t o f A T heory o f B e d a i o n

C h a p te r VI PROCEDURE OF EXPERBOTTATION The t h e o r y a s o u t l i n e d i n P a r t I i s b e l i e v e d to be o o rre o t fo r a l l ty p es o f d e c isio n s i t u a t i o n s .

The more p r e ­

c i s e a n a l y s i s h a s b e e n e l a b o r a t e d o n l y f o r d e o i s i o n s i n w h ich a c h o i c e m ust b e made b e tw e e n one o f two p o s s i b l e a l t e r n a ­ tiv e s .

T h is a n a l y s i s s h o u l d h o ld f o r a n y s u c h s i t u a t i o n .

To t e s t t h i s t h e o r y e m p i r i c a l l y a p s y c h o p h y s i c a l e x p e r i m e n t w as u s e d .

The r e a s o n s

f o r t h i s c h o ic e a r e :

In th e f i e l d

o f p s y c h o p h y s i c s w© a r e a b l e t o s e t up s i t u a t i o n s w hich a r e r e l a t i v e l y f r e e fro m i n f l u e n c e s w h ic h c a n n o t be c o n t r o l l e d . I n a d d i t i o n , we a r e a b l e , i n t h i s a r e a , to o b t a i n q u a n t i t a ­ t i v e m e a s u r e m e n ts t o t h a t d e g r e e o f p r e c i s i o n w hich i s r e ­ q u ire d f o r p ro v in g o r d isp ro v in g a q u a n ti t a t iv e th e o ry .

A

m eth o d o f c o n s t a n t s t i m u l i was em ployed i n a two c a t e g o r y e x p e r i m e n t i n w h ic h a ju d g m e n t was to be made a s t o w h e th e r one l i n e w as l o n g e r o r s h o r t e r t h a n a n o t h e r l i n e . A p p a ra tu s: Two b l a c k m e t a l b o x e s w e re u se d f o r p r e s e n t a t i o n o f th e s tim u li. in s id e each box.

O r d i n a r y e l e c t r i c l i g h t b u l b s w ere p l a c e d I n f r o n t o f e a c h box was an o p e n i n g , 3 /8

i n c h w id e , r u n n i n g t h e l e n g t h o f t h e b o x .

A m etal s t r i p ,

r u n n i n g t h r o u g h g r o o v e s on e a c h s i d e o f t h e o p e n i n g , c o u ld b e moved back a n d f o r t h s o a s t o c o v e r up a l l o r a n y d e s i r e d

p o r t i o n o f th© o p en p a r t .

The o p e n in g I t s e l f w as c o v e r e d

w i t h h e a v y g ro u n d g l a s s t h r o u g h w h ic h t h e l i g h t c o u ld s h i n e . The b o x e s w e re m o u n te d upon a t a b l e 31 i n c h e s h i g h , so t h a t t h e o p e n i n g s i n th© f r o n t o f th e b o x e s w ere v e r t i ­ c a l.

The d i s t a n c e b e tw e e n t h e n e i g h b o r i n g e d g e s o f t h e two

v e r t i c a l l i n e s w as 9 i n c h e s .

A b lac k c a rd b o a rd s c re e n w ith

two s l i t s i n i t was m o unted i n f r o n t o f t h e a p p a r a t u s so t h a t t h e o n l y t h i n g v i s i b l e fro m t h e f r o n t wt.s a homogeneous b l a c k b a c k g r o u n d and t h e

two v e r t i c a l l i n e s .

The e x p e r i m e n t s

w ere a lw a y s c a r r i e d o u t i n t o t a l d a r k n e s s so t h a t n o t h i n g c o u ld be s e e n u n t i l t h e v e r t i c a l H u e s w ere I l l u m i n a t e d . The s u b j e c t s s a t i n a c h a i r 130 i n c h e s away from t h e a p p a r a t u s , an d

)n a l i n e d i r e c t l y midway th© two v e r t i ­

cal stim u li. The two l i n e s w ere p r e s e n t e d s i m u l t a n e o u s l y to che s u b j e c t f o r a d u r a t i o n o f .5 s e c o n d s .

The d u r a t i o n o f th e

p r e s e n t a t i o n o f s t i m u l i was c o n t r o l l e d by an e l e c t r o n tub© ta o h ls to s c o p ic tim e r.

When t h e t a o h i s t o s c o p © was t u r n e d o n ,

th u s illu m in a tin g th e v e r t i c a l lin e s , sta rte d .

an e l e c t r i c s t o p c lo c k

A f t e r .5 s e c o n d s t h e l i g h t s w ent o f f a u t o m a t i c a l l y

b u t t h e c l o c k k e p t r u n n i n g u n t i l th e s u b j e c t ’ s r e s p o n s e a c t i ­ v a t e d a v o i c e key w h ic h s t o p p e d t h e c l o c k . c i r c u i t u s e d i e shown i n F i g u r e 1&»

The e l e c t r i c a l

A fte r each resp o n se,

t h e e x p e r i m e n t e r , u s i n g a v e r y dim f l a s h l i g h t , r e c o r d e d th e p r o p e r d a t a and s e t t h e a p p a r a t u s f o r th© n e x t p r e s e n t a t i o n . The s t i m u l u s l i n e a t t h e l e f t o f t h e s u b j e c t was a lw a y s k e p t a t a l e n g t h o f 7 i i n c h e s .

T h is w© s h a l l r e f e r

53

to as th e s t a n d a r d ,

Th© l e n g t h o f t h e o t h e r s t i m u l u s l i n e

w as a d j u s t e d b y m eans o f th© s l i d i n g m e t a l s t r i p w h ic h had a c o n v e n ie n t m a tr ix on i t s b ack .

T h is l i n e we s h a l l c a l l

th e v a r ia b le s tim u lu s . F i f t e e n p o s i t i o n s o f t h e v a r i a b l e s t i m u l u s were u s e d , s e v e n p o s i t i o n s shortex* t h a n t h e s t a n d a r d , s e v e n p o s i ­ t i o n s l o n g e r t h a n t h e s t a n d a r d , a n d one p o s i t i o n e q u a l t o th© s t a n d a r d *

I n s i x t e e n t h s o f a n i n c h d i f f e r e n c e b e tw ee n

th e v a ria b le and

th e s t a n d a r d , th e s e

f if te e n p o sitio n s

w ere:

- 8 , - 6 , -4* - 2 , - 1 ,

0 , * 1 , * 2 , *4 , + 6, +8,

th e v a r i a b l e ranged

fro m a n i n c h l o n g e r

-1 6 , -1 2 ,

> 1 2 , >16*

T h u s,

th an th e s ta n d a r d to

an in c h s h o rte r

t h a n t h e s t a n d a r d . T h is

r a n g e i s much l a r g e r t h a n t h a t u s e d i n th e u s u a l p s y c h o ­ p h y s i c a l e x p e r i m e n t s , b u t was n e c e s s a r y h e r e to make s u r e t h a t t h e b a s e v a l u e f o r d e c i s i o n tim e was r e a c h e d , fo r purposes of f i t t i n g

T hat i s ,

t o o u r t h e o r e t i c a l f u n c tio n © i t i s

n e c e s s a r y t o know th© d u r a t i o n o f ^ im m e d ia te * d e c i s i o n .

