A Statistical and Comparative Analysis of Individual Written Language Samples

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a statistical am

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INDIVIDOAL WRITTEN X Ato AOR &Uf l^

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1ay John W* Ghotloa

A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of philosophy, in the Department of Psychology, in the Graduate College of the State University of Iowa Jdly, 1942

ProQuest N um ber: 10984052

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uest ProQuest 10984052 Published by ProQuest LLC(2018). C opyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying 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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ACKNOWLEDGMENTS The writer la indebted to Dr. Wendell Johnson and to Dr. Don Lewis for the helpful suggestions end ^ ejl

direction which mode this investigation possible.

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TABLE OP CONTENTS Page X XX

Introduction........

1

Problee.................................

8

IXX Procedure................. XT

Eeeults................................. 25 Reliability of Data ........................ Oroup Differencee In Language Ueaauree. . . . . . OuBulatiTe Type-Frequency curve ..............

T BLaouaelon . . . . . . VX

.

....... . . . . .

Sumeary and Conclusiona.

10 U 81 78 101

.....................Ill

Bibliography...............

116

Appendix X . . . . . . . . . . . . . . . . . . . . . .

116

iv TABLE OF TABLES Table

Fag®

X ....... . . . . . . . .................... II

IS

. . ....................................

X X X ......................................... IV , .

............ . ........

xs xs Z6

V .........................................

S

5

V I .............................

$6

V K .................................... . . . VIII......................................... XX.. . ...................................... I

.......

X X ............ . in ...

. ............

87 88 40 48 44

.............................

48 47

XIXI.................................. X I V ........ IV. . . . XVI . . . . . m i

. ..

rrai

. . . ................

49

......................

51

.............................V

58

..........................

54

................. ............

XIX ..

.

55 57

X X ............................... XXI

. . .....................................

XXXI................. - ....................

59 60 88

XXIII.................................... XXIV m

. . . ........................

65 @4 as

V

TABLE OF TABLES (continued) Table x m

Bags • , * ..............................

xmz .

68

...........................

78

XX7IIX . . . .............. . . . . . . . .......... 31 XXIX

......

88

X X X .......................................... 85 XXXI.................................... n m

_

88

^

XXXIII . .

...........................

XXXI?...................................

98 94

tab &b op

n a m

1 I.

Introduction

The importance of language as a determining factor in human behavior has long boon recognised*

In deeextLptions of human learning,

conditioning, reaction time, intelligence, and a hoct of special abili­ ties, the verbal factor bee assumed the proportions of an unknown quan­ tity*

Contemporaneously, there is a tendency to describe personality

and personality deviations in terms of language. Determining conditions antecedent to so-called functional disorders are looked for in the language of the deviating individual*

important psychological pheno­

mena such as set and attitude are considered by some to be governed largely by language or verbal conditions* The study of language as a segregated phenomenon is indicated* The study of language has until recently been considered the domain of the grammarian, philologist and linguist* The interest of the grammarians has been didactic, an interest which has tended to minimize and ignore quantitative relationships which exist In language usage*

Although the

grammarians are awakening to a need for quantitative descriptions, the quantitative investigation of language behavior and its relationships would appear to be of particular interest to psychologists; such inves­ tigation would seem to be useful In furthering our knowledge of psycho­ logical phenomena* To this end we seek language measures which are amenable to statistical and mathematical manipulation*

Having devised such measures,

our next step is to determine how these measures are interrelated and how they are related to other psychological variables*

Johnson (7) has de­

vised or adapted several techniques which should prove useful in a

2

quantitative analysis of language behavior.

Other investigations have

studied the relationship between the number of different words to the total output of words and the relationship between the rank of a word and ita frequency.

Still others have reported word Hate, lists usually

collected for didactic purposes.

Finally attempts have been made to

estimate the extent of individual or group vocabularies.

A comprehen­

sive review of studies and of theoretical bases suggestive of quanti­ tative investigation of language behavior has been presented by San­ ford (10)• The present Investigation is concerned with the relation of certain language variables to (1) the length of sample from which they are derived and (Z) to certain psychologically pertinent factors.

In

general* the language measures employed are based on a cotint of the number of different words (types) and the relationship of such measures to the total number of words* and to the factors of X.Q.* 0.A.* locality (city* town* rural)* and sex.

Similar measures based on parts of speech

categories and their relationship to X.Q.* C.A., locality and sex will be reported.

Finally the relationship of the reliability of these measures

to the length of samples from which they are derived will be given atten­ tion. Certain previous investigations have been concerned with closely related problems.

To begin with* Carroll (5) has presented an

equation describing the relation of the number of different words (D) upon the total number of words (N) in a sample of language.

A necessary

condition to Carroll1s formulation of this relationship is that a speci­ fied relationship hold between the frequency of a given word in a lan­ guage sample and its rank in order of decreasing frequencies.

Zipf (15)

3 discovered that when he platted frequency of ft word against the number of word# having that frequency on lagorithmic coordinates, the points approximated a straight line except for the few most frequently occurring words*

W r m this fast he formulated the harmonic series law of word

distribution, which states that the most frequent word in a large sample of language makes up 1/10 of the sample» the second most frequent word V & 0 of the sample, the third most frequent word l/30 of the sample, etc* this formulation can he put in the form of the equation

A in which £ is the frequency of occurrence of any given word In a lan­ guage sample, & is its rank in order of decreasing frequencies, and If is the total number of words in the sample* Skinner (15) has also presented results pertaining to the relationship between £ and £,

In analysing the results obtained from

1,000 responses to his verbal summstor, he plotted ranks of words in order of decreasing frequencies (g) against frequency (F) expressed as a percentage of the total sample on logarithmic coordinates, and found the points to fall on a straight line* A deviation from linearity was again noted in the more frequently used words*

Skinner (IS) also reanalysed the Kent-Bosanoff (8)

data on free association response words in the same manner*

Be found

that when the rank order of words in terms of mean frequency per thousand was plotted against mean frequency per thousand on logarithmic coordinates, the resulting curve was approximately linear for the 100 responses most likely to occur,

She equation

where £ is the frequency with which a given association will occur in 1,000 responses and £ is its rank in terms of mean—frequency per thousand, he finds to be descriptive of the 75 words having the strongest first associations in the Kent-Rosanoff list*

Be states that this formula is

Slightly less accurate for the total sample, and his calculated and ob­ served points appear to agree satisfactorily*

However, he states that

this equation has little practical significance since the frequency and rank of a word must be ascertained before the equation can be used* nevertheless, he feels that it has an important bearing on theories of language, Carroll argued that if one accepts the harmonic series law of word frequency distribution, I.e., y » -1LKR Where £ Is the frequency of any word In a language sample, £ its rank in order of decreasing frequencies, £ the total number of words in the verbal output sample, and £ is a constant which is an indirect index of diversity, then it can be demonstrated on a rational basis that the following equation holdsi D - | (0.428 ♦ ! - lag, , ♦ log- g) where £ is the number of diff©rent words in a sample, H the total number of words in that sample and £ is an empirically determined constant. This equation, if it can be shown to be applicable in general, has very important implications with regard to language since, in the first place, if £ is known for a specified N, predictions can be made to other N*s, and, Secondly, the nature of the curve allows a determination of a maximum value of £, a value which can be correlated to a given type of vocabulary

5

of the individual.

Carroll tested this equation with a verbal output

•ample obtained by means of. the verbal eummator technique, and op several language samples from literature, and found the empirical points to fall very near to the computed curve* the language samples which formed the protocols of these in­ vestigations into the relationship between £ and N and between £ and Jt, have been accumulated from different sources and massed into one language sample or are the product of verbally proficient writers.

Thorndike (14)

has emphasised that if language is to be viewed as behavior, the motiva­ tion, backgrounds, and Individual characteristics of the writers or speakers must be taken into consideration.

He further suggested that

the relationship between £ and £ reported by Zipf may in some measure be a statistical artifact produced by combining language from varied sources, such combination resulting in a loss of individual variation, ha the light of this criticism it seems desirable to apply the mathe­ matical formulations of these relationships to samples of language which are the product of but a single individual, in order to test their ade­ quacy more fully, A second point of interest in the consideration of previous studies la that various attempts have been made to relate the number of different words in a senile to psychologically pertinent factors.

Fair­

banks (S) working with spoken language and Mann (9) with written language compared superior university freshmen and schisophrenic patients in terms of the mean percentage of different words per 100-word segment, i.e,, the 100-word type-token ratio.

Both Investigators found the mean type-

token ratio for super freshmen to be significantly greater than for schisophrenic patients. Indicating a wider vocabulary range for freshmen

than for schisophrenic patients.

Fairbanks suggests that for spoken

language, there might be a positive correlation between the 100-word type-token ratio and intellectual level.

On the other hand, M a m (9)

found that differences in intelligence test scores, level of educational attainment, and duration of confinement had relatively little influence on the type-token ratio of patients in terms of accounting for differences between her two groups. found.

2h neither study were significant sex differences

Fossum (6), studying spoken language obtained from junior college

students in a regular speech Glass, found by means of a correlation tech­ nique that the 100-word type-token ratio based on 18 segments appeared to be related to parental occupation, correlation of .56, and to speaking rate, correlation of -.45, but not to vocabulary as measured by the Jlelaon-Denny Beading Test, correlation of .03, nor to intelligence as measured by the percentile score on the Ohio State Psychological Test, correlation of .09. Fossum found no sex differences In type-token ratio measures in his group. Thirdly, counts of the number of words in parts of speech cate­ gories have been made by Fairbanks (6) and Mann (9). They related these counts to other variables under consideration.

Fairbanks (5) found that

for spoken language there were differences in the use of various parts of Speech between her freshmen and schizophrenic groups.

The schizophrenics

used proportionately more pronouns and verbs and proportionately fewer nouns and articles.

On the other hand, for written language, Mann (9)

found that the results of the grammatical parts of speech count were not Signifleant, although there seemed to be a tendency for the patients to use more nouns than the freshmen, a result which does not agree with the comparable result obtained by Fairbanks.

Fourthly, Fossum (6) has attempted to relate the reliability of the type-token ratio to the length of spoken language sample.

Be

found the correlation between 100-word type-token ratios for the two helves of 1,800-word samples to he .88 and he estimated fay means of the Spearman-Brown prophecy formula that a sample of 14,000 words would he needed to give a reliability coefficient of ,88. Many important facts about language have been reported, and It is of undoubted importance to know whether the relationships already reported will hold for individual language samples.

Many investigators

have used verbal output samples in which the individual characteristics of the writers and speakers have been lost through massing of the data. In other instances, where Individual variations have been of major in­ terest in the investigation, the samples of Individuals have been highly selected.

It is proposed in this study to Investigate language char­

acteristics of individual verbal output samples in which the population sampled will allow for considerable generalisation of the results.

The

question of whether or not individual verbal output samples will bear out the equations descriptive of massed language data is an Important one.

Furthermore, the relationship between language measures and I.Q.,

C.A., sex, etc., appears to need further investigation in populations less highly selected in these characteristics than the ones which have been so far reported.

8 IX*

The Problem

The object of this study may be oriented around the analysis of the number of different words (2) as a function of the total number of words (N)»

This relationship may be symbolized by the formula 0 • f (N)

Zn this equation it is apparent that we can hold N constant and study D in relation to other variables* we can study the variation in D with eoncGmmitant variation in N* and finally we can study the variation in 0 and S in relation to other variables* such as intelligence test score* age* etc* The basic unit of analysis is the language sample of a single individual. With this introduction the purpose of this study can be summarised in the following statements and questionss 1*

To test empirically the equation derived by Carroll* namely* * - ! « . » *■«.«) where D is the number of different words in a sample of length H and K Is an empirical constant to be determined from the data. It is a further purpose to test the assumptions under which this equation was developed.

