LB

1131 B28

[BRARY

THE UNIVERSITY OF CALIFORNIA

SANTA BARBARA

PRESENTED BY

Frances Hoi den

UNIVERSITY OF IOWA STUDIES IN CHILD WELFARE

PROFESSOR BIRD T. BALDWIN, PH. D., EDITOR

FROM THE IOWA CHILD WELFARE RESEARCH STATION

VOLUME II NUMBER 1

MENTAL GROWTH CURVE OF

NORMAL AND SUPERIOR

CH] LDREN

STUDIED BY MEANS OF CONSECUTIVE INTELLIGENCE EXAMINATIONS

BY

BIRD T. BALDWIN

AND LORLE I. STECHER

PUBLISHED BY THE UNIVERSITY, IOWA CITY

tj.ivo.1 i i \jr \jjt\Ljir \J

SANTA BARBARA

CONTENTS

I. THE MENTAL GROWTH CUBVE 5

1. Statement of the Problem. 5

2. Data for this study 6

Chart I. Typical Record Card for Successive Examinations. 6

3. Method of Determining the Mental Growth Curve 8

4. The Analysis of the Mental Growth Curve 10

Table I. Mean Mental Age in Months of Superior and Aver- age Boys and Girls for Successive Chronological Ages.... 10

Chart II. Mental Growth Curves for Superior and Aver- age Children 11

Chart III. Growth Curves in Height 13

Table II. Mean Intelligence Quotients of Superior and Aver- age Boys and Girls for Successive Chronological Ages 14

5. The Analysis of the I. Q. Curve 14

6. The Analysis of the Curve of the Rate of Mental Growth 15 Chart IV. I. Q. Curves of Superior and Average Children.. 15 Table III. Mean Rate of Mental Growth of Superior and

Average Boys and Girls for Chronological Age Intervals.. 15 Chart V. Rate of Mental Growth for Superior and Average

Children 16

7. Mean Group Differences at Successive Examinations 17

8. Discussion and Literature 18

Table IV. Mean Intelligence Quotients at Successive Ex- aminations 18

Table V. Mean Chronological Age and Mean Interval be- tween Successive Examinations 19

9. Summary and Conclusions 22

II. THE POSSIBILITY OF PREDICTION OF MENTAL GROWTH 23

1. Intelligence Status of Individuals at Successive Examina- tions 23

Table VI. Original Data Arranged in Order of Mean I. Q.

—Boys 24

Table VII. Original Data Arranged in Order of Mean I. Q.

—Girls 30

2. Deviation of Individuals from their Mean I. Q. Level 36

Chart Vla-VIb Successive I. Q.'s 36, 37

Table VIII. Mean Individual Deviations from Intelligence

Quotient Level 37

Chart VII. Individual I. Q. Curves for Boys 38

Chart VIII. Individual I. Q. Curves for Girls 38

4 CONTENTS

3. Differences in I. Q. at Successive Examinations 39

Table IX. Percentage Distribution of the Differences in

Intelligence Quotients 40

Chart IX. Percentage Distribution of the Differences in I. Q 41

4. Intercorrelations 43

Table X. Intercorrelations of Intelligence Quotients, for

Two, Three, Four, and Five Examination Groups 45

Table XI. Percentage of Children Tested by Same Examiner 45

5. The Probable Error of Estimate 46

Table XII. Differences between the Obtained and Predicted

Intelligence Quotients on Second, Third, Fourth, and

Fifth Examinations 47

Table XIII. Distribution of Differences between Obtained

and Predicted I. Q.'s 48

Chart X: Distribution of Differences between Obtained and

Predicted I. Q.'s 49

6. Summary and Conclusions 52

III. THE RELATION BETWEEN1 PHYSICAL AND MENTAL GROWTH 53

1. Data 53

2. Resemblances in the Mental and Physical Development of Brothers and Sisters 53

Chart XI. Individual Mental Growth Curves of Brothers and Sisters 54

3. Mean Mental Age of Physiologically Accelerated and Re- tarded Children 55

Chart XIV. Mean Mental Age in Months of Physiologically Accelerated and Retarded Boys and Girls 55