It

may a l s o be n o t i c e d t h a t t h e v a r i a b l e p o s i t i o n s a r e g ro u p e d h e a v i l y a r o u n d th© p o i n t o f o b j e c t i v e e q u a l i t y .

T h is w as

f e l t to be a d v is a b le s in c e th e t h e o r e t i c a l l y p r e d ic te d c u rv e s show th© m ost r a p i d a c c e l e r a t i o n I n t h i s a r e a , Th© v a r i a b l e s t i m u l u s p o s i t i o n s w ere p r e s e n t e d i n th© f o l l o w i n g p r e a r r a n g e d o r d e r :

- 6 , - 2 , - 1 2 , * 2 , >12,

♦4 , —4 > —1 6 , >8 , 0 , - 8 , —1 , >1 , > 16, >6 , —8 , >1 2 , 0 , >4, - 1 2 , - 4 , >8 , - 1 , - 1 6 , >6 , - 6 , >1, - 2 , 4*16, > 2,

A fte r th is

o r d e r was camp 1©t e d th© r e v e r s e o r d e r w as g i v e n and t h e n t h e w h o le f o r w a r d and r e v e r s e s e q u e n c e c o n t i n u e d .

55 C onduct o f th e E x p e rim e n t: F i v e s u b j e c t s w ere u se d I n t h e e x p e r i m e n t .

E ach

s u b j e c t made ju d g m e n ts u n d e r f o u r d i f f e r e n t s e t s o f I n s t r u c ­ tio n s .

F o r e a c h o f t h e f o u r c o n d i t i o n s , e a c h s u b j e c t made

40 Ju d g m e n ts a t e a c h v a r i a b l e s t i m u l u s p o s i t i o n , m aking a t o t a l o f 2400 ju d g m e n ts by e a c h s u b j e c t .

The e x p e r i m e n t a l

s e s s io n s r a r e l y l a s t e d o v e r an h our f o r any s u b je c t because o f t h e f a t i g u i n g n a t u r e o f t h e e x p e rim e n t*

An a v e r a g e o f

a b o u t 120 ju d g m e n ts c o u ld be made i n one h o u r . 1.

The c o n d i t i o n w h ic h s h a l l h e r e a f t e r be r e f e r r e d

t o a s t h e ”U s u a l C o n d i t i o n ” was t h e f i r s t t o be g i v e n . I n s t r u c t i o n s t o th© s u b j e c t f o r t h i s

c o n d itio n fo llo w :

In stru c tio n s When t h e room i s d a r k e n e d , you w i l l s e e two v e r t i c a l l i n e s i l l u m i n a t e d f o r a p e r i o d o f t i m e . You a r e to make a ju d g m e n t a s t o w h e th e r t h e l i n e on t h e r i g h t i s l o n g e r o r s h o r t e r t h a n t h e l i n e on t h e l e f t . I f t h e l i n e on t h e r i g h t i s s h o r t e r , you w i l l s a y " s h o r t e r " ; i f t h e l i n e on t h e r i g h t i s l o n g e r , you w i l l s a y " l o n g e r . ” Do n o t s a y a n y o t h e r w o rd s b e f o r e t h e ju d g m en t o f l o n g e r o r s h o r t e r . When you g i v e y o u r Ju d g ­ m e n t, e n u n c i a t e th e word c l e a r l y and d i s t i n c t l y and f a i r l y l o u d l y . A f t e r m ak in g e a c h judgm ent you a r e t o e x p r e s s y o u r c o n f i d e n c e t h a t t h e jud gm en t was c o r r e c t I n 50$ c o n f i d e n c e means a v e r ­ th e fo llo w in g te rm s: a g e o r medium c o n f i d e n c e , t h e amount o f c o n f i d e n c e on© u s u a l l y h a s i n m ost o f o n e ’ s ju d g m e n ts ; 7 5 $ means c o n f i d e n c e d e f i n i t e l y a b o v e a v e r a g e , t h e am ount o f c o n f i d e n c e you h a v e when you a r e q u i t e s u r e you a r e r i g h t ; s i m i l a r l y , 25$ means d e f i n i t e l y b e lo w a v e r a g e c o n f i d e n c e , th e am ount you h a v e when you a r e o n l y g u e s s i n g ; 100$ c o n f i d e n c e i s a t th© e x tr e m e end o f th© s c a l e o f c o n f i d e n c e a n d means c o m p le te c e r t a i n t y , no p o s s i b i l i t y o f e r r o r ; s i m i ­ l a r l y , 0$ c o n f i d e n c e i s a t th e o t h e r end o f th e s c a l e o f c o n f i d e n c e a n d roe an s no c o n f i d e n c e i n

The

56 y o u r ju d g m e n t w h a t e v e r , you a r e be w rong a s r i g h t .

Ju st as lik e ly to

Thu©, you a r e t o c o n s t r u c t a " m e n t a l s c a l e " o f c o n f i d e n c e w i t h 50$ i n t h e m i d d l e , 25% and 75% on e a c h s i d e o f t h e m id d l e r a n g e , and 100$ a n d 0$ *way o u t a t t h e end© o f t h e s c a l e * Som etim es s u b j e c t s r e p o r t t h a t i n the p r o ­ c e s s o f m aking a ju d g m e n t t h e i r c o n f i d e n c e f l u c ­ t u a t e s c o n s i d e r a b l y o v e r an a p p r e c i a b l e r a n g e , t h i s h a p p e n s r a r e l y b u t i f i t d o e s h a p p e n , th e n t h e c o n f i d e n c e r a t i n g w hich you g i v e i s t o be a p p ro x im a te ly an a v e ra g e o f th e f l u c t u a t i o n s w h ic h o c c u r r e d . The l a s t two s e n t e n c e s i n t h e f i r s t p a r a g r a p h w e re i n s e r t e d b e c a u s e o f th© u s e o f a v o i c e k e y t o s t o p th e c lo c k .

The se c o n d and t h i r d p a r a g r a p h s , d e s c r i b i n g

t h e c o n f i d e n c e s c a l e a r e r e p e a t e d v e r b a t i m from Jo h n so n (1 3 ).

The l a a t p a r a g r a p h i n

Lhese i n s t r u c t i o n s was i n ­

s e r t e d i n an e f f o r t to s t a b i l i z e th e u se o f th e c o n f i d e n c e ra tin g s fo r a l l th e s u b je c ts . are

Our t h e o r e t i c a l p r e d i c t i o n s

s t a t e d i n te r m s o f t h e means o f g i v e n d i s t r i b u t i o n

fu n c tio n s.

A co n fid e n ce r a t i n g i s ,

h o w e v er, g i v e n a f t e r

t h e ju d g m e n t h&3 b e e n made and so may v e ry l i k e l y r e p r e ­ s e n t n o t t h e mean o f t h e f l u c t u a t i o n s b u t t h e v a l u e o c c u r ­ r i n g a t th© tim e t h e d e c i s i o n was m ade.