Zm

Can the relationship between 2 pirically determined curvet

2 be expressed by some em­

If such a curve can be determined

can the constants in this curve be given any rational meaning! 8. Does £ for specified 2'® differentiate X.Q* groups* age groups* location groups* and sex groups?

And what is the extent and

direction of these differences? 4. 00 sections of the language samples* categorized by parts of speech, reveal any relationships or differences wliich are not

apparent in the aampl s at a whole?

How are the parte of

epeeah which go to make up the total sanqple interrelated? Shat ie the minimum else sample that can be drawn to reveal the relationships and differences under investigation?

10 7XU

Subjects and Procedures

ike part of a remedial education survey, sponsored by the Iowa Child welfare Research station and financed by the Federal Work Projects Administration, approximately 1,000 public school children wrote manueeripts of 3,000 words each under conditions to be specified below*

The collection and preliminary analysis of these manuscripts

was serried out by Work projects Administration personnel under the supervision of persons with background training in psychology, who bad been given special training for this particular assignment*

The

staff of supervisors worked under the technical direction of Br» Wendell Johnson**^ The survey operated for a period of about two years ^Professor George D* Stoddard served as general director of the survey, of which the language study was a part* In five counties of the state of Iowa* These counties are distributed throughout the state in such a way that no two counties were adjacent* Each county survey was operated as a unit, coordination being achieved by a state-wide supervisor stationed at the university*

in each county

a H schools, including the one-room rural schools, were invited to participate in the program* Unit supervisors were instructed to collect 5,000-nord language samples for an allotted number of pupHe in their respective units*

As It took several hours for a child to write the number of

words required, extensive cooperation from the school administrators and teachers was necessary*

The plan called for collecting an equal

number of samples from city, town and rural school children, from equal numbers of boys and girls, and an equal number from each grade from

four through twelve*

localities with a population of 25,000 or over

wore called cities, ether localities and consolidated schools were considered as town schools, and rural schools of the one-room variety were considered as rural for purposes of this study*

Since, as a

rule, the one-room rural schools have only eight grades, it was neces­ sary to classify town school pupils who had a rural school background and whose parents were fanners, as rural in order to fill out the rural categories at the older ages*

In collecting this sample the pupils

were matched by sex for grade, age (within six months), X*Q* (within five I*Q* points) and socio-economic level (within the limits of 1920 U.S* census occupational classification system)*

Ho pupil under eight

years nor over eighteen years of age was included in the sample* She writing was done under the supervision of a worker who remained in the classroom throughout the writing session* Writing sessions averaged about forty minutes in length and, on the whole, four or five writing sessions were required for a child to complete his assigned task* The worker in charge read the following Instructions before the children began to write* "Tou are to write about anything you want to write about* just make it up as you go along*

That is, don't write anything

you have memorised such as stories or poems*

just start with

the first thing you think of and try to keep on writing steadily** If a child stopped writing for longer than five minutes or complained that he couldn't go on, the worker was instructed not to tell him what to write about, but to tell him to write on whatever he was thinking

12

About.

No positive suggestion a* to topics van allowed.

Legibility

of the manuscript erne emphasised and speed was not encouraged.

Bach

day's writing wee handed in to the monitor at the close of the session* the worker counted the number of words written* entered them in his record and dismissed the subject when he had reached the prescribed quote* from this basic sample of approximately 1*000 language samples* an experimental sample of 108 was selected to conform to the factorial design in Table X. Sines a complete record was available on each child it was possible to sort the larger sample of manuscripts into the fifty-four cells of the design and select at random two sub­ jects for each cell*

There was no matching by sex in the experimental

sample as was the case in the survey sample.

Intelligence was tested

by means of the Otis Quick-Scoring Mental Ability Testa.

The Alpha

test was administered to pupils in grades one through four* the Beta test to pupils in grades five through nine* and the Gamma test to pupils in grades ten through twelve.

In classifying the subjects ac­

cording to the design In Table X* no distinction was made between the various forms of these three tests. Ages were computed as of the day the children started writing.

Criteria for the locality levels of the

design are the same as those mentioned above for the collection of the basic sample.

The design permits a distribution of 56 subjects at

each of three X*Q. levels*

(1) 89 and under* (Z) 90 to 109* and (3)

%4o and overi 56 subjects at each of three age levels* (1) 12 years* 5 months and under* (8) 12 years* 6 months to 14 years* 11 months* and (5) IS years and over* 56 subjects at each of three locality levels*

13

Table X Factorial Design of Experimental Sample Halo city town rural

1

I.Q. Z

X*Q* 5

city town rural

Age 1*

*** Z

Z

%

Z

Z

a

Age Z

Z

z

%

z

z

a

Age 3

z

z

Z

8

z

a

Age 1

a

a

a

z

a

a

Age 8

a

a

a

a

a

a

Age 5

a

a

a

a

a

a

Age 1

a

a

z

a

a

a

Age 8

a

a

z

a

a

a

Age 3

8

8

a

8

8

8

* A®e 1-149 months and under Age 8-150 to 179 months Ago 5-180 months and over

#» I*Q* 1-89 and under X«Q. 8-90 to 109 £•$• 3-110 and over

#** The numbers refer to the lumber of randomly selected subjects in the ceU

14

(1) city, (2) town* and (5) rural) and fifty-four subjects in each of the tax groups*

Furthermore, many combination® of X*Q*, age, locality

and sex levels are possible* Weans and standard deviations for distributions of I.Q* and age for the total experimental sample and for the main sub-groups, i*e*, in terms of X*Q*, age, locality and sen, are presented in Tables IX and HI, Following the collection of the language samples, the manu­ scripts were typed and edited* The definition of a word. It should be realised,is eruci&l in a study of this type*

Quite a bit of freedom

Is permitted in defining a unit of language and the way in which the unit Is defined is necessarily a condition that is important in con­ nection with any statements made about language phenomena*

For this

reason the rules for editing the manuscripts are presented in full* These rules define the fundamental language unit better than any formal definition eould*

The following rules wore followed in editing

the samples * 1*

Type all words exactly as they are written by the subject* Record each correction by writing it in parenthesis after the word for which it is a correction*

Zm Correct each misspelling, recording the word as spelled by the subject and writing the correction after it, in accordance with (1) above* Classify as a misspelling any word which as spelled by the subject does not constitute a standard English word (current edition of the Century Dictionary to be used as authority) or a recognisable "slang”, nonstandard word (recognizable to the present investigators)* 8,

Classify as a substitution and correct in accordance with (1) above, any of the following, a* Any correctly spelled homonym or an apparently "intended"

Table II Keans and Standard Deviations of Distributions of Agee in Months for the Total Group and for the Kain Sub-Groups

.1

Group , ■ ,, 1 Age Groups

149 months and under 160 to 179 months 180 months and over

Mean

Standard Deviation

129*806 164*889 189*659

12*684 8*473 7*779

163*917 168*083 157*855

26*186 26*519 26*455

165*194 159*861 156*778

24*120 28*156 26*469

160*796 161*759

26.887 27*020

161*278

26*445

X*Q» Groups 89 and under 90-109 110 and over location Groups City Town Sural Sex Groups Male Female Total Group

16

Table ZZZ Means and standard Deviations of Distributions of Otis XnteUlgenee Tost Scores (I*Q* Unite) for the Total Group and the Main Sub-Groups Group

Ifean

Standard Deviation

Age Groups 149 months and under 150 to 179 months 180 months and ever

101*978 101*598 99*028

14*251 14*297 14*957

35*355 101*831 116*159

5*070 4*461 4J

101*056 100*111 100*367

14*012 14*240 15*585

100*556 100*667

14*455 13*500

100.611

15*888

I*Q. Groups 39 and under 90-109 110 and ever Location Groups City Town Rural Sex Groups Female Total Group

17

wrd) i«g«, "their" substituted for an apparently intsndsd "there"* "bare" for "bear", "four" for "for*, sto* Judgment in such cases sill involve reasonable Interpretation of context. b. Any correctly spelled non-homonymous substitution which apparently distorts the "intended** sense| e.g.* "of you sen" for "of your own", "is would be" for "It would be." judgment in such oases will* again* involve reasonable interpretation of context. 4*

Do not insert any word apparently or obviously omitted by the subject. For example* if the subject writes* "It would fun to play ball*" do not Insert the word "be" at the point where the subject obviously omitted it.

5. Record slang or non-standard words as written by the subject. When a dang or non-standard word has a standard equivalent* record this equivalent in parenthesis after the dang wordj e.g.* write "sneaked" in parenthesis as a correction for "enuk". Any dang or non-standard word having no standard equivalent is to stand as written by the subject and misspellings of such words when recog­ nisable are to be recorded in accordance with (1) above. 6. Any proper name which consists of more than one word is to be counted as one word; e.g.* "JOhn Jones" is one word; "Bast St. liouls" is one word; but "Bast St. Louis* Illinois" Is two words* sLnee they constitute two proper names* the name of a city and the name of a state; "The Chicago and northwestern Railroad" are three words since (1) "the" is never to be regarded as an integral part of a proper name* always being counted as a separate word and (2) any claes-name to which a proper name is attached is to be counted as a separate word; e.g.* "railroad"* "hotel"* "theatre"* "street"* etc.* even in such an example as "the Betel Roosevelt"* "the" and "Betel" are to be counted as separate words* A proper name is one that designates the sole bearer of the name* ass there is only one •Ghleago and northwestern" railroad* only one "Great Atlantic and pacific" tea company* only one "General Ifstors" corporation* etc. The names given above in quotes* therefore* are proper names and each is counted as one word. In "A 1940 Multi-Motored Amphibian P45 Boeing Transport"* on the other hand* the various words are qualifying adjectives; there are many Transports— -Boeing names one type* and it* rather than "Boeing Transport" is a proper name in this case; there are many Boeing Transports* and P45 merely serves as an adjective— there night be Hi* P46* etc.* and under each of these there might be a blue model* a red model* and a green model— and there are many individual P45'e. Again "Amphibian"

18 serves as an adjective, and an for the terms, "a", *1940" and "multi-motored" • In the m a p l e of "Dubuque Senior Klgh School", Dubuque 1« an adjective, of course; "Senior High School" however# ie not, one word in the came senee that "Chicago and Northwestern* le one wordj "Chicago and Northwestern" designates the only railroad that goee by that name* hut there are thousands of eenior high schools; therefore# "eenior" and "high" are to be regarded ae adjectives; "Dubuque Senior High School" ie to be re­ garded a* four worde* "Mrs*", "Mr#*, "Klee" and other modes of addrese are to be counted ae eeparate words and not ae integral parts of proper names; e.g., "Mr. Jbhn Jones" are two words* Titles are not integral parts of proper names, but are to be counted as separate words; e.g., "Doctor Jones" are two, words; "Senator Hill" or "Professor smith" are two words* Abbreviated titles which consist of more than one unit, e.g., lf*D* or Ph.D., or unabbreviated titles which con­ sist of more than one word, e.g., "Speaker of the House" or "Bean Emeritus", are to be counted as single words* 7, Any number is to be counted as one word and all figures are to be written or changed to longhand words* "One", "twenty-seven", "one thousand sixteen" are each a single word* Where time is denoted in numbers, it should be counted as a number; e.g., 7*55, write as "seven thirtyfive" and count as one word* Where street numbers are denoted, write as customarily spoken; e*g*, "lfcfcO Harrison Street" write as "twelve twenty Harrison Street"* When numbers are placed at the beginning of sentences for no obvious reason they are not to be included in the typewritten copy and are not to be counted* For example, in one or two eases it was noted that the sentences had been numbered by the child. Such numbers are not to be counted* 8* Contractions are recorded as written; e*g*, "didn't" is not to be changed to "did not"; "didn't" is one word* 9* Record abbreviations as written by the subject, with full term in parenthesis* 10*

Hyphenated words properly hyphenated (Century Dictionary to be used as authority) are to be counted as single

19 words| e*g** **hltoh^iikerH ia one word* two words im­ properly hyphenated are to bo counted as two words* Oozrsctions in sash oases are to be made according to inatruetiono given above* 11*

Any two words* as corrected and tabulated* are different unless spelled exactly alike* except# a*

Plurals and posseseives* and contractions involving apostrophes* are to be differentiated even though they are spelled alike* r-

.