4. The Relation between Physical Traits and Mental Age 56

Table XV. Intercorrelations between Physical Traits, Chron- ological and Mental Age 57

Table XVI. Partial Correlations between Physical Traits,

Chronological and Mental Age 57

5. Summary and Conclusions 58

IV. GENERAL CONCLUSIONS 58

REFERENCES 60

MENTAL GROWTH CURVE OF NORMAL AND SUPERIOR CHILDREN

I. THE MENTAL GROWTH CURVE

1. Statement of the Problem. Contemporary discussions of the mental growth curve have their parallel in the early history of anthropometry, when scientists attempted to find the general laws of growth and to depict the trend of the average curve of physical development. Refinement of technique and a better analysis of the growth process have shown wide individual dif- ferences in the growth of children, which make it impossible to represent these variations adequately by a single mean curve. It is now known that there are differences in the curves for boys and girls, for tall and short children, for physiologically accel- erated and retarded children, as well as for children of different race, different environment, and different social status.

On the analogy of the physical growth curve a number of writers have constructed theoretical mental growth curves, gen- erally with rather a steep rise in the early years of life and a flattening out after the age of puberty. One author has suggested, without experimental data, that this curve should really be con- cave in the early years, owning to what he believes to be the slow rate of development during infancy. The concept of different rates of development in the subnormal classes has become so firmly established that text-books generally visualize for the student the supposed growth curves of the three classical levels of feeblemindedness. It has also been suggested in the literature that superior children grow at a faster rate and have a steeper curve than the average.

All of these problems concerning the general trend of the growth curve, the rate of improvement of children of different intellectual ability, variability in mental development, the pos- sibility of prediction in mental growth, and the relation between physical and mental growth can be solved only through a study of consecutive re-examinations and observations of the same group of children throughout a number of years. The data of this study

6

IOWA STUDIES IN CHILD WELFARE

furnish the basis for the beginning of an empirical determination of these aspects of the mental growth process.

2. Data for this Study. In September, 1917, several hundred children were examined at the Iowa Child Welfare Research Sta- tion by the Stanford Revision of the Binet Scale, with a view to following the mental development of the children from year to year.1 The continuity of the work was interrupted by war con- ditions2 and by the shifting3 of the school population particularly characteristic of a university town, but 143 individual records are sufficiently complete for the purposes of this analysis. Chart I

CHART I

TYPICAL RECORD CARD FOR SUCCESSIVE EXAMINA- TIONS.

NAME

, K

DATE or

DATE or EXAM.- 1 ,1-8-17 £ .i/r 3> nffjn 4 n/5fco 5 GRADE

CHRONOLOGICAL AGE

Curing the first year the Yerkes-Bridges Point Scale was given at the same time as the Stanford Revision, or a day later. Although this study is limited to the data from the Stanford Revision, the Pearson coefficient of correlation hetween the ratings by the two scales, all of the examinations being made by the same individual, was found to be for 76 cases +.888 with a P.E. of ±.016.

*The original plan for the re-examinations had the support of the Acting Director of the Child Welfare Research Station, Ellsworth Faris, during the Director's absence in military service.

8A number of children, who had left the university school were followed up and examined in the public schools. A fifth examination on one girl was obtained through the courtesy of Professor L. W. Cole, who examined her in Colorado Springs.

MENTAL GROWTH CURVE 7

shows a typical record for successive examinations. The records may be divided into four groups: (a) 56 having two examina- tions; (b) 51 additional cases having three examinations; (c) 42 of the three examination cases on whom a fourth examination was obtained; (d) additional 36 cases having five consecutive ex- aminations.

The conditions for a study of this kind were particularly favor- able. The University Observational Schools, in the same building as the Child Welfare Research Station, are attended largely by the children of the professional and business men of the city and of prosperous farmers nearby. The tuition is small, making the expense comparable to that of children attending the public schools of the town where text-books are not supplied. The tone of the school is free and democratic. The children are accustomed to all sorts of educational and psychological experiments and re- gard the annual re-examination as a regular part of the school pro- gram. There is no reason to believe that any undue amount of communication or discussion went on among the children in re- gard to the mental tests; in fact, the examiner frequently noted the fact that a child remembered having been asked a certain question a year ago but did not give further evidence that the answer had been learned. The investigation had the interest and support of the school staff, most of whom were college graduates who were anxious to make the experimental conditions as favor- able as possible.