I n some c a s e s i t

m ig h t even r e p r e s e n t a r e a c t i o n t o h a v in g made a g iv e n j u d g m e n t.

T h erefo re,

th e e f f o r t to s t a b i l i z e th e p o s itio n o f

th© c o n f i d e n c e r a t i n g s was m ade. B e f o re th© a c t u a l e x p e r i m e n t a t i o n b e g a n t h e s u b ­ j e c t s w ere g i v e n s u f f i c i e n t p r a c t i c e t r i a l s t o a c c u s to m them t o t h e s i t u a t i o n .

Ho a r b i t r a r y l i m i t was s e t on th©

57

numb o r o f p r a c t i c e t r i a l s *

They were c o n tin u e d , u n t i l t h e

s u b j e c t s w ore s u f f i c i e n t l y a t e a s e w i t h t h e p r o c e d u r e * 2.

I k e " A c c u ra c y C o n d i t i o n ’* was g iv e n t o t h e s u b ­

j e c t s a f t e r t h e " U s u a l C o n d i t i o n " had b e e n c o m p le te d *

The

f o l l o w i n g a d d i t i o n a l I n s t r u c t i o n s w ere g i v e n t h e s u b j e c t s ! A ccuracy I n s t r u c t i o n s I n t h i s p a r t o f t h e e x p e r i m e n t you a r e t o make y o u r judgmoiibs a s a c c u r a t e l y a s you c a n . See i f you c a n b e e v e n m e re a c c u r a t e you w ere b e fo r e * T ry t o mate® no e r r o r s *

th a n

Remember, a c c u r a c y i s t h e i m p o r t a n t t h i n g h e ro * The a b o v e i n s t r u c t i o n s a r e assu m e d

go

in c r e a s e

th© r e s t r a i n ­

i n g f o r c e s o p p o s i t e to l e a v i n g t h e r e g i o n o f d e c i s i o n above w hat th e y w ere u n d e r th e " U s u a l C o n d i ti o n * " 3*

The "S p eed C o n d i t i o n " w as a d m i n i s t e r e d a f t e r

t h e " A c c u r a c y C o n d i ti o n * w i t h th e f o l l o w i n g i n s t r u c t i o n s : S peed I n s t r u c t i o n s I n t h i s p a r t o f t h e e x p e r im e n t you a r e t o mate© y o u r ju d g m e n ts a s r a p i d l y a s you c a n . Remember, s p e e d i s th e m ost i m p o r t a n t t h i n g I n t h i s p a r t o f t h e e x p e r im e n t* T h e s e I n s t r u c t i o n s aw© assu m e d to lo w e r th© r e s t r a i n i n g f o r c e s b e lo w w h a t t h e y w e re i n th© " U s u a l C o n d i t i o n . " 4* t o be g i v e n .

The " C o n s t a n t - E r r o r C o n d i t i o n " was t h e l a s t The i n s t r u c t i o n s w ere as f o l l o w s :

{These i n ­

s t r u c t i o n s w ere p r e s e n t e d a s th o u g h s p e c i f i c f o r th© s u b j e c t i n v o lv e d *

F o r t h r e e o f th© s u b j e c t s t h e y w ere p r e c i s e l y a s

s t a t e d belovm

F o r t h e o t h e r two s u b j e c t s t h e word " s h o r t e r "

s h o u l d be s u b s t i t u t e d f o r t h e w ord " l o n g e r " w h e r e v e r i t o ccu rs and v ic e v e rs a .) I n s t r u c t i o n s t o ________ I n a l l o f t h e t h r e e p r e c e d i n g v a r i a t i o n s you h a v e c o n s i s t e n t l y been making a n e r r o r i n s a y i n g " s h o r t e r " t o o many t i m e s . Even when th© l i n e was s l i g h t l y l o n g e r you would v e r y f r e q u e n t l y s a y sh o rte r. I w ould l i k e you t o t r y n o t t o make t h i s e r r o r a g a in in t h i s v a r i a t i o n , P l e a s e h e a r i n mind t h a t you h a v e a t e n d e n c y t o s a y s h o r t e r w h ic h i s p r o d u ­ c in g t h i s e r r o r i n your judgm ents, and t r y to c o r ­ r e c t t h i s te n d e n c y . S ee i f you c a n e l i m i n a t e t h i s e r r o r . T h e se i n s t r u c t i o n s a r e assu m ed t o i n c r e a s e t h e r e s t r a i n i n g f o r c e a g a i n s t m ak in g a d e c i s i o n i n o n e d i r e c t i o n more t h a n i n t h e o t h e r .

The i n s t r u c t i o n s a s s t a t e d abo ve

s h o u l d make t h e r e s t r a i n i n g f o r c e a g a i n s t " s a y i n g *s h o r t e r * " g r e a t e r th an th e r e s t r a i n i n g f o r c e a g a i n s t " sa y in g ’ lo n g e r .* " D e s c rip tio n of th e S u b j e c t s : The f i v e s u b j e c t s u s e d i n t h e e x p e r i m e n t were i Ben Ti H e r m a n

(B. R . ) ,

Mr.

a g r a d u a t e s t u d e n t i n t h e C h i l d Wel­

f a r e R e s e a r c h S t a t i o n ; H i s s H e le n S a n d s (H. S . ) , a h e ad t e a c h e r i n t h e Iowa P r e - S c h o o l L a b o r a t o r i e s ; M i s s J o h a n n a Boet ( J . 3 1 ), a g r a d u a te s t u d e n t i n the Child P e l f a r e R e s e a rc h S t a t i o n ; M iss Nancy P h i l l i p s

(N. P . ) , a g r a d u a t e s t u d e n t i n

t h e D e p a r t m e n t o f P s y c h o l o g y ; a n d Miss G r a c e S h a t t y n (&. S . ) , a g r a d u a te s t u d e n t i n th e Department o f P sychology.

A H o f th e s u b j e c t s , w i t h t h e e x c e p t i o n o f LL V/., w e re c o m p l e t e l y n a i v e as t o t h e p u r p o s e o f the e x p e r i m e n t and knew n o t h i n g o f t h e t h e o r y i n v o l v e d .

S u b j e c t 3 . v/. was

a oq.ua i n t e d w i t h th e p u i p o s e o f t h e e x p e r im e n t a n d knew t h e g e n e r a l o u t l i n e s o f t h e theory*. I n t h e " Cons t a n t - h r r o r C o n d i t i o n " s u b j e c t s 3 . w . , E. S ., and above.

Gr.

S .,

w ere g i v e n t h e i n s t r u c t i o n s a s s t a t e d

The o t h e r two s u b j e c t s w ere g i v e n th e i n s t r u c t i o n s

w ith " lo n g e r" and " s h o r t e r " r e v e r s e d . Data R ecorded: F o r e a c h jud gm en t t h r e e m e a s u r e s w ere r e c o r d e d , n a m e ly , th e ju dgm ent " l o n g e r " o r " s h o r t e r , " t h e t im e fro m t h e s t a r t o f t h e p r e s e n t a t i o n o f th© s t i m u l i t o t h e r e s p o n s e by t h e s u b j e o t , and t h e s u b j e c t ’ s r a t i n g o f c o n f i d e n c e .