', ‘l

r;

b* Any word which begins with a capital letter solely by virtue of its place in the sentence Is not to be classified as different from a word spelled as it Is in all ether respects* IS* All recognisable words are to be counted and tabulated except in the ease where some symbol is used to Indicate a previously written word* these symbols are not to be counted as that word* For example* "John is going to town tonight* * ” * * school* « « « "be late* Etc* there are nine written words and only nine are to be counted* 15*

Sentences are to be left as the child has written them* Bo not change the pronoun to agree with the noun in the following example* "Hath has one side on his paper*** nor change the tense in this example* "It is raining last night*. Count these as they stand* After the manuscripts were typed and edited* the types

and tokens were recorded and tabulated separately for each manuscript. This tabulation made it possible to abstract the following language measurest 1*

the number of types in any 100-word segment. 500-word segment* lQOCMrord segment, and in the total 3.000 words*

Thus* SO

measures from 100-word segments* six measures from 500-word segments* three measures from 1*000 word segments and one measure for the total manuscript were computed* For each

30

subject these were averaged to give the mean number of types in 100# 800# end 1,000-word segment* respectively.

The mean number of types

In a specified segment can be symbolised by g* with a subscript to denote the else of the base from which it is computed.

The four

measures described above can be symbolized by D ^ , BgQQ* B^.QQO* 08#OOO* 2#

The type-token ratio for one hundred word, five hundred

word, one thousand word and three thousand word segments.

The type-

token ratio can be defined as the mean percentage of types in any specified segment.

Xf the number of tokens is symbolized by 1J#

th«n the type-token ratio can be aymboliaed bjr

where the sub-

% script 1 specifies the sLze of the sample on which the type-token ratio was based.

In our case, the following type-token ratios

were computed!

® wo-^g

*i.o-%§g

*5.000

In which g Is a symbol for type-token ratio. g and g# as defined above are equivalent measures so long as the number of tokens# g# on which they are based is equal for the different individuals In a distribution*

However* in instances where

a distribution is made up ofmeasures based on a varying N* the two measures are not equivalent.

In thisstudy* where g and g gave equi­

valent measures* g was preferred because it made comparison with results of other studies possible* 8*

The cumulative type frequency curve is obtained by cumulating

the types added in sash successive lOCMrord segment*

It Is the curve

that results when J}» the number of types* Is computed as a function of g# the number of tokens.

Since each language sample was sectioned,

into thirty segments* there are thirty points available in the compu­ tation of this curve* 4* data*

The frequency and rank of each type was computed from the

The frequency of a type is the number of times it occurred in

the language sample* A ranking of the types* in whole number steps* and in order of decreasing frequency* was made* Types of equal fre­ quency, were given an average rank number* a word in this sequence is its rank. symbolised by

The numerical position of

The frequency of any type is

and its rank by Ei#

Following the computation of the above language measures* the language sample was split into four sub-samples.

The division

was made on the basis of these parts of speech! nouns* verbs* adjec­ tives* and adverbs.

It did not seem profitable to analyse the pro­

nouns* prepositions, conjunctions and articles at this time since these parts of speech are much more limited in the number of available types*

An attempt was made to classify the words on a functional

rather than on a formal basis.

In each instance the function of the

word in the context in which it was found determined its classifica­ tion* For example* the word run in "He will jnann and “She had a £gg| in her stocking*1 are considered as two different types in this classi­ fication* the first a verb and the second a noun* whereas in the previously described definition they would be counted aS one word according to editing rule number 11*

Curm©*s (2) text* A grammar of

22

the English Language* was used ae a reference and final authority In ease of doubt*

On the basia of this grajinaatical analysis these ad­

ditional measures were abstracted* 5* The number of nounal* verbals adjectival and adverbal tokens* 0#

The number of nounal* verbal, adjectival and adverbal typos*

7*

The type-token ratio for noting, verbs. adjectives and adverba.

This measure is not equivalent to (%) above elnee the number of tokens on which the number of types la baaed la not equal from individual to individual*

Usually type-token ratios are not directly comparable un­

less they are baaed on the same number of tokens for each individual* but in this instance* it is felt that distributions of type-token ratios derived from a varying number of tokens can be justifiably used because the total number of tokens is the same in all the manuscripts* If the parts of speech type-token ratios are weighted by their respec­ tive number of tokens* their sum will be found to equal d* the number of types in the language sample* 8*

Percentage of neunai* verbal* adjectival and adverbal types*

This measure was computed by summing all the nounal* verbal* adjec­ tival and adverbal tokens for each Individual and then finding the percentage which the separate nounal* verbal* adjectival and adverbal types are of this total.

23

rr. numit* Bpltftfamty of Xt should be realised that tho recording, tabulating, and counting operations in this study were unusually extensive. Attainment Of absolute accuracy in a study of this type is both expensive and extremely difficult in a reasonable length of time.

Errors were re­

duced to a minlnaia by having all operations done twice and by constant supervision of the wexteers* Further, the procedures for recording, tabulating, and counting the data were so set up as to make possible continuous checking throughout the operations*

One set of verbal

samples was tabulated independently by two units of the project in Order to get sows indication of the accuracy of the work.

Forty

verbal sample* comprised this set and tho correlation between the two counts of the number of types in each manuscript was .985. Xt will be recalled that our data consist of 5,000-word language samples, the individual words of which have been tabulated in such a fashion as to allow for the determination of the number of different words# types, In 100-word segments, or in any segment which is a multiple of 100 words*

Xh order to test the reliability of the

type-token ratios the technique of correlating *eplit«halves* was em­ ployed. The segments of each of the 108 language samples were split into two halves, the first 1,500 words constituting one half and the last 1,500 words constituting the other, lfean type-token ratios for 100 and 500-word segments were computed for these two halves and the correlation between the halves computed.

The product-moment correlation

24 coefficient for tho moan type-token ratios for 100 -word segments was •829# and for the 500-word segment type-token ratios the correlation coefficient was #888 • Since these typo-token ratios were computed for only half of the $,000 words# it is desirable to have some estimate of what the correlation would be if the whole sample were used as a basis for computing the ratios.

Such an estimate can be made by means

of the SpearmaxHBrown prophecy formula.

Estimated reliability co­

efficients for the full length of 5.000 words are .906 for the 100word type-token ratio and #904 for the 500-eiord ratio. An assumption basic to the use of the Spearman-Brown prophecy formula is that# in this case# the language sample be homogeneous throughout its length in the above two measures.

If the two halves are homogeneous# i.e.,

measure the same aspect of language# then one would expect the mean type—token ratios for the group to be approximately the same for the two halves.

These means were found to be 62.58 and 62.64 for the

first and last halves# respectively# with regard to the 100-word typetoken ratio# and 40.85 and 40.66 for the first and last halves# re­ spectively# with regard to the 500-word type-token ratio. On this basis# the assumption of homogeneity throughout the verbal sample for these two measures appears to be tenable. It may be# however# that 5#0Q0 words is an insufficient number to reveal any trends in the behavior of these two measures. One long sample of 18#00Q words was available and was used to test the hypothesis of homogeneity on a longer language sample.

This sample

was obtained under the same conditions and rules as the shorter samples# except that the subject volunteered to do the task. Several subjects

25 volunteered to write long samples, but only in this one instance mas the task carried beyond the 5,000 word quota*

It is recognised that

one subject, as each, has no statistical status and that no generaliza­ tion whatever can be made to the language behavior of other children* It is offered as a particular case of language behavior and because it nay be provocative of future leads*

She child who arete this long sample

sas fifteen years old, attended senior high school, had an I.Q* of ISO, and came from a teen school,

the long sample sas sectioned Into six

5,000 word sub-samples and the 100, 500, 1,000, and 5,000-word type-token ratios computed for each sub-sample.

these results are presented in

fable IV* Since the type-token ratios in the first three eoluens, i.e., for 100, 500 and 1,000 sards, are means, It sas possible to do an analysis of variance in which one estimate of the population variance is obtained from the deviations of the individual type-token ratios and the other from the variation in the means. %

None of these three analyses proved

significant, the 7-ratios being less than one in the case of the 100-word m , 1*756 for the SOO-word T O and 1.646 for the 1,000-word TIB. For significance at the five per cent level of confidence, F-ratios of 2*30, 2*54 and 3*20 respectively, would be required.

The 5,000-word TTR

could net be tested by this technique since there is but one measure of it in each sub-sample. On the basis of this analysis one would infer that the dif­ ferences between the various sub-sample TTB’s for 100, 500, and 1,000 words can be attributed to chance and that the hypothesis of homo­ geneity has not been discounted.

However, this statement holds only

if the six sub-samples are randomly selected from a population of such

26

table IV Type-Token Ratio Measures o£ an 18,000 ward language Sample 100 * word TTR*

Moan 500word TTR

1,000word TTR

Moan S,000word TTR

5,000-word Sub-sample 71.5700

50.85

48.40

51.80

69*15

48*87

40.80

89.57

66*87

47.18

40.00

89.87

70*15

48.60

41.07

50.57

69.85

47.87

88.50

87.40

70.40

45.97

56*40

84.10

* TTR is an abbreviation for type-token ratio, ## All type-token ration are expressed ae percentages*

27

sub-eaaplss*

Since there appears to be a downward trend in the mag­

nitude of tfeeee type-token ratios with an increase In the number of eeards written, except in the ease of the 100 -werd type-token ratio, this assumption of randomness nay not be fulfilled*

It the sub-

samplea cannot be assumed to be randomly selected, the results of the y-test ean be ignored and the data Interpreted in terms of a trend* It is the opinion of this investigator tnat in this one instance the results presented in Table IV are indicative of a trend toward a re­ duction in the use of types with an increase in the number of words wirtten*

With the exemption of the 100-word TTH, the TTR's may not

be considered as homogeneous throughout the length of this sample of language*

Factors operating to produce such an effect may be (1)

reduction in the number of topics available to the child tending to a greater repetition of types related to topies already written on, (£) change in motivating conditions, such as loss of interest, bore­ dom, eeapetiSlen with other activities, and (5) an adaptation to the writing situation tending to produce stereotyped behavior* Further, the fact that the 100-word TTR does not show this trend may be indica­ tive of chance factors operating in the other three ratios, or it may indicate that the various type-token ratios are not measuring the same aspect of language* In any event, it may be considered as demonstrated that for 5,000 words the 100-word and 500-word TTR's are homogeneously distri­ buted throughout the length of the sample* but that, on the basis of one case, this homogeneity may not be assumed to be necessarily present much beyond 5,000 words*

28 Apreblem closely related to that of reliability in posed by this question*

*«hat Is ths minimum number of words that need to

bo sanqiled from erne Individual to obtain an adequate measure of his language behavior in toms of type-token ratios!*

the answer to this

question is of a»xi practical Interest than theoretical* sines the number of words sampled has been* necessarily* arbitrarily determined* If a positive answer can be made to this question ouch laborious and time-consuming work entailed in language studies may be partially eliminated* Sines no child wrote his full quota of 5*000 words in one day and since there appears to be practically no carry-over in any given child >s topics from day to day* it is felt that the first part of a child's output could be oemaidened as relatively independent of his last part*

Correlations of TTR's for the first and last part of

the sample* based on successively larger numbers of words* should give an indication of the reliability of tho TTR as the base number of words is increased* for this purpose the following correlation coefficients were computed for 108 pairs of subjects t (!) TTR Of first 100 words against TTR of last 100 words.

r • *878

(A) Mean 100-word TUB. of first 500 words against mean 100-word TTR of last500 words*

r * *669

(5 ) Mean 100-word TTR of first 1*500 words against 100-werd T O of last1*500 words* r - .816 (4) first 500-word TTR against last 500-word TO.

r - .657

(5) Ifisan 600-word T O for first 1*500 words against mean 500-word T O of last 1*500 words*

r * *669

(6 ) first l*0 OO-word T O against last 1 *0 0 0 w w d to*

r m *615

29 If it is assumed that the various type-token ration under eon•idoration are equivalent measure** me eee that the 1 ,000-word TTR le practically aa good a meaeure of the individual9* language ae the average 100 and 500-word TTR’s for 1*500 words*

Further* the 1,000-word TTR

give* a reliability whieh compares favorably with that estimated for average 100 and SOO-word TTR1# based on the full 3*000 trorde* *815 as compared to *904 and •908# For most purposes* a type-token ratio based on 1,000 wards will prove adequate and in some instances TTR9a based sn only 600 words might prove useful* Filially we seek to answer the question!