The examinations were given by four psychologists1 during the period between September, 1917, and May, 1921. In all 485 mental age determinations were made on 143 children. Of these 178 were given by Miss Vest, 8 by Miss Schriefer (who was de- voting her time to the examination of other children entering the school), 77 by Miss Wagoner, and 222 by Miss Stecher.

With a view to tracing the possible effect of the personal equa- tion, the material was arranged (Table XI) so as to show what proportion of the children in a given group were examined by the same examiner.2 In the Five Examination Group both the first and second examinations were made by Miss Vest in 91.4% of the cases; in the Four Examination Group Miss Vest gave 30.2% of the repeated examinations, in the Three Examination Group

1Eloise Vest, A. M., Louise Schriefer, A. M., Lovisa Wagoner, A. M., Lorle I. Stecher, Ph. D.

In the statistical treatment of the data in this study the writers had the co-operation of Gladys M. Fairbanks, A. M.

8 IOWA STUDIES IN CHILD WELFARE

22.2%, and in the Two Examination Group 28.6%. Consecutive examinations of the same children were given by Miss Stecher as follows: in the Two Examination Group 3.5% of the first and second; in the Four Examination Group 18.6% of the second and third, 18.6% of the second and fourth, 100% of the third and fourth; in the Five Examination Group 40% of the third and fourth, 40% of the third and fifth, 100% of the fourth and fifth. That re-examination by the same person is of practically no sig- nificance in raising the correlation is shown in connection with the coefficients of correlation on page 45.

The subjects of the study were of average and superior intel- ligence with a range of I. Q. from 90 to 167. The four groups were nearly equal in mental ability as shown by the mean I. Q. of the boys and girls of the different groups.

Group 5 Exam. 4 Exam. 3 Exam. 2 Exam.

Boys 120.6 114.0 112.8 115.0

Girls 118.8 113.6 112.3 113.4

It will be noted that the mental ability of the boys was prac- tically the same as that of the girls.

3. Method of Determining the Mental Growth Curve. Terman (26) 1919, p. 127, has stated that "the standardization of the Binet scale on the basis of age norms makes it a valuable instru- ment for the investigation of mental growth curves." The mental growth curves presented herewith are probably the first curves for superior and average children of the development of general intelligence studied by means of repeated examinations on the same children.

The mental examinations on which these growth curves are based were made at irregular intervals, ranging on the average from 6 to 16 months within the period of four years. In order to plot the curve at the customary one-year intervals, the mental ages, instead of being assigned to the year nearest the chronological age, as is the usual custom, were calculated and weighted in such a manner as to give the mental age at exact years. This method assumes that the child continues to grow mentally at the same rate between the examination intervals. A child actually meas- ured at the age of 5 years-5 months would, under the usual method, be considered as five years and its mental age averaged with the mental age of other children who might actually have varied between 4 years-7 months and 5 years-6 months at the time of the examination. To prevent this distortion of the real age,

MENTAL GROWTH CURVE 9

mental and chronological, a new mental age was computed for each chronological age during the period of measurement. The method used was as follows :

For each child the difference between every two successive chronological ages and every two successive mental ages was cal- culated and the rate of improvement obtained by dividing the difference in mental age by the difference in chronological age. For example, take the case of a boy who had his second examina- tion at the age of 6 years-1 month, and his third examination at the age of 7 years-2 months, giving a difference in chronological age of 13 months. His mental age at the earlier examination was 8 years-8 months, and at the later, 10 years-2 months, the differ- ence in mental age being 18 mental months. The mental age difference divided by the chronological age difference results in a rate of improvement of 1.38. This means that he grew 1.38 mental months for every month of chronological age. The mental age at the time of the earlier examination was then corrected by subtracting from the mental age of 8 years-8 months, or 104 mental months, the number of mental months equivalent to one month's growth at the rate of 1.33 (which is the rate at which he was growing previous to 6-1). This gives a new mental age at 6 years of 104 mental months — 1.33 mental months, or 102.67 mental months. The corrected mental age at 6 years was 102.67 months. The corrected mental age at 7 will be the mental age at 6 years-1 month, -f-11 months at the rate of 1.38, or 102.67-f- (11X1.38) or 117.85 mental months.