C h a p te r V I I COMPARISON OF RESULTS WITH PREDICTIONS IN CHAPTER I I I The d a t a g a t h e r e d i n

t h i s ex p erim en t a r e o rg a ­

n i s e d f o r a n e v a l u a t i o n o f t h e d e r i v a t i o n s fro m C h a p te r III.

These d e r i v a t i o n s a r e r e p e a te d h e re to g e th e r w ith th e

re le v a n t r e s u lts .

( O b v i o u s l y t h e s e d a t a c a n n o t be u s e d f o r

an e v a l u a t i o n o f th e p r e d i c t i o n s in v o lv in g th r e e c a t e g o r i e s o f j u d g m e n t .) D e r i v a t i o n J..

As r e l a t i v e f r e q u e n c y a p p r o a c h e s

50$ , d e c i s i o n t i m e a p p r o a c h e s a maximum. T a b le 4 p r e s e n t s t h e n e c e s s a r y d a t a f o r an e v a l u ­ a tio n of t h i s sta te m e n t.

The d i s t a n c e i n s t i m u l u s u n i t s

( s i x t e e n t h s o f a n i n c h ) b e tw e e n t h e h i g h e s t v a l u e o f d e c i s i o n tim e a n d th© 50$ p o i n t o f t h e r e l a t i v e f r e q u e n c y o g i v e a r e p r e s e n te d f o r e ach of th e f i v e s u b j e c t s , fo r a l l fo u r c o n d i­ t i o n s o f ju d g iie n t.

The 50$ p o i n t o f t h e r e l a t i v e f r e q u e n c y

o g iv e h as been c a l c u l a t e d u sin g th e M u ller-U rb an w e ig h ts . The h i g h e s t d e c i s i o n - t i m e v a l u e s h o u l d n o t be e x p e c t e d t o c o r r e s p o n d e x a c t l y w i t h t h e 50$ r e l a t i v e f r e q u e n c y p o i n t i n s u c h an a n a l y s i s s i n c e t h e d e c i s i o n - t i m e v a l u e u s e d a lw a y s f a l l s a t one o f th© v a r i a b l e s t i m u l u s p o s i t i o n s w h i l e t h e 50$ r e l a t i v e f r e q u e n c y p o i n t u s u a l l y f a l l s b e tw e e n two stim u lu s v a lu e s .

T h erefo re, i t

i s a q u e s t i o n o f how many

s t i m u l u s u n i t s s e p a r a t i o n l i e ; b e tw ee n t h e two p o i n t s .

As

Table 4 D i f f e r e n c e s B etw een Maximum D e c is io n - T im e a n d 50$ R e l a t i v e .Frequency S u b je c t

H. S . B. VV. a# s . jr« b . N. P .

U sual

1 .4 2 .32* •42* 1 .0 0 1 .0 8

A c c u ra c y

.10* 1 .5 3 .96* 1 .4 4 •84

Speed

.17* .82* 1.2 3 • 59 .7 2

C o n stan t

1 .1 7

.3 0 *

• 57 .10* .73

A verage

.715 *743 .795 *783 .843

* Maximum D e c is io n - T im e c l o s e r t o 50$ p o i n t t h a n any o th e r s tim u lu s p o in t#

can b e s e e n fro m t h e

T able, in 8 o u t o f th e 20 c o m p a r is o n s

t h e maximum d e c i s i o n - t i m e i s a t t h e s t i m u l u s p o s i t i o n c l o s ­ e s t t o th© 50$ p o i n t o f r e l a t i v e f r e q u e n c y . tio n s ,

W ith two e x c e p ­

a l i t h e o t h e r maximum d e c i s i o n - t i m e s l i e

a t th a t stim ­

u l u s p o s i t i o n w h ic h i s n e x t c l o s e s t t o t h e 50$ p o i n t o f r e l a t i v e frequency*

The two e x c e p t i o n s a r e :

" c o n s t a n t * c o n d i t i o n ; an d s u b j e c t N* p . ,

s u b j e c t H. S . ,

" u s u a l” c o n d itio n *

I n b o t h t h e s e i n s t a n c e s t h e maximum d e c i s i o n - t i m e i s two s t i m u l u s p o s i t i o n s away from t h e 50$ p o i n t o f r e l a t i v e freq u en cy . The d a t a can a l s o be e v a l u a t e d fro m t h e p o i n t o f v ie w o f t h e d i s t a n c e ( i n s i x t e e n t h s o f a n i n c h ) b e tw ee n t h e two p o i n t s .

The l a s t colum n i n th e T a b le g i v e s t h i s a v e r a g e

d is ta n c e f o r each su b je c t*

For no s u b je c t i s

t h i s av erag e

d i s t a n c e g r e a t e r t h a n o n e s i x t e e n t h o f a n in c h * One can s t a t e t h a t f o r e i t h e r m ethod o f c o m p a r is o n , th© c o r r e s p o n d e n c e be tw ee n maximum d e c i s i o n - t i m e and 50$ r e l a t i v e f r e q u e n c y i s e x t r e m e l y d o s e J? t Th© a n s w e r t o t h e q u e s t i o n o f when t h e c o r r e s ­ p o n d e n c e betw een d a t a and t h e o r y i s c l o s e o r i s n o t c l o s e m u s t be made on a r e l a t i v e l y a r b i t r a r y b a s i s . No a p r i o r i r u l e s c a n u s u a l l y be l a i d down f o r s u c h a J u d g m e n t The p a r t i c u l a r s i t u a t i o n w i l l d e t e r m i n e w h e th e r i n c o n s i s t e n c i e s i n t h e d a t a a n a d e v i a t i o n s fro m t h e p r e d i c t i o n s c a n be c o n s id e re d u n im p o rtan t o r a r e s u f f i c i e n t t o w a rra n t th e c o n c l u s i o n t h a t th e t h e o r y i s n o t c o r r o b o r a t e d . In th e f o l ­ lo w i n g p r e s e n t a t i o n o f r e s u l t s t h e a u t h o r h a s s t a t e d h i s own Ju d g m e n ts i n t h i s r e s p e c t .

D e riv a tio n

The d e c i s i o n - t i m e c u r v e b e g i n s t o

r i s e a t a p o i n t f a r t h e r rem oved fro m t h e 50% p o i n t th a n does th e r e l a t i v e freq u e n cy c u rv e . T h is d e r i v a t i o n i s

c o m p l e t e l y b orn o u t by t h e d a t a

a s can be s e e n by t h e T a b le s i n t h e A p p en d ix vihere t h e c o m p le te d a ta f o r th e s u b j e c t s a re p r e s e n te d .

I n ©very c a s e

t h e d e c i s i o n tim e h e e p s i n c r e a s i n g w h i l e th e r e l a t i v e f r e ­ q u e n cy i s s t i l l a e r o p e r c e n t

( o r on© h u n d re d p e r c e n t ) .