"How strongly aare the

type-token ratios interrelated** An answer to this question will also give a partial answer to the questions

*po the different type-token

ratios employed in this study measure the same aspect of languagef* An answer to these questions was sought by intercorrolating the four type* token ratios (all four based on 5,000 words*)

These correlation co­

efficients are as follows! ®M0

*500

®l,000

.954

*500

*5,000

.870

.MS

.745

.925

.952

the multiple-correlation coefficient of R^qq, % q 0 * end H^qoo ®5,000 is *99*

Besides the fact that the four TTRfe are highly inter­

related it Is noted that the greater the difference between the base number of words the less the eorrelatlon* Since* for each individual* these TTR9a are based on the same language sample* this result is to be anticipated* to seme extent, on §. priori grounds*

Further* inspection

30 of the eoatter-dlagraae of these lntercorrelatlone revealed that the ! relationships are linear* On these grounds, we would judge the four TTR's to measure essentially the same aspect of language*

31 Group Differences in language Measures Differences between the levels of I*Q.* C*A*, locality and seat wore inveetigated by moans of the analysis of variance technique* The analysis of the factorial design was carried out for the following language measures t 1* Language measures derived from the total samples a. Type-token ratio^ for 100-word segments* ^All type-token ratios are presented as percentages rather than as decimal fractions* b* Type-token ratio for 600-word segments* c* Type-token ratio for 1*000-word segments* d* Type-token ratio for the total 5.000 words* 2* Language measures derived from sections of the samples cate­ gorised by the following parts of speech* nouns* verbs* adjectives* and adverbs*

Each of these four sections of

the samples were analysed separately in terms of the fol­ lowing measures* a* Humber of tokens* to* Bomber of types* e* Type-token ratio computed as the total number of types divided by the total number of tokens of each category* d* The percentage which the types of each category is of the total number of types in the four categories* from these measures* a total of twenty analyses of variance was made*

In the tables presenting these results the following symbols

S3 art used to dealgnate tho various levels of the factors under con­ siderations 1* I*Q* levels 1^ — X*Q*

89

and under*

I» - I.Q.

90

to 108. inclusive.

Xg - X*Q* 110 and over* 2* Chronological age levels - C*A* Ag

C*A*

of 18 years, five monthsand under* of

18 years, six monthsto14 years, 11 months.

Inclusive* Ag ~ c.A, of 15 years and over* 8*

Locality levels - City lg «* Town 1$ - Rural

4* Sex S^ - Boys Sg - Girls In the twenty applications of the analysis of variance tech­ nique, 808 interaction variances were computed, and since only three of these were significant and, then only at the five per cent level of confidence, it was felt that, on the grounds that these measures are highly interrelated, it would be safely assumed that there is no interaction among the four factors under consideration as far as these language measures are concerned*

By chance one should expect about

ten or eleven of the interaction variances to be significant at the

five per cent level of confidence. Because the main purposes of this analysis were exploratory, it was decided that the more conservative error variance estimate should be used to test the main effects.

In 19 of the 80 individual

analyses, the Z x i x L x S variance afforded the more conservative estimate of the error variance and consequently was used as the error term even though the degrees of freedom available for the F-test were much reduced.

In the one instance where the I x A x U S

variance

was less than the majority of the interaction variances, an error variance was computed by summing all of the sums of squares of the interaction terms and dividing by the sum of the degrees of freedom of all of the interaction terms. In cases where the 7-test was significant, differences between levels were tested by means of Fisher*s t-test.

The error

variance used as a basis for these t-tests was computed as the residual variance after the variation due to the main effects had been deducted from the total variance.

This procedure is perraissable on the hypo­

thesis of no interaction and since this hypothesis of no interaction seems tenable, the standard error of difference was computed from these residuals because it permitted a greater number of degrees of freedom In evaluating t. Analyses of type-token ratios, Xntereorrelatlons of the 100, 500, 1,000 and 5,000-word typetoken ratios indicated that these measures could be considered as equivalent measures.

Further evidence of this equivalence is gained

from the analyses of variance of these four measures.

The results of

34

the analyses of variance of tho factorial design of 106 Iowa school children are presented in fables V, VI, VII, end VIII,

It is noted

that eaeh of these measures gives group differences which result in F*e which are very nearly equal and that differences between levels, when the t-test nay leg!sally be applied, show t-values of approxi­ mately the same magnitude*

Further, the direction of the differences

is the same for eaeh of the four measures* For each of the four type-token ratios, the F-test indicated that the X*Q* and C.A* factors were significant*

Differences between

means of I*Q* levels were more marked than were differences between C.A. levels*

there appeared to be a progressive Increase in type-

token ratio with increment in both I.Q. and C*A*

However, the dif­

ferences between 1^ and 3jg were distinctly more marked than were the differences between Ig ssnd Ig# A similar trend was noted for differences between means of the three C.A. levels where the difference between *1

and Ag was much greater than the difference between Ag and Ag* This

effect may be an artifact due to the arbitrary method used in forming the 1*Q* and C*A* levels, or it may indicate a leveling off of the type-token ratio values at the upper I.Q. and C.A. levels*

Further

investigation is needed to determine more exactly the relationship of the type-token ratios to I*Q* and C*A* On the basis of this analysis one would predict that a cor­ relation exists between the type-token ratios and I*Q* score and between type-token ratios and C.A*

The correlation of type-token ratios with

1*Q* scores might be attenuated by allowing C.A. to be unrestricted and on the other hand the correlation between C.A. and type-token ratios

35

table v Result* of Analyst* of Variance of TTR#* for lQO-word Segment* (%oo) ** S.QGO-erord language Sample* Written lay 108 leva School Children Faster

d.f.

I,Q. C.A. locality Soat Brror

Heanpi

t t 8 1 8

Variance

411#8917$ $98.95895 19.10260 40.82880 20.69772

Difference

F

19.997** 19.309** 1.982

t

58.7085 h 63.5917 H 2k 65.2778

2, . 3* 4.8854 1£, 2* 6.669$ IS 1.8861

5.197** 7.290** 2.095*

58.6555 H 64.0069 % *» 64.6944

A,. A* $.$717 Ai. A5 6.0611 Afc* AS 0.6894

6.961#* 6.786#* 0.765

h H H

62.0167 65.5001 02.0612

b

01.8444 65.0740

In thin and all succeeding table* value* eigntfleant at the one per cent level of confidence are Indicated lay **. and value* *lgnifleant at the five per cent level of confidence are indicated by *•

8 6

w a » vz I M d t i of Analysis of Variants* of Tilt'* for 6QO-*ord Ssgasnts (Hgfvj) of 8t000*iwi Language S u p l M Stltton by 108 l a m School Children Jfct$«r l.Q. . OU . lewllty 8sx Bnr

Hson* I, Xt Zg

86.7417 41.4088 46.6167

4. A. Ag

57.8944 41.6000 .48.7788

% 40.7806 1* 41.0417 % 89.9445 6. Sj

40.2885 40.6844

d.f.

fkrianee

ft * 8 1 6

F

445.63086 287.88780 11.81690 10.08540 85.18874

Difference

17.611** 11,451**

t

X,. U 4.8666 IT. lZ 6.8760 tj, Ijj 8.8084

6.114** 7.686** 8.480*

1 , A, lT. A. A*. A*

4.609** 5.884** 1.888

4,8066 8.5778 1.1188

warn m Beetalt® of Analyst# of Variance Of for 1,000-word BegBKrafcs ( % aooo) ^ 5,000-word language Sample* u n t t e n ^ 103 Iowa School Children lector I.#* C.A, locality Base Xrroer

Naan*

d«f« ■ 2 a a 1 6

Variance

F 17„3JI8** 9.06#**

201,81086 19,64776 8.48850 28.19876

uLffawmM

A

88.9948 SS.8978 8S .4084

I j . J , 4.8087 I., X. 6.4189 l£ , i j 8.1118

4.C2S** 7.192** 8.867*

% 29.9084 Ag 55.5566 *» 54.4561

Ajj 5,4472 A j, A , 4.6277 Ajj, Ag 1.080S

% L Jj

5.8664** 6.0770** 1.818

Table VIII Results of Analysis of Variance of TTR's for 3,000-^rord Segments (Rg q q q ) of 5,000-word language Samples TSritten by 103 Iowa School Children Factor I.Q . 0*1* lo c a lit y Error

d*f*

Variance

3 2 2 X 3

306*99340 130*53460 28*77950 0*05330 15*57071

19*716** 8*387*# 1.1

Means

Differences

13*9000 22.7417 24*6306

It* % 3.8417 Xl* la 5.7506 1.8889 4.

4.705** 7.018** 2.513*

20*0139 22*5053 23.7556

*%• *8 2*4839 ^1 * *8 5.7417 Ag 1*2523

5*048** 4*582** 1*534

% 25*0500 Xg 21*9417 % 21*2806 S, 22*0635 Sg 22*1129

t

39 ml^rb be attenuated if I.Q. is allowed an unrestricted range due to tho possible counteracting influence of these too factors, although there might bo reinforcement rather than attenuation.

In any ©vent,

it io desirable to determine the relationship between I.Q. and typo-* token ratio with tho effect of C.A. reduced to a minimum, and to deter­ mine the relationship between C«A. and type-token ratio with the in­ fluence of I.Q. minimised.

One method of accomplishing this end ie

to determine the correlation of I.Q. with type-token ratio within C.A. level* and of C.A. with type-token ratio within I.Q. levels.

These

correlations may be viewed as empirically determined partial correla­ tion coefficients, in the first case with C.A. held constant and in the second with I.Q. held constant*

In each ease throe measures of the

partial correlation coefficient are obtained. On the basis of the assumed equivalence of the four type-token ratios being studied, only the correlations of the 3,000-word type-token ratio with C«A. and I.Q. were computed.

The correlation between

g,000-word type-token ratio and I.Q. and between 5,000-word type-token ratio and C.A. within I.Q. and C.A. groups was also computed.1

These

*See Lindquist, E.F. Statistical Analysis In Educational Research. Houghton t&fflin Co., 1940, pp. 219-228. correlations are presented in Table IX. In each case the unrestricted correlation along with the correlation within groups as w e n as the empirically determined partial correlation are presented. A comparison of these two correlations reveals that the unrestricted correlation and the within groups correlations tend to be very much alike in this Instance.