The resultant mental ages were averaged for each chronological age from 5 to 14 for all of the boys and all of the girls of the group and for the normal and superior boys and girls separately. The resultant mental growth curve is shown in Table I and Chart II.

The rates of growth used for correcting the mental ages from the exact year to year by the method of monthly rates described above were averaged by chronological age groups to give the total growth of each child for all year intervals. The resultant composite rates were averaged for each year interval to obtain the annual rate of growth. The corrected mental ages were then divided by the chronological ages at the exact years in order to determine the new rate of improvement between every two suc- cessive mental ages. These new rates were averaged by years to give the rate of mental growth shown in Table III and Chart V.

10

IOWA STUDIES IN CHILD WELFARE

The new I. Q.'s for each exact chronological age were averaged to give Chart IV and Table II.

4. The Analysis of the Mental Growth Curve. The mental growth curves obtained by the individualizing method from con- secutive measurements of superior and average boys and girls be- tween the ages 5 to 14 present at first glance the appearance of a straight line. The familiar parabolic character of the theoret- ical growth curve is lacking, since our data furnish us no de- terminations for ages 14 to 16, during which this slowing up of mental growth is supposed to take place.

TABLE I
MEAN MENTAL AGE IN MONTHS OF SUPERIOR AND AVERAGE BOYS AND
GIRLS FOR SUCCESSIVE CHRONOLOGICAL AGES
(Based on 487 Consecutive Examinations)
	Boys	Girls
	Intelligence	Intelligence	Intelligence	Intelligence
Chronological	Quotient	Quotient	Quotient	Quotient
Age	110+	90-110	110+	90-110
	(Superior)	(Average)	(Superior)	(Average)
5	70.6	60.7	72.0	62.5
6	88.7	75.6	85.0	73.9
7	102.2	87.4	102.2	88.9
8	118.7	100.4	116.3	100.9
9	131.4	109.2	131.1	112.9
10	144.0	117.7	145.5	122.4
11	160.5	130.5	158.5	133.3
12	181.0	143.1	184.1	141.5
13	190.0	157.2	196.0	166.5
14	208.9	168.0	201.0	182.9

It is apparent from these curves that superior and average chil- dren develop at different levels and that children of these dif- ferent intellectual levels grow increasingly dissimilar with in- crease in chronological age. For example, at the age of 5 the superior and average boys have a mental age of 71 and 61 mental months respectively, but at 14 the superior have 209 and the aver- age 168. The difference of 10 points at 5 years has increased to 41 points at 14 years. The girls show similar differences.

This divergence in the growth curves of average and superior children has long been assumed as probable but has not heretofore been empirically demonstrated. The concept of the I. Q. pre-

220

MENTAL GROWTH CURVE CHART II

11

GROWTH CURVES FOP SUPERIOR AND AVERAGE CHILDREN

/ 5 6 7 a 9 IO II IZ

Qhronological Age in Yeor9

supposes a certain divergence in the curves of the superior and the average child, as the superior child has to grow at a rate greater than one mental month for one chronological month in order to maintain a constant I. Q.

12 IOWA STUDIES IN CHILD WELFARE

The general straight line appearance previously noted is espe- cially apparent in the growth curve for boys. Further analysis reveals, however, a very significant change in the trend with the approach of adolescence. This is especially marked in the curve for girls where there is a rise in mental development in the supe- rior girls between the ages 11 to 12 and in the average girls a year later, between the ages 12 to 13. The superior boys show a similar acceleration in mental growth at about 12 — somewhat later than in the case of the superior girls. The boys of average mental ability have not yet shown this acceleration up to 14 years, which is the latest age for which we have a sufficient number of cases. It seems unlikely that this rise in the curve of mental growth can be explained by defects in the measuring scale at the adolescent ages. There is no reason to believe that the scale was not equally well standardized at all ages. The increased incline of the curve extends, moreover, through several ages, and it is not probable that the tests would be too easy throughout these years.