A

more c o m p le te d i s c u s s i o n o f t h i s r e s u l t w i l l be p r e s e n t e d i n t h e f o l l o w i n g C h a p t e r when th e t h e o r e t i c a l c u r v e s a r e f i t t e d t o th e e m p iric a l d a ta . D e riv a tio n

rfh» maximum d e c i s i o n tim e i n c r e a s e s

w i t h an I n c r e a s e i n th© m a g n itu d e o f r e s t r a i n i n g f o r c e . T a b le $ p r e s e n t s th© d i f f e r e n c e i n s e c o n d s b e ­ tw een t h e h i g h e s t and l o w e s t p o i n t s o f d e c i s i o n - t i m e f o r e a c h s u b j e c t i n e a c h o f th© f o u r c o n d i t i o n s .

T h is d i f f e r ­

e n c e m e a s u r e i s u s e d r a t h e r th a n th© a b s o l u t e maximum d e o i s i o n - t i m e so t h a t o u r c o m p a r is o n s w i l l be i n d e p e n d e n t o f th e b a se v a lu e o f d e c is io n - tim e . d e c isio n )

is

The b a s e v a l u e (" Im m e d ia te *

s o m e th in g w h ic h d e p e n d s upon t h e r e a c t i o n - t i m e

o f th© i n d i v i d u a l ( a s d e te r m i n e d by p r e v i o u s a t t i t u d e and th e in s t r u c t i o n s )

I n a way v&th w h ich t h e p r e s e n t t h e o r y

i s co n cern ed . I t w i l l be rem em bered t h a t th e " a c c u r a c y ” c o n d i ­ t i o n i s assum ed t o i n c r e a s e t h e r e s t r a i n i n g f o r c e s o v e r t h a t o f th e " u s u a l " c o n d i t i o n ; t h a t t h e " s p e e d * c o n d i t i o n i s assum ed t o l o w e r th e r e s t r a i n i n g f o r c e s below t h a t o f th©

64

T a b le 5 D i f f e r e n c e i n S e c o n d s Betw een H i g h e s t a n d L o w est P o i n t s o f t h e D e c is io n - T im e Curve S u b je c t

U sual

H. S . B. W. a. s.

• 64 1.8 5

J . B. N. P .

.40 .69

1 .3 0

A c c u ra c y

.73

2 .4 6

2.37 *74 1 .1 4

Speed

.56 1.50 .74 .19 .28

C o n stan t

.5 8 2 .4 6

.77 .47 .56

" u s u a l " c o n d i t i o n ; a nd t h a t th e " c o n s t a n t " c o n d i t i o n i s assumed t o i .c r e a s e t h e r e s t r a i n i n g f o r c e s i n one d i r e c t i o n , th u s i n c r e a s i n g th e average r e s t r a i n i n g f o r c e over t h a t o f the "speed" co n d itio n , ‘f a b l e

5

shows t h a t i n ©very c a s e th© r e s u l t s a r e i n

l i n e w ith th e theory*

The d i f f e r e n c e b e t w e e n t h e h i g h e s t

and l o w e s t d e c i s i o n - t i m e p o i n t s i s a l w a y s g r e a t e r f o r t h e " a c c u r a c y ” c o n d i t i o n t h a n f o r t h e " u s u a l " c o n d i t i o n ; a lw a y s l e a s f o r the "speed" c o n d itio n than f o r the "usual" condi­ t i o n ; a n d a lw a y s g r e a t e r f o r th© " c o n s t a n t " c o n d i t i o n t h a n fo r th e "speed" condition* D e r i v a t i o n 3 seem s t o

;>e c o r r o b o r a t e d w i t h o u t

exception. D eriv ation

4

.

The p r e c i s i o n o f t h e r e l a t i v e

f r e q u e n c y o g i v o i n c r e a s e s a s th© r e s t r a i n i n g f o r c e i n c r e a s e s * T h i s d e r i v a t i o n may b© a l t e r n a t i v e l y s t a t e d :

The

sig m a o f t h e r e l a t i v e f r e q u e n c y o g i v e d e c r e a s e s a s she r e s t r a i n i n g f o r c e i n c r e a s e s — s i n c e t e sigm a i s i n v e r s e l y r e l a t e d to th e p r e c i s i o n .

Table

6

p r e s e n t s th e sigmas of th e

r e l a t i v e freq u en cy o g iv es f o r each s u b je c t under each condit i on • A g lan ce through t h i s

^ a b l e u n d e r t h e columns

h e a d e d " s i g m a " shows a n o t h e r f a c t o r t o be o p e r a t i n g *

The

g e n e r a l t r e n d i s f o r the sigm as t o d e c re a s e in the su c c e s­ sive co n d itio n s.

The more t im e th© s u b j e c t s s p e n t m aking

judgm ents i n t h e e x p e rim e n ta l s i t u a t i o n ,

th© more a c c u r a t e

66 t h e y becam e.

T h is i s n o t a s p r e d i c t e d fr o m t h e t h e o r y b u t

i s e a s i l y u n d e r s t a n d a b l e us cm a d a p t a t i o n phenomenon.

The

m ere p r o c e s s o f becom ing a c c u s to m e d t o t h e s i t u a t i o n , b e i n g m ore a n d laore a t e a s e w i t h th e p r o c e d u r e and b e in g a b l e t o a d j u s t o n e ’ s p e r c e p t i o n t o t h e demands o f t h e s i t u a t i o n may v e ry e a s i l y le a d to th e o b serv ed r e s u l t o f in c re a s in g accu­ r a c y o f ju d g m e n t.

T h is d i s t u r b i n g f a c t o r p r e v e n t s a n a d e ­

q u a t e t e s t o f th© d e r i v a t i o n . T h ere a r e ,

how ever, d e v i a t i o n s f ro m t h i s d e c r e a s ­

i n g t r e n d and t h e s e d e v i a t i o n s seem t o be i n l i n e w i t h t h e p re d ic tio n s.

T h u s, s u b j e c t H. S . and s u b j e c t B. W. b o t h

show s ig m a s w h ic h i n c r e a s e from t h e " a c c u r a c y ” t o th e "sp eed ” c o n d itio n , in l i n e w ith th e t h e o r e t i c a l p r e d ic tio n s * The s ig m a s s h o u l d , a c c o r d i n g t o th e t h e o r y , d e c r e a s e fro m t h e " u s u a l " t o t h e " a c c u r a c y ” c o n d i t i o n s and a g a i n from t h e "sp eed " to th e " c o n s ta n t" c o n d itio n . fo re,

In th e se c a s e s ,

th e re ­

t h e a d a p t i v e phenomenon i s w o rk in g i n t h e same d i r e c ­

t i o n a s t h e f a c t o r s t a k e n i n t o a c c o u n t i n th e t h e o r y ,

w ith

t h i s r e in f o r c in g p ro c e ss i t i s n o t s u r p r is in g th a t four of th© f i v e s u b j e c t s show s ig m a s w hich d e c r e a s e f r o n t h e " u s u a l" to th e "ac c u ra c y " c o n d itio n

( s u b j e c t N* D. shoves a

n e g l i g i b l e i n c r e a s e ) and a l l f i v e show s ig m a s w h ic h d e c r e a s e from t h e " s p e e d " t o t h e " c o n s t a n t " c o n d i t i o n . I t i s r a t h e r e q u iv o c a l o s to w h e th er o r n o t D e ri­ v a t i o n U i s s u p p o r t e d by t h e d a t a .