This result is to be expected since the range in C.A. and I.Q.

40

Table XX Table of Correlations of 5,000-word Type-Token Ratio with C.A. and I.Q. Correlation of

r

g

C.A. unrestricted) % #G00 ^ith C.A. Within X^ % 000 C*A * Within Xg Ej'ooo math C.A. Within Is

«SSR

108

,483 .398 .*55

38 36 56

Rg^OOO With I.Q. (C.A. unrestricted) *5,000 With I.Q. Within A* *8,000 With I.Q. Within Aj Ra'oOO With I.Q. 10.thin Ag

.517

108

H

QQO

.646 .558 .546

96 56 36

Within Oroupa Correlation of Bg ooo With C.A. "5,000 Wlth I.Q.

.325 .420

108 108

41 Is reduced relatively much more than is the range of the type-token ratio scores.

It would seem that a better Index of the strength of the rela­

tionship of the 5,000-word type-token ratio to I.Q, and to C.A. is the correlation of 8,000Hiord type-token ratio with I.Q. within C.A* levels on one hand and S,QQO-word type-token ratio with C.A. within I.Q. levels on the other, since in each ease counteracting influences are somewhat re­ duced.

However, inasmuch as the locality and sex factors were not sig­

nificant, the within groups correlations permits the estimation of the significance of the correlation of I.Q. and of C.A. with 9,000-word typetoken ratio. With 100 degrees of freedom, both correlations are sig­ nificant at the one per cent level of confidence when tested by means of Fisher9s t-test.^ the t«-value for the within groups correlation of 6 .A. ^See Lindquist, E.F.

Op, Pit, pp. £10-211.

with 5 ,000 -word type-token ratio is 5.51}

the equivalent measure for the

within groups correlation of I.Q. with 5,000-word type-token ratio is 4.64. The positive results of these correlations are indicative of a relationship between type-token ratios and I.Q. and between type-token ratios and C.A., but the relationships are not strong enough to predict a type-token ratio for an individual from knowledge of his age and his I.Q. score. On the assumption that the correlation of C.A. and I.Q. is sere, the multiple correlation coefficient of type-token ratio with C.A. and I.Q. is only .608, a result which suggests that C.A. and I.Q. are not sufficient factors for completely determining the type-token ratio. Analysis of nounal. verbal, adjectival and adverbal sections of the IjLnmiaga «nTlfft1.

Huwbwr a.

tok»n» of w ch nwrt at apaoc)} eatogory. floune. The results of analysis of variance using the

number of nounal tokens as a language measure is presented in Table X.

Table X Results of Analysis of Variance of Number of Nounal Tokens in 5,00Q-*rord Language Samples Written by 10$ lavra School Children Factor I*Q* C*A* Locality sea Error

Means h ¥ h

498*028 550*589 557*667

*i H H

551*556 524*475 550*056

h H %

586*589 508*417 511*278

Variance

d*f*

F 6*168*

581*0869$ 75*61585 705*77195 59.40750 61*78519

2

$ Z 1 s

Differences

11*591**

t

II* % h* % *%• h

52*361 59*659 7*278

8*774** 5*159** 0*586

% H.b H h' h

77*972 75*1X1 2*861

4*150** 5.979** 0.152

The results of this analysis point to significant differences in X*Q* and locality levels* respectively, the latter being significant at the one per cent level and the former at the five per cent level of con­ fidence* The direction of the differences In means of I.Q. levels is in an increase in the number of nounal tokens used with an Increase in X*Q* level*

Again, the difference between 1^ and Xg is much more

marked than is the difference between Xg and Is# The difference in means between the Ig, and I5 levels is not significant, whereas the differences between the means of

and Xg and between 1^ and Ig,

respectively, are significant at the one per cent level of confidence* The means of the locality levels show the significant dif­ ferences to lie between city and rural groups and between city and town groups*

The difference between the town and rural group means

is not edgniflcant*

In this case the performances of the town and

rural school children appear to be somewhat similar* b* Verbs*

Results of the analysis of variance in the number

of verbal tokens Is presented in Table XI*

The variance among locality

levels is significant at the one per cent level and the variance be­ tween sex groups is significant at the five per cent level of confidence* The variance derived from C.A* levels is considerably larger than the error variance, but is not significant* The means for locality levels indicate that the town children use the greater number of verbal tokens, that the rural children use less than the town children but more than the city children*

The city

children on the average use fewer verbal tokens than either the town

44

Table XX Results of Analysis of Variance of Number of Verbal Tokens in 3,000-word Language Samples Written by 108 Iowa School Children Factor I.Q. C.A. Locality Sex Error

Means h h H

d.£.

Variance

2 2 2 1

F

79.44115 188441780 779449195 459462810 85.65550

8

Differences

8.X3G 9.102** 5.567*

t

711.556 709.667 636.612

h. 718.389 ht 712.612 a * 676.654 659.028 745.917 % t€ 702.889

% . 2$ 86.889 % 45.861 % 45.028

4.229** 2.155* 8.094*

®I 681.981 723.240 %

8 ls

2.459*

®2 41.259

45

or rural children on the basis of these means.

Ill differences between

city, town and rural group means are significant# the sex group means show the girls to use significantly mors verbal tokens, on the average, than do the boys# e# Adjectives# the results of the analysis of variance of the number of adjectival tokens used by this sample of Iowa school children are presented in table XII#

Hie F-teat employed in this

analysis gave no significant F-values although the use of a less con­ servative estimate of the error variance would give significant Fvalues for the G«A# factor# lieana of both Q#A# and X#Q» levels show a trend which is at least indicative of a possible relation of this measure to C#A# and 1 #Q#

d#

Adverbs#

fable XXXI presents the results of the analysis

of variance when the number of adverbal tokens is used as the language measure*

The locality and sex factors give F-values which are both

significant at the five per cent level of confidence#

The decreasing

order of magnitude of the locality levels is town, rural and city, with differences between town and city and between rural and city means being significant, whereas the difference In means between rural and City levels is not significant# The difference between means of the sex groups is significant at the one per cent level of confidence#

The girls, on the average,

use more adverbs than do the boys# ft* Number of Tvdes of each part of speech category# In the series of analyses involving type-token ratios and

46

Table 111 Results of Analysis of Variance of Number of Adjectival Tokens in 5,000-word Language Samples Written by 108 Iowa school Children Raster i.o. C,A, Locality SOX Error

Means h *8

h

516,111 334,561 351,684

316,778 522,506 H ■** 362,975 *1

h. 559,556 Jb 556,667 528,834 H H *8

551,057 537.000

d#f* 2

£ 8

% 8

Variance 113,27680 229,09570 10,58040 9,80040 61.14391

Differences

4?

Table XIII Results of Analysis of Variance of Humber of Adverbal Tokens In 5,000-word Language Samples Written by 108 Iona School Children Faster I.Q. C.A. Locality Sen Error

d*f*

Variance

2 % Z 1

21.97475 29*64060 555*87396 266.35470 47*65498

8

Means

F

7.5795* 5*5558*

Differences

Ix 274*500 % 259*278 t% 269*645 Ax 258*195 Afc 276.167 A| 269*561 62*561 25.500

4.553** 2*691* 1.862

S2

51.408

2.808**

H

%

h h H

« CD *

% %

254*834 297.19$ 271*695 252*205

48

number of part# of speech tokens, X08 subjects were used in the fac­ torial design, but in this and the two succeeding series of analyses of variance the number of individuals in the factorial design were reduced by half*

This means that instead of having two randomly

selected eases in each cell of the design, only one subject per cell was used*

Except for this feature the factorial design was unaltered*

This change was necessitated by an urgent demand for economy of both time and money* and it was felt that since this aspect of the inves­ tigation was almost purely exploratory, it could best withstand the enforced economy* When the decision to change the number of individ­ uals in the design was made, words in the language samples had already been classified by parts of speech, so that it was possible to use the entire 108 subjects for number-of~tokens aspect of the grammatical analysis*

Thus, for the series of analyses consisting of (1) number

of types, (Z) type-token ratio, and (5) per cent of total types for the parts of speech sections of the samples, only $4 subjects, the minimum number needed to fill each cell of the design, were used*

The

54 subjects to fill this design were chosen from the original 108 sub­ jects in the factorial design used in the two previous series of analyses* In this ease, when there was but one subject in each cell of the design, the within groups variance is identically the I x A x 1 x S variance*

This variance was used as the error tern and is uniformly

referred to as the X x A x 1 x S variance* *•

Kbunal typep*

In Table XIV the results of the analysis

of variance, in which the number of nounal types is the language measure being investigated, are presented*

Significant F—values were obtained

49

Table XIV Results of Analysis of Variance of Humber of Hbunal Types in S.OOQ-word Language Samples Written by $4 Iowa School Children Factor I.Q. C.A. Locality Sex Error

Means

885.888

Tg

511.554

A1 Afc

254.778

471•57350 40*20075 115.00075 4.05650 50.58115

8

Differences

h' *s h» h

F IS*553** 3,727*

%

72.666

54820* * 5 .1 9 3 * *

CD

it

Z 2 a 1

*

818.556

Variance

I

h

d.f.

26.118

1.575

1.000

0.055

269.667 284.667

h.

285.667

**

284.667

H

240.778

H H

266.965 278*444

h h ‘h H h >

42.889

2 .2 5 5 *

45.869

2 .5 0 7 *

50

for I.Q. and locality factors, the former being significant at th® on® per cent level of confidence and the latter at the five per cent level* Means of the X.Q. levels again indicate a trend in the use of nounal types, a trend similar to that found for the type—token ratio measures.

Application of the t-test results in significant t-values

for differences between means of

and 2^ levels as well as for dif­

ferences between X^ and Xg* The difference in means between Xg and I3 levels does not give a significant t-value. Means of locality levels show practically no difference in the performance of city and town school children on this measure. The difference in means between the rural group and both the city and town groups was sufficient to give a significant F-value.

Differences

between the means of the rural level and either the city or town level is significant at the five per cent level of confidence. b.

Verbal types.

The results of the analysis of variance of

the number of verbal types in 3,QOCMrord language samples written by these $4 Iowa school children are presented in Table XV. I.Q. factor roouitod in a eignificant F-value.

Only the

The n»an of the

level is significantly greater than is the mean of either The difference between the means of c* Adjectival types.

and

is not sLgnifleant.

Table XVI contains the results of the

analysis of variance of the number of adjectival types. 6 .A.

or X%9

Both X.Q. and

factors give significant F-values at the five per cent level of

confidence.

The direction of the difference in means, in the case of

both X.Q. and C.A.* is in favor of an increase in th® use of adjectival

51

Table XV Result* of Analysis of Variance of Number of Verbal Type* in 8,000*word Language Samples written by 64 Iowa School Children Factor I.Q. C.A. Locality SOX Error

d.f. 2

* 2

i 8

Variance 77.97850 45.97850 58.68575 0.58070 15.45811

6.044* 2.974 2.603

Differences % 160.224 Xg 178.889 I® 203.*779 % 162.111 Aj 192.111 Ag 186.667 la 197.222 Lg 172.167 Lg 171.600 % S2

181.858 179.269

Xi* Ig 18.665 X1# I3 41.555 Ig, Xg 22.890

1.878 4.181** 2.306*

52

Table XVI Results of Analysis of Variance of Number of Adjectival Types in 5,000-word Language Samples Written by 54 Iowa School Children Factor I.Q* C.A. Locality Sex Error

*1

% H

Variance 6.291* 6.767*

93.56685 100.64685 6.72685 1.60160 14.87256

2 8 2 1 8

Means

Differences

104.779 129.278 150.333

V *2 24.499 2 .* *3 45.554 I V h 21.055

2.626* 4.382** 2.257*

A- g ^2 % V Ajj. a5

5.551** 4.906** 1.576

101.889 h Ag 134.835 Ag 147.668 % % H

d.f.