The mental growth curves of the boys and girls cross repeat- edly. There is, however, a tendency in the earlier ages for the average girls to be a little higher in mental age than the average boys, in the later ages for the girls of both groups to be a little superior to the boys. While not without exception, this adoles- cent superiority of girls is in accordance with other facts indica- tive of the earlier maturity of girls.

There has been in recent years a movement to discredit charac- teristic changes in intellectual traits as a result of adolescence. This point of view, which is probably a reaction to undue senti- mental emphasis of those changes current in the psychology of twenty years ago, is expressed by Terman (25) 1917, p. 60, who maintains there is little evidence of periodicity, or irregularity as far as general intelligence is concerned, and throws doubt on the existence of the adolescent spurt. Although there is obviously no time in the mental development of the child when new mental traits suddenly appear, the rise in the mental growth curves ap- parent at the ages of 11 to 14 may be attributed to increased strength of traits that have long been developing, or to increased mental vigor similar to the accelerated growth in physical traits.

The existence of such a period of increased vigor would not necessarily interfere with the stability of the I. Q., providing the scale was adapted in difficulty to such a change. It certainly would not affect the individual's position in the group relative

MENTAL GROWTH CURVE CHART III

13

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to a norm, since the norm at these ages would also be higher if all children developed in a similar way. A child 's physical status in height, for example, remains relatively constant with reference to its group from age 6 through adolescence, as shown by Baldwin (1) 1914, though the norms and individual curves may show adolescent accelerations.

The mental growth curves are strikingly similar to the physical growth curves in height as shown in Chart III. This chart here published for the first time illustrates the differences in the growth of tall, average and short girls and of a tall and a short

14

IOWA STUDIES IN CHILD WELFARE

boy as compared with the norms for boys and girls. The norms for average boys and girls are based on 6 to 10 years of semi- annual measurements for 60 boys and 60 girls. The curves for tall girls are based on similar material for 52 cases distributed above the norm, and the curves for short girls on 28 cases con- siderably below the norm. The curves show the same phenomena that have been pointed out in connection with the mental growth curves. In both cases the curve at the higher level shows the acceleration at an earlier age.

TABLE II MEAN INTELLIGENCE QUOTIENTS OF SUPERIOR AND AVERAGE BOYS AND GIRLS FOR SUCCESSIVE CHRONOLOGICAL AGES
Chronological Age	Boys	Girls
Intelligence Quotient 110+ Superior	Intelligence Quotient 90-110 Average	Intelligence Quotient 110+ Superior	Intelligence Quotient 90-110 Average
5 6 7 8 9 10 11 12 13 14	117.6 123.3 121.6 123.6 121.7 119.9 121.5 125.7 121.5 124.3	101.2 105.0 104.0 104.6 101.1 98.1 98.8 99.4 100.8 100.0	119.9 118.0 121.7 121.1 120.5 120.3 119.8 127.9 125.7 119.7	104.1 102.6 105.9 105.1 lt)4.6 102.1 99.9 98.2 106.7 108.9

5. The Analysis of the I. Q. Curve. The mean intelligence quotients (Table II) and the I. Q. curves (Chart IV) for superior and average boys and girls show some of the same characteristics observed in the mental growth curves. The curves are in general approximately horizontal, confirming within limitations the con- stancy of the I. Q. There appear to be, however, certain definite phenomena associated with physiological development that show themselves in a decrease or increase in the I. Q. at certain chrono- logical ages. A study of the physical development of young chil- dren shows that there is considerable fluctuation between the ages 4 and 7. These I. Q. curves suggest a similar condition with a small spurt in mental development, appearing a little later in the boys than in the girls. Both superior boys and girls show a rise in the I. Q. between the ages of 11 and 12. Average girls

MENTAL GROWTH CURVE

15

CHART IV

160 ISO 140 ISO

I. Q. CURVES or

SUPERIOR AND AVERAGE CHILDREN

SUP 'f* 'to* ^— ^— Bars

AvtKAtl — — —• SlAlf

a 9

Age in Yeora

10

II

12.

also show this adolescent acceleration, although it appears a year later than in the case of superior girls. The I. Q. curve and the mental growth curve of the average boys do not show this phe- nomenon, possibly because they have not reached this stage of acceleration.