On th e w h o le , c o n s i d e r ­

i n g th e r a t h e r s t r o n g t r e n d f o r t h e sig m a s t o d e c r e a s e and

t h e e x c e p t i o n s I n l i n e w i t h t h e t h e o r y , one w o u ld be i n ­ c lin e d to a c c e p t D e riv a tio n 4 a s t e n t a t i v e l y c o rro b o ra te d . D e riv a tio n

I f t h e r e s t r a i n i n g fo re© i s o f

d i f f e r e n t m ag n itu d e i n d i f f e r e n t d i r e c t i o n s ,

th e 50$ p o i n t

o f r e l a t i v e f r e q u e n c y i s s h i f t e d t o w a r d s ^he s i d e o f th© g re a te r re s tra in in g fo rce .

(The o t h e r p o i n t s

in D e riv a tio n

5 w i l l b e d e a l t w i t h in t h e f o l l o w i n g C h a p t e r . ) S u b j e c t s H. S . , B. W., a n d 0 . S . had b e en t o l d i n t h e " c o n s t a n t " c o n d i t i o n t h a t t h e y had p r e v i o u s l y b een ma­ k i n g a n e r r o r I n th© d i r e c t i o n o f s a y i n g s h o r t e r to o many tim e s.

F o r t h e s e s u b j e c t s , t h e n , th© r e s t r a i n i n g f o r c e

a g a in s t " sa y in g ’ s h o r t e r '" i s g r e a te r 'l o n g e r * '"

than a g a i n s t " s a y i n g

A c c o r d i n g t o t h e t h e o r y th e 5G$ p o i n t o f t h e

r e l a t i v e f r e q u e n c y o g i v e s h o u l d s h i f t i n th© d i r e c t i o n o f sh o rte r. T a b le 6 g i v e s t h e m eans o f th e r e l a t i v e f r e q u e n c y o g i v e s c a l c u l a t e d w i t h t h e us© o f th e M u l l e r ~Drban w e i g h t s . T h ese v a l u e s g i v e t h e p o s i t i o n o f t h e 50% p o i n t on t h e s t i m ­ u l u s c o n tin u u m , ♦ b e i n g t h e d i r e c t i o n where t h e v a r i a b l e i s l o n g e r t h a n t h e s t a n d a r d , a n d - b e i n g t h e d i r e c t i o n where t h e v a r i a b l e i s s h o r t e r th a n th e s t a n d a r d .

Th us, a v a l u e

o f + 2 . 5 $ m oans t h a t t h e 50% p o i n t o f t h e r e l a t i v e f r e q u e n c y o g i v e o c c u r s when t h e v a r i a b l e i s 2 .5 8 s i x t e e n t h s o f an i n c h l o n g e r t h a n th e s t a n d a r d . Th© r e s u l t s a r e i n a l l c a s e s a c c o r d i n g t o th e th e o re tic a l p re d ic tio n .

I n t h e c a s e o f s u b j e c t H. S . ,

th©

-p td a «h cd m 4*

Means

and Standard D eviations in Stimulus of the R e la tiv e Frequency O give

U n its

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H *AtO W\© -4 -cm •

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nsk nam ely 4 6 .0 and 2 .6 0 r e s p e c ­ tiv e ly . F o r S u b j e c t G, S .

( F i g u r e s 20 a , b , c , a n d d)

t h e s e c o n s t a n t s a r e 3 6 .5 end 1 .6 5 r e s p e c t i v e l y a n d a r e a g a i n id e n tic a l f o r a l l c o n d itio n s. F o r S u b j e c t J . B. ( F i g u r e s 21 a , b , c , a n d d) t h e y a r e 15*0 a n d .7 0 f o r a l l c o n d i t i o n s * F o r S u b j e c t N. F .

( F i g u r e s 22 a ,

b, e , and d)

t h e s e c o n s t a n t s a r e 43*0 and 1 .7 0 f o r a l l f o u r c o n d i t i o n s . The p r o b le m o f e m p i r i c a l l y " p r o v i n g " o r " d i s p r o ­ v i n g ” a q u a n t i t a t i v e t h e o r y r e d u c e s , i n P s y c h o lo g y a s i n o t h e r s c i e n c e s , t o t h e q u e s t i o n o f w h e th e r o r n o t t h e e q u a tio n of a t h e o r e t i c a l r e l a ti o n s h i p f i t s

th e d i s t r i b u t i o n

o f e m p iric a l d a ta . T h ere a r e two g e n e r a l p r o c e d u r e s which may be used in f i t t i n g

t h e o r e t i c a l c u r v e s t o e m p i r i c a l d a t a when

c o n v e rsio n o r tra n s fo rm a tio n c o n s ta n ts a re in v o lv e d .

(Puch

c o n s t a n t s a r e o n e s w h ich r e l a t e e m p r i i o a l u n i t s t o t h e o r e ­ tic a l u n its .)

11 0

a*

P l a c i n g no r e s t r i c t i o n s ( e x c e p t t h e g e n e r a l

s h a p e o f th© c u r v e ) on t h e p r o c e s s o f f i t t i n g a n d a l l o w i n g t h e c o n v e r s i o n c o n s t a n t s t o em erge fro m t h i s p r o c e s s * t h e o r e t i c a l c u rv e ; how w e l l t h e y f i t

The

m ust th e n be e v a l u a t e d on t h e b a s i s o f the e m p i r i c a l d a t a a n d how n e a r l y a l i k e

a re th e o b ta in e d c o n s ta n ts . b.

D e t e r m i n a t i o n o f th© c o n v e r s i o n c o n s t a n t s

b e f o r e h a n d and t h e n p l a c i n g t h e r e s t r i c t i o n upon t h e p r o ­ c e ss o f cu rv e f i t t i n g c h an g e d *

t h a t t h e s e c o n s t a n t s m u st r e m a in un­

The t h e o r e t i c a l c u r v e s m ust th e n be e v a l u a t e d i n

t e r m s o f how w e l l t h e y f i t t h e e m p i r i c a l d a ta * Te h a v e u se d m ethod (b) i n f i t t i n g

th e t h e o r e t i ­

c a l f u n c t i o n s o f d e c i s i o n - t i m e and r e l a t i v e f r e q u e n c y t o t h e e m p i r i c a l d a ta *

The v a l u e s o f t h e c o n v e r s i o n c o n s t a n t s w ere

d e t e r m i n e d fro m t h e " u s u a l ” c o n d i t i o n and t h e n k e p t u n c h an g e d f o r a l l o th e r c o n d itio n s*

T hese c o n s t a n t s m ight a l s o h a v e

b e en e s t i m a t e d fro m a l l f o u r c o n d i t i o n s t o g e t h e r b u t i t was f e l t t o be a m ore s e v e r e t e s t o f t h e t h e o r y t o use b u t one c o n d i t i o n f o r s h i s p u rp o se * Thus f o r t h e " a c c u r a c y , ” " s p e e d , ” a n d " c o n s t a n t e r r o r ” c o n d i t i o n s o n l y one f a c t o r i n f l u e n c i n g t h e t h e o r e t i ­ c a l c u r v e s was v a r i a b l e , n a m e ly , t h e m a g n itu d e o f t h e r e ­ s tra in in g fo rce. L e t us now exam ine t h e g r a p h s o f th© i n d i v i d u a l su b je c ts* F o r s u b j e c t H. S* ( F i g u r e IS ) t h e r e s t r a i n i n g f o r c e value© f o r t h e " u s u a l , ” " a c c u r a c y , ” " s p e e d , " an d

" c o n s t a n t e r r o r ” c o n d i t i o n s a r e fo u n d t o be i n o r d e r 1 .1 # 1*3# 0 * 9 , a n d 1 .0 #

The i n c r e a s e s a n d d e c r e a s e s i n r e s t r a i n ­

in g f o r c e are a l l in l i n e w ith th e p u rp o se s o f th e e x p e r i ­ m en tal c o n d itio n s .