187.946 154.353 U 2.111

Sj_ 126.407 8g 129.862

52.944 45.779 12.835

t

53 types idth Increases In C.A. and/or I.Q. All the differences in means between levels of I.Q. and C.A. are significant except for the dif— ference between the means of Ag and A$* d. Adverbal typed# Results of the analysis of variance when the number of adverbal types serves as the language measure are pre­ sented in Table XVII.

In this analysis the I x A x L x S variance was

not used as the error variance because it was smaller than the majority of the first and second order interaction variances*

In this case it

was felt that a better estimate of the error variance would result from the computation of the error variance from the remainder sums of squares* i.e., the remainder of the individual variations after the variation due to the main effects had been deducted*

The error variance

derived from the remainder sums of squares was more than twice as large as the I x A 1 x S variance* 100.956 as compared to 42.160.

On the

basis of this error term* the C.A. factor gave an F-value significant at the one per cent level of confidence*

The difference between the

means of Aj» and A$ did not give a significant t-value, while the dif­ ferences between means of A^ and Ag levels gave t-values significant at the one per cent level of confidence*

The direction of the dif­

ferences points to an Increase in the mean number of adverbal types for an increase in C*A* level* 5* Type-token ratios for each part of speech category. a* Type-token ratio for nouns.

The results of the analysis

of variance when using the type-token ratio for nouns as a language measure are presented in Table XVIII.

In this analysis I.Q. and C.A.

factors give significant F—values* the latter at the five per cent

54

Table XVII R esu lts o f A n alysis o f Variance o f Bomber o f Adverbal types in 5,000-*ord Language Samples W ritten by 54 Zona School ch ild ren le c t o r

d .f*

Variance

F

I.Q . C.A. L o c a lity Sex Error

2 2 2 1 46

2.40075 10.82240 0.27185 1.01410 1.00986

8.878 10.821**

Means 4

h

Differences

65.444 65.556 70.556

h 57.611 ht 71.389 H 69.889 h. 66.667 *2 is

6 5 .m 67.667

«i S2

65.148 67.839

Ag Aj» Aj Ag. Aj

14.278 12.278 2.000

4.264** 5.667** 0.597

55

Table XVIII Result* of Analysis of Variance of TTR for Nouns of 5#QG0-*rorct language Samples Written by 64 Iowa School Children Factor X.Q. C.A. Locality Sex Error

Means

h H H

42.5225 49.9278 52.3945

44.5000 Ag 49.2225 H 51.8225

h

% % S

47.2225 51.9167 46.2056

®x 47.5075 So 49.5269

d,ff

Variance

Z Z Z 1 3

SIS.67910 262.71655 167.06465 62.72670 54.45951

F 9.456** 4.826* 3.069 1.162

Differences 7.4055 V h 10.5722 h> H 2.9667 h> h H* H As V H

4.9225 7.5225 2.6000

1.600* 1.642* ,.042 ,.723 1.641** >.915

56

level and the former at the one per cent level of confidence* Differences between means of the I.Q. levels give signifi­ cant t-values for the differences

between 1^ andand between 1^

and Ig but not for the difference

between 1% and Ig. The direction

of the differences in means is. again. In favor of anIncrease in type-token ratio with an increase

in I.Q. level. The differences in

means among I.Q. levels prove to be more marked than do differences In means among G.A. levels. Differences between means of C.A. levels are significant only os between Aj_ and Ag»

This difference gives a t-value significant

at the one per cent level.

The direction of the differences is for an

increase in type-token ratio for nouns with an increase in C.A. b.

Type-token ratio for verbs. Analysis of variance results

for the type-token ratio for verbs are presented in Table XIX. Fvalues for I.Q. and locality factors prove significant at the five per cent level of confidence. th. difference between ^ end I5 Man. i. significant at the one per cent level of confidence, while the differences between Man. of

and Ij and between Ia and I5 fall juet short of aignifi-

canoe at the five per cent level of confidence.

Again there is a

systematic increase in type-token ratio for verbs with an increase in I.Q. level. Ueans of locality levels show the differences between city and town levels and between city and rural levels to be significant, while the difference between the town and rural level significant.

is not

On the average, city children use proportionately more

57

fable XU Besults of Analysis of Variance of TfR for Verbs of 5»000-#tord language Samples Written by 54 Iowa School Children

Factor I.Q* G*A* locality Sex Error

Means 25*2667 27*0056 ** 50*4589

h

H

25*7500 28*5000 28*4611

% h H

50.7728 23*7556 26*1856

H

27*5148 26.4926

H

d*f.

Variance

F

2 2 % X 8

281*62515 154*27555 228*55590 9*12590 45*44191

5.097* 2*955 5*050#

Differences

t

% • h 3*7589 % • h 7*1722 *5 5*4335

1*956 3*752## 1.796

7*0166 4*5886 2*4280

5*671## 2*401# 1*270

h* h h* h %

58

verbal types than do either town or rural children, while rural children use proportionately' more verbal types than do town children* c. !Pype-token ratio for adjectives*

Besulta of the analysis

of variance of the type-token ratio for adjectives are presented in fable XX.

F-values for I*Q* and C*A* factors prove significant at

the five per cent level of confidence*

However, the F-value for the

locality factor, while not definitely significant, is more than twice the error term* Means of I.Q* levels show the difference between means of 1^ and both Ij> and Ig to be signifleant at the one per cent level of con­ fidence, cant*

The difference in means of \ end fg is clearly not signifi­

Again we note a progressive rise in type-token r atio with rise

in I*Q. level* Means of C*A* levels show a trend similar to that of levels in that there is a rise in type-token ratio with a rise and in the fact that differences in means of

I»Q* in C*A*,

and both A*> and Ag are

significant at the one per cent level# while the difference in means of

and

A$ is again clearly not significant* d. Type-token ratio for adverbs* Analysis of variance results

for type-token ratio for adverbs are presented in Table XXI* This language measure gives significant F-values for X*Q, and locality fac­ tors, both factors giving F-ratios significant at the five per cent level of confidence* In this instance, differences between means of I.Q. levels indicate a greater difference between the means of Ijjand Ig. Only the differences in means between

and Xg and between 1^ and Xg are

59

Table IX Results of Analysis of Variance of TTR for Adjectives of 5,OOO-word Language Samples Written by 54 Iowa School Children gfeeter I.Q. C.A. Locality Sex Error

Means

d.f.

Variance

2 Z z 1 8

556.81550 506.56780 104.44055 60.16670 45.88518

Differences

6.557* 6.900* e.5?9 1.571

t

*1 55.5889 % 40.5778 h 41.8554

*1, 3$ 6.9889 % 8.4445 Lj, Ijj 1.4556

5.175** 5.855** 0.661

Ai 55.7854 40.5946 H *5 41.2225

A1# Ag 6.8111 Ax, Ag 7.4589 Ag, Ag 0.6287

5.092** 5,577** 0.285

H % H

58.2611 41,0667 56.2725

h. 57.4777 59.5888 H

60

Table XXI R esu lts o f A n alysis o f Variance o f TTR fo r Adverbs o f 5j000-*ord Language Samples W ritten by 54 Iowa School Children fa c to r I.Q . C.A. lo c a lit y Sex Error

Mesas *1 If

h Ai

H

22.4778 24.8884 28.5384

d .f .

Variance

F

2 2 2 1 8

167.55690 58.66556 162,19245 85,76470 38.48159

4.554* 1,596 4.280*

D ifferen ces *i» h

h ‘ h H. h

t

2.4056 6,0566 5.6500

1.527 5.845** 2.517*

5.9722 5.5166 2.4556

3.790** 2.252* 1.559

25.8111 26.4534 28.1500

h. 23,4611 H 22.4888 H 24.9445 26.0889 ®2 24.5074

h ‘ h H

61 signifioant when tested by Fisher’s t-tsst*

Again we note a rise in

the magnitude of the type-token ratio with a rise in X*Q* level* Locality level means indicate that the city levels have a Significantly greater mean type-token ratio for adverbs than do either town or rural levels*

The difference In means of the town and rural

levels is in favor of the rural level* but the difference does not give a significant t-value. 4*

Percentage of parte of speech types of the total types* a*

Per cent nounal types* The analysis of variance results

using the percentage of noural types as a language measure are presented in Table XXIX*

None of the factors under consideration gave a signifi­

cant F-value. b* Per cent verbal types* Results of the analysis of variance for percentage of verbal types are presented in Table XXIII* Only the f value for the I.Q* factor proved significant at the five per cent level of confidence* although the variance for the locality factor Is almost three times the error variance* The means for Ij> and Xg are approximately equal while the children in

level* on the average* use a significantly greater per­

centage of verbal types than either the children In Lj and Ig levels* c* Per cent adjectival types*

Results of the analysis of

variance of the percentage of adjectival types are presented in Table XXIV*

The F-test shows the C.A. factor to be significant at the one

per cent level of confidence* Differences In means of both

and Ag when compared with A^

give significant t—values at the one per cent level of confidence*

On

6S

Table XXIX Results Of Analysis of Variance of Pox1 Gent Nounal Types In 5,000-word language Samples Written by 54 Iowa School Children Factor I.Q* O.A. Locality Sex Error

Mm im h h

38.667 43.087 42.566

*i H H

43.388 40.000 41.000

ia h

*

41.556 43.355 39.500

H

41.185 41.741

h

d.f.

Variance

Z z z X 8

107.245 54*575 66.245 4.170 66.151

83

Table XXIII R esu lts o f A n alysis o f Variance o f per Cent Verbal Types In 5,000-srord language Samples W ritten by 64 Zewa School Children Factor I.Q. CeA. locality Sex Error

% *8

Variables the evidence garnered from the application of the analysis of variance technique to 80 language variables, reveals their capacity to differentiate groups classified according to the factors investigated* A summary in tabular form is presented in Table XXVI.

Considering the

fact that the results of the analyses of variance of these 80 variables as described in the previous section is rather ponderous, a skeletonised version of these results appears to be appropriate.

The summary will

collect the significant results for each of the pertinent factors* A.

The I.Q. Factor. Of the 80 analyses of variance involving

the I*Q* factor 14 resulted in significant F-values* Of these, seven are significant at the one per cent level and seven at the five per cent level of confidence*

In general, the direction of differences of the

means of I.Q. levels for these variables is in a numerical increase in the value of the measure for increases in I.Q. level. 1.

Segmental type-token ratios The 100, 500, 1,000 and 3,000-word type-token ratios all give

F-values significant at the one per cent level of confidence, Means of the three I.Q. levels for the segmental type-token ratios are positively related to I.Q. level. 8* Variables dependent on counts of nouns Three of the four measures derived from counts of nounal types and tokens resulted in significant F-ratios. Th© type-token ratio and number of types, respectively, are significant at the one per cent level of confidence, while the percentage of nounal types failed to reach either

68

69

JP

JP

j* j p j ? 4*

4 4*

jp

jp

jp

J1

4

4* 4* 4*

jp

jp 4*

% w>

* ►r*

» » p

3

3

JP 4* 4 * h " ♦4**1* ^ 4* i .n n |j^ n

4

*

y wuK

» jp 4*

»s4

«

»

► r4 4* 4*

4* 4* 4*

»

3

70

criterion of significance*

In each ease# differences in means of these

measures among I.Q. levels ii in favor of an ineroaoo in tho moan value of tho measure with an increase in X.Q. level* 5*

Variable* dependent upon a count of vorbo Three of tho four moaaureo involving eounta of verbal types

and tokens result in significant F^values, - all significant at the five per eent level of confidence*

These variables gave significant F-valuess

number of verbal types* type-token ratio for verbs* and percentage of verbal types.