6. Tine Analysis of the Curve of the Rate of Mental Growth. Our tables of original data do not include calculations of the actual number of mental months growth for one chronological month between examinations, although these were used in all

TABLE III MEAN RATE OF MENTAL GROWTH OF SUPERIOR AND AVERAGE BOYS AND GIKLS FOR CHRONOLOGICAL AGE INTERVALS
Chronological Age Intervals	Boys	Girls
Intelligence Quotient 110+ Superior	Intelligence Quotient 90-110 Average	Intelligence Quotient 110+ Superior	Intelligence Quotient 90-110 Average
5-6 6-7 7-8 8-9 9-10 1<K11 11-12 12-13 13-14	1.5 1.2 1.5 1.4 1.4 1.8 1.8 (1.1) 1.5	1.0 1.1 1.2 1.3 1.0 1.1 1.3 1.3 1.1	1.2 1.5 1.2 1.3 1.5 L6 2.2 1.9 1.9	.8 1.1 1.1 1.2 .8 1.1 1.1 1.6 1.4

16

IOWA STUDIES IN CHILD WELFAKE

cases as a basis for the curve of the rate of mental growth. In- spection of the tables will show for individual children great fluctuation in the rate from examination to examination. A child whose rate from the first to the second examination is 1.56 mental months for each month of chronological age may show between the second and third examination a rate of .23 mental months for each chronological month. Part of this discrepancy is of course due to the experimental error of each single mental age determination, but the size of many of the irregularities cannot be explained on this basis. It appears that there is no rate of improvement which is characteristic of the individual and uni- formly maintained throughout his years of mental growth al- though an approximately constant rate is maintained in many cases.

Table III and Chart V show the mean rate of mental growth for these children. The average children grow approximately

CHART V

Cnronolag/cot Agt interval*

•» •« <J

one mental month for each chronological month, while the supe- rior children have a higher rate (shown by the curve at a higher level) except in the case of boys between 12 and 13, where the small number of cases results in a decreased rate (printed in parenthesis in Table III and represented by a dotted line in Chart V). The effect may also be noted in the mental growth curve for superior boys, Chart I.

There is little difference, on the average, in the rate of growth of these two groups of children. In no case is the difference

MENTAL GROWTH CURVE 17

greater than seven-tenths of a year. These figures cannot of course be considered as norms, since they depend upon the selec- tion of cases included in the study. The addition of more cases of very superior intelligence, or of more cases of I. Q.'s below 100 would have increased the difference.

The general prepubertal increase in mental development be- comes, evident earlier in the case of superior children than in average children, and in the case of superior girls about a year earlier than in average boys. In comparing the curves it should be kept in mind that a child who has been growing at a certain rate and then reaches a period of little or no increase will have to reattain the rate of growth at which he was previously de- veloping before an actual acceleration in growth can be consid- ered as taking place. The period of acceleration is therefore later than the point in the curve at which the steep rise begins. In general all of these curves show less difference between average and superior boys in regard to these adolescent phenomena than between average and superior girls, who are usually a year apart in their general development.

Our data do not permit us to give a definite answer to the ques- tion whether superior children grow more superior as time goes on through an increase in the rate of mental growth. The curves for the two groups of children seem to diverge slightly at the higher ages, especially in the case of girls at the adolescent years. The facts in regard to the change of I. Q. to be reported later on page . . seem also to indicate some characteristic differences in the growth of children of different I. Q. level. We should hesi- tate, however, to make any generalization in regard to this matter from the material presented in this study.

7. Mean Group Differences at Successive Examinations. Table V is purely descriptive, presenting the mean chronological age at successive examinations and the mean interval between exam- inations for use in interpreting the findings in other tables. The findings of Table IV are averages of the I. Q.'s obtained at each examination by the children of each particular group.

It is a very significant fact that the mean I. Q. of each of the four groups of children increased with each successive examina- tion, which must be regarded as an effect of greater habituation or practice. The increase in the mean I. Q. is proportionate to the number of re-examinations.