I n o th e r w ords, th e e x p e rim e n ta l c o n d i­

t io n s produced th e d e s ire d e f f e c t . S'S)

(S e e C h a p t e r V I, p a g e

A g l a n c e a t th© F i g u r e s w i l l show t h a t t h e d e c i s i o n -

tim e s t a r t s t o r i s e l o n g b e f o r e t h e r e l a t i v e f r e q u e n c y cu rv e r i s e s .

T h is i s m ore m arked f o r t h e h i g h e r r e s t r a i n ­

in g f o r c e s but c l e a r i n a l l o a ses.

The t h e o r e t i c a l c u r v e s

seem t o f i t t h e e m p i r i c a l d a t a r a t h e r w e l l f o r a l l f o u r c o n d itio n s. F o r S u b j e c t 13. V/* ( F i g u r e 19) t h e r e s t r a i n i n g f o r c e v a l u e s , i n t h e same o r d e r a s a b o v e , a r e 0 . 9 , 1 . 1 , 0 . 8 , a n d 1*4*

The same t r e n d s o f d e c i s i o n - t i m e a s com pared t o

r e l a t i v e f r e q u e n c y a s w ere fo u n d a b o v e a r e f o u n d h e r e , t o o . W hile t h e o u r v e s f o r t h e " u s u a l ” and " s p e e d " c o n d i t i o n s

f i t t h e d a t a v e r y w e l l , f o r th e o t h e r two c o n d i t i o n s t i e d e c i s i o n - t i m e d a t a shows a c o n s i s t e n t d e v i a t i o n fro m t h e th e o r e tic a l cu rv e.

The e m p i r i c a l d a t a a t t h e e x tr e m e s l i e

c o n s i s t e n t l y below t h e t h e o r e t i c a l c u r v e .

A p la u s ib le ex­

p l a n a t i o n p r e s e n t s i t s e l f I f we r e f e r b a c k to F i g u r e 1 4 . The c o n f i d e n c e f u n c t i o n f o r t h i s s u b j e c t was v e r y s t e e p ; much s t e e p e r t h a n f o r a n y o f th© o t h e r s u b j e c t s . he e i t h e r t e n d e d t o h a v e v e r y l i t t l e c o m p le te c o n f i d e n c e I n h i s ju d g m e n t s .

That i s ,

con f i d n e e o r e l s e T h is means t h a t th©

C o n fid e n c e s c a l e was l e s s o f a d i s c r i m i n a t o r y i n s t r u m e n t fo r th is su b je c t.

S i n c e t h e r e was a l i m i t o f 100 on t h e

sc a le ,

th© a v e r a g e c o n f i d e n c e v a l u e s a t t h e e x t r e m e s become

p u sh ed tow ard t h e c e n t e r th u s p ro d u c in g t h e o b se rv ed d i s c r e ­ p a n c y b e tw e e n th e t h e o r e t i c a l c u rv e a n d t h e e m p i r i c a l d a t a . As o n e w ould e x p e c t fro m t h i s i n t e r p r e t a t i o n ,

th is e ffe ct is

m ore m ark e d f o r th e h i g h e r r e s t r a i n i n g f o r c e s { " a c c u r a c y ” and " c o n s ta n t e r r o r ” c o n d itio n s ) s in c e i n such I n s ta n c e s th© d e c i s i o n - t i m e c u r v e h a s a s t e e p e r s l o p e a t th e e x t r e m e s . T h is e f f e c t i s s t i l l n o t i c e a b l e , h o w e v e r, f o r t h e l o w e r re s tra in in g fo rces

( " u s u a l ” and " s p e e d ” c o n d i t i o n s ) a t th©

v e r y e x t r e m e s w here t h e r e a r e s e v e r a l d e c r e a s i n g d e c i s i o n t i © p o i n t s , a l l w ith an a v e ra g e c o n fid e n c e o f 100.

The

r e l a t i v e f re q u e n c y cu rv es f i t w e ll e x ce p t f o r th e " c o n s ta n t" c o n d itio n . For s u b je c t 0 . s tra in in g fo rce,

S.

( F i g u r e 20) t h e v a l u e s o f r e ­

i n o r d e r , a r e 1 . 2 , 1 . 3 , 0 .7 * a n d 0 .5 *

For

t h i s s u b j e c t th e changes in r e s t r a i n i n g f o r c e a r e i n l i n e w ith o u r e x p e c ta tio n s w ith th e e x c e p tio n o f th e " c o n s ta n t e r r o r ” c o n d i t i o n , w h ere t h e r e s t r a i n i n g f o r c e i s l o w e r th a n i n th e "speed" c o iid ltio n .

( % i s i s t h e o n l y I n s t a n c e w here

t h e r e s t r a i n i n g f o r c e m a g n itu d e s do n o t f o l l o w o u r e x p e c t a ­ tio n s .)

T h ere d o e s n o t seem t o b e a n y e x p l a n a t i o n o f t h i s

d e v ia tio n ex cep t f o r th e p o s s i b i l i t y

t h a t on b e i n g t o l d

t h a t s h e h a d been m ain g a s e r i o u s e r r o r t h i s s u b j e c t s i m p ly d e c id e d to " g iv e u p ."

( I f t h e s u b j e c t d o e s n ' t c a r e w h e th e r

s h e i s 2* ie h t o r w ro n g , h e r r e s t r a i n i n g f o r c e s a g a i n s t ma­ k i n g a d e c i s i o n a r e w e a k .)

The f i t s o f t h e t h e o r e t i c a l

c u r v e s t o th© d a t a seem f a i r l y good i n a l l b u t th© " a c c u r a c y ”

1 1 8

c o n d i t i o n w h e re t h e d e v i a t i o n s o f t h e e m p i r i c a l d a t a fro ra t h e t h e o r e t i c a l c u r v e (b elo w on t h e l e f t old© a n d a b o v e on th e r i g h t sid e )

seam s t o be d u e t o a s l i g h t n o n - c o r r e s p o n d e n c e

b e tw e e n t h e 50/* r e l a t i v e f r e q u e n c y c u r v e a n d th e p e a k o f d e c is io n -tim e in th e e m p iric a l d a ta .