The direction of differences among moans of X.Q* levels

for tho number of types and type-token ratio* respectively. Is posi­ tively related to X.Q* levels* while the direction of mean differences for the percentage of verbal types is reversed* the lev X*Q* group using a greater percentage of verbal types than either of the other two I.Q. groups* 4*

Variables dependent upon a count of adjectives* Ifieasures based on a count of tho number of adjectival typos

and tokens result in only two of the four measures giving significant F-ratios for tho X*Q* factor* Both of these are significant at tho five per cent level of confidence*

The direction of mean differences

for these two significant measures is positively related to X.Q* level* 5* Variables dependent upon a count of adverbs Of tho four measures involving adverbs* tho type-token ratio for adverbs and the percentage of adverbal types gave significant Fratios* the latter significant at the one per cent level of confidence and the former at tho fivo per cent level.

X.Q. levels prove to be

positively related to the moan type-token ratio for adverbs and negatively

71 related to the mean percentage of adverbal types, B,

The C.A, Factor. Nine of the SO language measures, when

each i» submitted to an analysis of variance in terms of the factorial design, result in a significant F-value for the C.A. factor*

Of these

nine measures, sin give revalues significant at the one per cent level and the remaining threw give F-values significant at the five per cent level of confidence.

For each of these nine measures, the means of G.A.

levels increase In value with an increment in C.A. level; in other words, the older the Child the higher the score in terms of these nine measures, 1,

Segmental type-token ratios The four segmental type-token ratios, when submitted to an

analysis of variance, result in F-values which, for the C.A* factor, are significant at the one per cent level of confidence in each case, the direction of mean differences is positive, i.e., the older the child the higher the numerical value of the type-token ratios. 1.

Variables dependent upon a count of nouns Only the type-token ratio for nouns resulted in a significant

F-value, and this at the five per cent level of confidence.

The older

children tended to have a greater type-token ratio for nouns. 5. Variables dependent upon a count of verbs Hone of the four variables derived from counts of verbal types and tokens results in significant F-valuea for the C.A, factor, 4,

Variables dependent upon a count of adjectives Three of the four variables involving counts of adjectives

prove significant for the C.A. factor.

For this factor, the number of

adjectival types is significant at the one per cent level.

This evidence

72 point# to an ln oma * in tho uao of adjectival token# and typo# a# tho children grew older* S*

Variables dependent upon a eount of adverb# Of the variable# in thl# category only the number of adverbal

type# give# a significant F-value (at the one per cent level) for the CJU faeter in the analysis of varianee*

The tendency is for an increase

in the use of adverbal types with age, although the two older groups are reversed, but the difference in means between these two groups is not statistically significant* C*

The Locality Pastor*

Six of the ZO measures, when sub­

mitted to an analysis of varianee, gave significant F-ratlos for the locality factor*

Two of these six are significant at the one per cent

level and the remaining four at the five per cent level of confidence* No general trend in differences among the means of the city, town and rural group# was noted* 1*

Segmental type-token ratios Segnental type-token ratios do not differentiate locality

groups*

Hone of these four measures gave significant F-ratio# for the

locality factor*

£• Variables dependent upon a count of noun# For the locality factor, only one, number of nounal tokens, of the measures in this classification, gave a significant F-value (at the one per eent level)*

The city group uses, on the average, a greater

number of noun# than do town or rural groups, while the rural group uses more than do the town group*

73 3*

Variable* dependent upon a count of verb* Vor the locality factor, the number of verbal token* and

type-token ratio for verba, reepectively, gave significant F-value*. Only the number of verbal token* 1* significant at the one per cent level of confidence*

The rank order of mean* for number of verbal

type* 1* town, city and rural In order of decreasing magnitude, chile for the type-token ratio for verb* the corresponding rank order 1* city, rural and town* 4*

Vailablea dependent upon a count of adjective* For the locality factor, measure* baaed on count* of adjec­

tival type* and token* do not produce any significant F-valu*s. 5* Variables dependent upon a count of adverb* Three of the four variable* derived from counts of adverbal type* and tokens successfully differentiate locality groups a* judged by the F-test.

These three measure* are the number of adverbal tokens,

adverbal type-token ratio, and percentage of adverbal types* are significant at the five per cent level of confidence*

All three

City group*

tend to use the least number of adverbal tokens and types, but have the greatest adverbal type-token ratio*

The town group use* the most ad­

verbal tokens while the rural group uses a greater percentage of ad­ verbal types* D*

The Sex Factor.

For the sex factor, only two of the 20

language variables gave significant results in terms of the analysis of variance*

These two measures are number of verbal token* and number of

adverbal tokens, respectively, both significant at the five per cent level of confidence• m both instances girl* use a greater number of these classes of token* than do boys*

74

In general* it may be said that in tern* of the language measures employed* the higher the X«Q* and the higher the age level the more highly differentiated is the language structure of the writers* the use of a proportionately greater number of nouns and adjectives characterizes high X*Q* and older age group*, while the use of a pro­ portionately greater number of verbs and adverbs characterizes the low X.Q. and younger age group*.

75 Cumulative Tvue Frequency Curve

In a recent article* Carroll ( 3 ) states that the equation D " | (**23 * K - log.H * log,K).

(X)

where Dis the number of different words in a language sample of length N« N Is the total number of words in that sample* and K is an empirically determined constant, held for the language samples he had under investigation*

If this formula could be demonstrated to

hold generally* it would be a powerful tool in language research• Parroll deduced equation (1) by means of certain logical and statistical considerations from the following equation* where

* m J i KB

(a)

F is the frequency with which any given word occurs* E is its rank in order of decreasing frequency* N the number of words in the sample from which F and E are computed, and K is an empirically determined constant which has the same meaning as the j£ in equation {!)• A necessary condition to the applicability of equation (1) is that equation (2) hold for the data and particularly* that the exponent of j£ have a value of 1*0*

To determine whether equation (2) holds for the language samples under Investigation* 18 of the 108 language samples were selected in such a fashion that two randomly selected cases came from each of nine C.A*, I*Q* groups* and the variables F and R were measured

7G fdr taeh sample*

Equation (2) can be reduced to

Log P *

log R + log 1

which la seen to bo linear In log P and log R*

If a plot of (log F*

log R) ©an bo considered linear* then tho line of boot fit can be determined bp means of the method of least squares*

A graphical re­

presentation of a typical plot of (log F, log R) and of (F*R) along with the best fitting curve is presented in Figure 1* Similar curves wore eomputed for each of the 18 selected samples of language*

It can be

noted that the fit is not good for the lower ranks* and since Carroll states that equation (8) holds only for ranks greater than about 80* the best fitting straight line was fitted to each of the 18 plots of (log P* log R) for a series of points in which the first 80 (approxi­ mately) points corresponding to the lower 80 ranks were eliminated* Estimates of the parameters* a and g, for 18 language samples are presented in Table XXVII. If equation (1) is to have any generality* then equation (8)* which is the harmonic series law of word frequency distribution* must hold for language samples in general*

Specifically it must be demon­

strated that a plot of (log F* log R) is linear and that the value of the exponent of R Is 1*0*

On the basis of the 18 plots of values of

(log 1. log R), it was judged that the assumption of linearity is reasonable* although the possibility of some other function's giving a better fitting reduction line should not be excluded. As for the exponent of R« it can be noted that the curves with the first 80 ranks eliminated result in values of a which are much closer to 1*0 than are

the values of a for the entire series of ranks*

Farther* we note that

77

2 .4

2.0

LOG F = -0.850 LOG R ♦ 2.437

Ul 1*6 LJ Q £ U. 1.2 (9 O

Or j

,e

4

LOG RANK

SS UJ

or

UJ li.

Of

RANK

Figure 1.*- Subject no. 12. Graphic representation of the relationship of the rank of a word (R) In decreasing frequency order to the frequency of occurrence (F). the upper plot shone the reduc­ tion line in terms of log F and log R. Etapirical points are shown In their relation to the curve described by the indicated equation*

m>u m m BaUaaiaa of Jtargpator*, a and K in fciso Fitted Sqiiatlen p • lafifiB for Eighteen language Sample* 68 flret Twenty Batik* *^3*** MabMP

aafta^. .fflimaap * K

ss 4ft 7* s 96 78 8 4 66 U 1& 86 44 87 41 6 100 22

0.968 0.8 2 6 0.066 0.8 69 0.866 0.796 0 .8 6 8 0*860 0*867 0.828 0.868 0.866 0.8 2 8 0*827 0.8 08 0 .8 m 0.829 0 .8 4 6

lean*

0.646

6.768 60.649 9.080 9.708 10.211 11.700 8.516 60.989 66.646 11.619 10.142 62.948 11.891 10*746 14.495 10.003 16*899 12.448

m---------i 1 .866 1.081 1 .0 0 0 0.996 8*991 1.041 0.989 0.967 0.9 49 0.948 1.009 0.889 0.841 1.065 0.808 1.0 10 0.907 0.8 60 0.974

2.0 88 4 .6 8 6 6.298 6.626 6.981 4 .866 8.578 7.582 6.701 6.969 4.3 7 0 9.294 7.246 5.909 14.628 6.872 8.319 12.286

79 when the first m ranks are eliminated, several of the 18 equation* give estimates of a which are practically 1*0.

On the other hand we

note quite a range in the a values, free 0.808 to 1.336, and we are confronted with the problem of determining if these eetimatee of a ere sufficiently oloee to 1*0 to support the assumption that the value of this parameter is 1.0. On the assumption that the value of the parameter a is 1.0, we sen test the hypothesis that the mean value of £ for these 18 language samples differs from 1,0 within the limits of chance by means of the t-teet.

the mean of the 18 a-values differs from 1.000 by

0.086 azad results in a t-r&tio of 1.178. which, with 17 degrees of freedom, gives a probability value greater than 0.8 but less than 0.5, a probability interval which, Judged by the ordinary criterion of significance, is not significant, this statistical test is not en­ tirely satisfactory, since the assumption we wish to test with reference * to the value of the parameter £ is that it is 1.0 in each Individual ease and not that the mean of a distribution of randomly selected language samples is 1.0, although the latter is necessarily true if the former holds.

On the basis of this test, It is reasonable to

accept the hypothesis that the mean value of the parameter £ might be 1.0, and, in some degree, the assumption of a haxmonie series law of word frequency distribution Is seen to be validated when approxi­ mately the first 80 ranks have been eliminated. Equation (1) is peculiar in that it contains only one para­ meter, |« An estimate of this parameter can be detexmined from any one point on the cumulative type-frequenoy curve.

If £ is constant, as it

80 wast be if equation (1) is to hold, then estimates of £ computed at various points along tho cumulative type-frequency curve should differ from oiio another in a chance fashion*

Since we can get a distribution

of £-values for each individual sanqple, as well as a distribution of K-valuea at each successive point along the curve for a group of in­ dividuals we can derive two estimates of the population variance* one based on the variance due to the difference in means at successive points and the other a remainder variance computed from the total sums of squares after the variation due to individuals and to successive points along the curve have been deducted.

On the assumption that

the various estimates of £ differ only by chance, the F-ratio of the two estimated variances should be non-signifleant• For the same 18 language samples used to test equation (&)» g-valuea were computed at each successive 500-word point along the cumulative type-frequeney curve♦ liean g-valuee for the 18 samples were alee computed at each successive 500-word point as well as the mean g-walue for each sample*

these data are presented in Table XXVXXX*

It is noted that there appears to be a systematic

tendency

for the

value of & to increase as the base number of words from which it is computed increases, although this tendency is not of equal strength in all eases**' 1 In one case, subject number 78* the value of B at H * 5*000 was net large enough for a valid computation of £• In order to complete the design the value of J computed at 8*500 words was used as the best estimate of £ at N *" 3*000*) The data in Table XXVIII were subjected to an analysis of variance in order to determine If the variation in mean ^-values at

81

Table XXVIII Table o f K-Values fo r E ighteen language Samples Computed a t Sucoeaalva Five-Hundred Word Polnta Subject Muriber 79 9 96 6 78 49 101 56 1* 44 4 97 8 100 86 22 48 89 Mean*

800 Words

1,000 Words

1*500 Words

2,000 Words

2,500 S se&e

5,000 Words

5.69 6*49 6.94 7*14 7*18 6.50 6.66 6.90 6.59 7.47 6.98 8.88 7.08 7.48 7.47 7.88 7.91 6.17

6.08 6.67 6.97 7.08 6.88 6.76 6.68 7.18 6.78 7.58 7.81 6.89 6.75 7.24 7.46 7.87 8.02 6.22

6.24 6.81 7.14 7.22 6.82 8.87 6.82 7.15 7.00 7.46 7.20 6.84 6.98 7.25 7.47 7.60 7.80 6.44

6.45 6.86 7.22 7.29 6.88 6.87 6.96 7.28 7.17 7.89 7.57 6.87 6.99 7.56 7.57 7.81 7.95 6.48

6.56 6.99 7.28 7.50 6.91 6.90 7.09 7.51 7.42 7.51 7.56 6.90 7.06 7.40 7.55 7.85 7.97 6.58

6.56 7.10 7.23 7.50 6.99 6.94 7.15 7.52 7.41 7.41 7.56 6.93 7.15 7.45 7.62 7.92 8.05 6.68

6.988

6.972

7.059

7.155

7.207

7.256

Mean 6.24 6.32 7.14 7.22 6.94 6.81 6.39 7.19 7.06 7.40 7.24 6.89 6.99 7.55 7.52 7.65 7.95 6.48

successive 500-word points could, statistically, bo allocated to chance factors.

The error variance used to test the sample also varianee,

i.e., variation derived from the means at successive 500-word points, was the interaction variance of individuals and sample slae.

The

results of this analysis of varianee is presented in Table XXIX.

The

F-ratio of 18.556 Is significant at the one per cent level of confidence This result may be interpreted as meaning that the mean JC—values com­ puted at successive 600-word points along the curve cannot be con­ sidered as representing populations which are equally variable or which have equal means.

On the basis of a significant F-teat, inter­

mean JC-valuee were tested by means of the t-test.

Of the 15 differences

among the six means, 12 give a t-value significant at least at the five per cent level and nine give t-values significant at the one per cent level.

If the means of the K-*values differed by chance only, one would

expect less than one of the 15 differences to be significant at the five per cent level when tested by means of

thet-test.

A further test of the adequacy ofthe hypothesis that K Is constant Is afforded by an analysis of the behavior of K in the 18,000word sample. JC-values were eengmbed at successive 1,000-word points throughout the 18.000 words.

Since J cannot be validly estimated at

very large values of N it was necessary to determine whether or not K could be validly computed at each of the successive 1,000-word points along this curve.

In equation (1), £ is a double-valued function of

jg, i.e., there are two values of N which will satisfy the equation for any given J3. Disregarding the portion of the curve described by equa­ tion (1) for negative values of N, the curve may be said to have its

fable XXXI Results of Analysis of Varianee of K-valuea for Eighteen Language Samples Factor

Sons of Squares

d.f,

Individuals

17.0892

17

Sample sis#

1.3304

5

0*5105

Error

1.4377

85

0.0139

Total

00.0795

107

Variance

18.550

Inter-Mean K-value Differences 300 Words

1,000 words

1,500 Words

0,000 Words

1.000 Worde

0.0440

1,500 Words

0.151

0.087

0,000 Words

0.005

0.181

0.094

8,300 Words

0.279

0.255

0.148

0.034

3,000 Words

0.308

0.084

0.183

0.103

8,500 Words

0.049

4$lfferenoes greater than 0.0848 are significant at the %% level of confidence. Biffereneee greater than 0.1116 are significant at the X% level of confidence.

R4 o r ig in a t p oin t ( 0 ,0 ) , to arise to a maximum and to fall Indefinitely fo r all values of £ beyond this maximum.

The usable poartlon of the

curve Is from its origin to ite maximum.

The maximum point on the

curve is determined from g and for e&eh value of £ a maximum j| can be computed beyond which the value of £ computed from equation (1) i s not valid.

If. for each & there is a maximum. jf, then for each

value of W there is a minimum value of J£ which is valid for that value of

These minimum values of £ for specified W*s can be determined

by setting the first derivative of equation (1) equal to aero and solving for K.

The first derivative of equation (1) is dD i . §g " | (K ♦ l o g , K - l o g , H - 0 .877)

and s e ttin g

. dH

to

(4 )

get

°

Log, H - K + l o g , K - 0.577

(5 )

as the equation from which we can determine the maximum point on the curve for specified values of N. In terms of the independent variable, £» the Units of the usable portion of the curve derived from equation (1) are from

S*0

to

j, . *# WS may, on this evidence, reject the generality of equa­ tion (1) for language samples like those used in this investigation, with the qualification that 5,000 words may be an insufficient number of words on which to base an estimate of J£ for prediction of £ ’s* An attempt was made to find an empirically fitted equation to represent the cumulative type—frequency curves.

Since it is reason*

able to assume that, for any individual, there is a limit to the number of types at hie command, it was felt that an equation of the hyperbolic

87 form would beat agree with tho character of the phenomena at hand* inasmuch as the hyperbolic curves are characterised by asymptotes, which can be correlated to the limit of the writing vocabulary of the individuals in similar situations*

However, it was found that the data

could not be satisfactorily reduced to a linear form of the hyperbolic curve, at least not a simple hyperbolic curve with two parameters*

Pos­

sible reasons for this failure will be discussed later# Of the attempt to fit curves with simple equations to these data, only a plot of log J£ and log N resulted in what could be con­ sidered a linear relationship*

The resulting linear function is of the

fora log D * a log N ♦ log b in which a and b are empirically determined constants*

If the above

equation holds, then log p is a linear function of log N, and D is a power function of N, of the general form P • bHS Equations of this form were fitted to the cumulative type—frequency data for the 18 language samples used in fitting equation (2)« Es­ timates of parameters a and b arrived at by means of a least squares solution of the (log ft, log P) plot, are presented in Table XXXI* A graphical representation of this relationship for a typical plot of (log », log D) and (N, B) is shown in Figure 2* The curve presented in Figure 2, is typical of the other fitted curves in that the fit for larger values of N is not satisfactory and would make prediction beyond the limits of these data rather hazardous* In order to determine what relationship exists between the

88

Table XXXX Estimates of Parameters, a and b. In the Pitted Function D * b 8* for 18 language Samples Subject Number

a

b

29

0*618

3*575

49

0*657

5*192

79

0*702

1.656

9

0*785

1.965

96

0.715

2.466

78

0*600

5.025

8

0*646

5*753

4

0.740

2.109

56

0.710

2.570

12

0*745

1*945

101

0*685

2*754

86

0.728

2.606

44

0*690

5.170

97

0*599

4.989

43

0.789

2.786

6

0.679

3.221

100

0*666

5.750

22

0.794

1.614

89

3.0 • >"

CO

2.6

2.0

LOG D = 0.713 LOG N + 0.392 1.5

4 1.0

LOG NUMBER OF WORDS (TOKENS)

700

OO

600

500

2.466 N

400

300

000

4

100

■003*

1600

2000

24C

NUMBER OF WORDS (TOKENS)

Figure A graphic representation of the relationship of the number of different word* (D) to the sample size (N). The upper curve Is the reduction plot In terms of leg B and log H. Plotted from the data computed from language sample written by subject no* 96. Em­ pirical points are shown in their relation to the curve described by the indicated equation.

90

estimates of these parameters and the factors of I.Q., C.A* and 3,000word segmental type-token ratio, three levels each of I.Q. and C.A. as previously defined and tiro groups, a low and a high, categorised according to the magnitude of the 3,000-word segmental type-token ratio, were subjected to an analysis of variance.

The results of the

analysis of variance of these two parameters for these groups is pre­ sented in Tables XXXII and XXXIII.

The results of the analysis for

parameter a indicates that only the type-token ratio factor results in a significant F-value • This result is to be expected since the typetoken ratio is a function of B, one of the variables in the equation. Inasmuch as the constant a determines the rate at which new words are added, it is not surprising that the difference in means between the low and high 3,000-word TTR groups should result in a significant dif­ ference, when tested by means of the t-test, in favor of a greater mag­ nitude in the value of a for the group with a larger type-token ratio. The X.Q. and C.A. factors show no systematic differences between means of the various groups that are of great enough magnitude to give sig­ nificant F-values • Since these factors have been shown to be associ­ ated In a systematic manner to the 3,000-word segmental type-token ratio the marked differences between the two lower levels of X.Q. and C.A. might presumably be attributed to this association* The results of the analysis of variance of estimates of para­ meter b for these groups indicate no significant factors. Apparently the exponent of If, I.e., the parameter a, is more influential in deter­ mining the differentiating characteristic of the curves than is the co­ efficient of N, i.e., the constant l£.

91

t a t t uam Results of Analysis of Variance of Parameter £ for Group# of X.Q.* C.A. and Type-Token Ratio Factor

Sums of Squares

d.f.

Varianee

F

I.Q.

0.004449

2

0.002225

1.642

C.A.

0.010095

2

0.005048

5.725

TTR

0.015547

1

0.015S47

11.474**

Error

0.016261

12

0.001555

Total

0.046952

17

Difference

Factor X.Q. 86 and under 90 to 109 (inclusive) 110 and over

0.669 0*707 0.695

149*ao. and undar ISO to 179 n o . (inc.) 180 mo. and over

0.686 0.709 0.704

TTR for 5,000 words Less than .251 Greater than .251

0.660 0.719

0.059

3.411**

92

Table XXXXIX Basulii of Analysis of Variance of Estimates of Parameter J> for Groups of X.Q.f Q.A.* and Type-Token B&tle Factor

Sums of Squares

d.f.

Variance

F

X.Q*

1.211855

2

0.605927

—

C.A.

1.220583

2

0.610884

TTR

1.606827

1

1.606827

Error

18.759541

18

1.061612

Total

16.778584

17

Factor

Ifiean

Xa£l& 89 and under 90 to 109. inclusive XXO and over

2.946 2.680 5.255

G|^ X49 months and under ISO to X79 months, inclusive X80 months and over

5.279 8.646 8.895

TTR for 8*000 worde 0.251 and lees 0.232 and over

5.259 2.641

—

Zh order to determine if the power function will hold beyond 8*000 worde, a curve wee fitted to the data of the 18*000-word sample* the sample wee divided into eix 5,000-JWord samples and a curve fitted to each 3*000-word. section ae well as to the total sample*

Estimates

of the parameters of the power function for the total sample and for each section is presented in Table XZ3OT and a graphical representa­ tion of the relationship for the 18,000 words is presented in Figure 5* Again, it is noted that the fit for the larger values of £* beyond £ equal about 14*000, is poor*

The empirical points diverge consider­

ably from the curve* A second empirically fitted curve was derived by generalising equation (1)* A transformation of equation (1) can be made by writing the function as follows* * “ •*(§) * (lag,

0.485),

(7)

which* since the terms in the right-hand bracket are all constants can be written as* lo«, * •