For th is su b je c t a g a in ,

t h e r e l a t i v e f r e q u e n c y c u r v e f i t s l e a 3 t w e l l f o r t h e "c o n ­ s ta n t" c o n d itio n . F o r S u b j e c t J . B. ( F i g u r e 21)

th e r e s t r a i n i n g f o r c e s

f o r t h e f o u r c o n d i t i o n s a r e i n o r d e r 0 . 7 , 1 . 0 , 0 . 3 , a n d 0 .9 * The r e s t r a i n i n g f o r c e i n a l l f o u r c o n d i t i o n s f o l l o w p e c ta tio n .

th e e x ­

The c u r v e s o f b o t h d e c i s i o n - t i m e and r e l a t i v e

f r e q u e n c y f i t w e ll f o r a l l th e c o n d itio n s h e r e .

The o n l y

i m p o r t a n t d e v i a t i o n s a r e asym m etry o f t h e e m p i r i c a l d e c i s i o n tim e d a t a i n t h e " u s u a l , " " a c c u r a c y , " a n d " c o n s t a n t " c o n d i ­ tio n s .

I n t h e s e c a s e s t h e e m p i r i c a l d a t a ru n s p a r a l l e l t o

b u t s l i g h t l y ab o v e .. he t h e o r e t i c a l c u rv e s on one s i d e .

T h is

i s c l e a r l y due t o t h e f a c t t h a t th e b a s e c o n s t a n t i s d i f ­ f e r e n t f o r " l o n g e r " and " s h o r t e r " w i t h t h i s s u b j e c t .

T h is

d i f f e r e n c e i n ba3© c o n s t a n t s i s n o t r e l e v a n t , h o w e v e r, to th e th e o ry . F o r S u b j e c t N. P . fo rce

( F i g u r e 22) t h e r e s t r a i n i n g

© m agnitudes i n o r d e r a r e 0 . 5 , 1 . 0 ,

in l i n e w ith e x p e c ta tio n .

. 2 5 , and 0 . 4 , a l l

The t h e o r e t i c a l c u r v e s seem to

f i t th e d a ta w ith o u t un u su al d e v ia tio n s f o r a l l th e c o n d i­ tio n s .

f u r t h e r A n a l y s i s o f " C o n s t a n t e r r o r " Condi t i o n I n t h e a b o v e d i s c u s s i o n we h a v e s t a t e d o n l y one num ber a s t h e v a l u e o f t h e r e s t r a i n i n g s t a n t e r r o r ” c o n d itio n #

f o r c e f o r t h e "con-*

A c t u a l l y t h e r e s h o u l d be two num­

b e r s s i n c e t h e r e s t r a i n i n g f o r c e s a r e o f d i f f e r e n t m a g n i­ t u d e s i n t h e two d i r e c t i o n s *

The v a l u e s o f r e s t r a i n i n g

fore© g iv e n above f o r th e "C o n sta n t e r r o r " c o n d itio n a r e th e a v e ra g e v a lu e s*

We s h o u l d , h o w e v e r,

be a b l e t o d e t e r ­

m in e t h e r e s t r a i n i n g f o r c e i n e a c h d i r e c t i o n

because o f

t h e p r e d i c t i o n t h a t th e 50$ p o i n t o f t h e r e l a t i v e f r e q u e n c y o g i v e m oves i n t h e d i r e c t i o n o f t h e s t r o n g e r r e s t r a i n i n g f o r c e by a d i s t a n c e a l o n g t h e a b s c i s s a e q u a l t o o n e - h a l f t h e d i f f e r e n c e be tw ee n t h e r e s t r a i n i n g f o r c e s *

I f we d e ­

t e r m i n e t h e a v e r a g e l o c a t i o n o f t h e 50$ p o i n t o f r e l a t i v e f r e q u e n c y on t h e c o n f i d e n c e s c a l e f o r th e f i r s t t h r e e c o n ­ d i t i o n s a n d r e g a r d t h i s a® t h e " n o r m a l f " th e n t h e d i f f e r e n c e b e tw e e n t h i s "norm ” a n d t h e c o r r e s p o n d i n g l o c a t i o n i n t h e " c o n s t a n t " c o n d i t i o n , c o n v e r t e d i n t o z u n i t s s h o u ld be e q u a l t o o n e - h a l f t h e d i f f e r e n c e b e tw e e n >:he r e s t r a i n i n g forces*

The p o s i t i o n o f t h e 50$ p o i n t o n th e c o n f i d e n c e

sc a le i s

g iv e n d i r e c t l y by : he i n t e r c e p t c o n s t a n t o f t h e

e q u a t i o n b e tw e e n 0 and z* F o r S u b j e c t H. 8* t h e a v e r a g e i n t e r c e p t f o r t h e f i r s t t h r e e c o n d i t i o n s i s ♦5*23*

T here i s a s h i f t t h e n o f

- • 3 3 C o n f id e n c e u n i t s o r - . 0 1 z u n i t s i n t h e C o n s t a n t co n d itio n .

The r e s t r a i n i n g f o r c e a g a i n s t " s a y i n g ’ s h o r t e r * "

i s 1 .0 1 and i n t h e o p p o s ite d i r e c t i o n i s

*99» a d i f f e r e n c e

w h ich I s n o t v e r y l a r g e . F o r s u b j e c t 3* b . th e a v e r a g e C o n f id e n c e p o s i t i o n of th e

50$ r e l a t i v e f r e q u e n c y p o i n t f o r th e f i r s t t h r e e co n­

d itio n s i s -1 .2 .

T h is p o s i t i o n i n t h e ’' c o n s t a n t " c o n d itio n ,

s h i f t s - 1 4 . 6 C o n f id e n c e u n i t s o r - . 3 2 z u n i t s .

The r e s t r a i n ­

i n g f o r c e o p p o s i t e t o " s a y i n g ’ s h o r t e r ’ " i s 1*72 and t h e r e s t r a i n i n g fo re © i n t h e o t h e r d i r e c t i o n i s 1*08* F o r 8 u b j e o t G-. S . t h e p o s i t i o n o f t h e 50$ p o i n t i© -1 4*4 f o r th e f i r s t t h r e e c o n d itio n s*

th e e x t e n t o f t h e

s h i f t i n t h e " c o n s t a n t " c o n d i t i o n I s - 5 * 6 C n f id e n c © u n i t s o r -.1 5 z u n its .

The r e s t r a i n i n g f o r c e o p p o s i t e t o " s a y i n g

’ s h o r t e r ” * *65 and i n

the o t h e r d i r e c t i o n i s

.35*

T o r S u b j e c t J . 13. th e 50F p o i n t l i e s a t an a v e r a g e p o s i t i o n o f - 5 . 1 on th e C o n f id e n c e s c a l e .

T his p o i n t , f o r

t h e " c o n s t a n t e r r o r " c o n d i t i o n s h i f t s *14*1 C o n f id e n c e u n i t s or * .9 4 z u n i t s .

T h is, i f

c o r r e c t , would mean t h e t t h e

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