18

IOWA STUDIES IN CHILD WELFARE

The mean I. Q. for the Five Examination Group increased from 115.39 through 119.5, 119.75 and 123.91 to 126.7. The mean I. Q. for the Four Examination Group increased from 111.06 through

112.02 and 115.16 to 118.20. The mean I. Q. for the Three Ex- amination Group increased from 110.59 through 111.80 to 115.21. The mean I. Q. for the Two Examination Group increased from

112.3 to 115.8. This increase in I. Q. has been noted by previous workers on a single retest in the summary by Rugg and Coll- oton (21).

TABLE IV MEAN INTELLIGENCE QUOTIENTS AT SUCCESSIVE EXAMINATIONS
Group	No. of Cases	Exam. 1	Exam. 2	Exam. 3	Exam. 4	Exam. 5
5 4 3 2	36 42 51 56	115.4 111.1 110.6 112.3	119.5 112.0 111.8 115.8	119.8 115.2 115.2	123.9 118.2	126.7

There is also an increase in the mean rate of improvement upon successive examinations. To investigate this phase of the practice effect, the data for the Four and the Five Examination Groups were worked over to give for each child the amount of increase in mental age months for each month of chronological age in- crease between the first and second examination, the second and third and the third and fourth. The means of these individual rates of improvement reveal a general increase in the rate of mental development which is especially marked between the third and fourth examination in the case of the girls.

Examination

Boys

Girls

No. cases 37 34

I-II

Eate 1.48 1.29

II-III Eate 1.42 1.64

III-IV Eate 1.73

2.40

8. Discussion and Literature. It is extremely probable that the theoretical mental growth curves found in so many text- books really misrepresent the facts of mental development. It has been the custom to draw the growth curves of children of different degrees of ability as if all of these curves began with zero ability at the time of birth and from that time on rose steadily. From all that we know in regard to differences in the mental capacity of young children, the curves of mental develop- ment, like the curves of physical development, begin at dif-

MENTAL GROWTH CURVE

19

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ferent levels (points). There are individual men- tal differences at birth as there are individual dif- ferences in height. It is not conceivable that the feebleminded child should begin at the same point with the child of average or superior ability and then drop back in the race as his more gifted brothers gain. The truth of the matter is, he runs on a relatively lower level throughout life.

Much of the work on retests of children has been done with feeble- minded subjects. While it is impossible in this study on normal and superior children to go into the question of growth curves of the feebleminded, it will orientate the problem if we review briefly such other studies as have been made with repeated exam- inations. Bobertag (6) p. 528, reported in 1912 as a result of retests on 83 children whom he had ex- amined the year before that children whose intel- ligence is above average advance more rapidly ; those whose intelligence is below average advance more slowly. He main- tained (p. 531) that if one

20 IOWA STUDIES IN CHILD WELFARE

limits one's self to a few successive years — 8, 9, 10, for example — one could say that the I. Q. is approximately constant. If, how- ever, one considers all the ages, or the whole developmental course of children's intelligence it is very questionable whether the as- sumption of a constant I. Q. is tenable.

Berry (4) in 1913 found on a retest of 82 children that the normal subjects made an average gain of 1 year, and the feeble- minded— mental ages 4-11 years — an average gain of .5 of a year. He did not report the correlation between the examinations.

Bloch (5) 1915 re-examined defective children by the Binet scale.

Stern (23) (24) 1914 and 1916, who discussed the subject at length, but without experimental data of his own, believed that the I. Q. did not afford an actually constant expression of degree of feeblemindedness but showed a tendency to fall in value as chronological age increased and the age of arrest was approached.

Descoeudres (9) 1915 retested 26 children of a special class and found the I. Q. very similar to the previous one with a greater tendency to increase. Cases with three or four examinations showed practically the same I. Q. with less than 50% variation.

Terman (25) p. 55, 1917 concluded from re-examinations that "the results of 140 such tests show as far as the age of 13 or 14, even when the tests are separated by as much as five years, changes of 10 points in 12 are relatively rare. In general, it can be said that the superior children of the first test are found supe- rior in the second, the average remained average, the inferior remain inferior, the feebleminded remain feebleminded and nearly always in approximately the same degree. The most marked ex- ceptions to this rule are found with the feebleminded whose in- telligence quotient shows a tendency to decrease considerably. ' '

Cuneo and Terman (8) 1918, retested 77 children and found high correlations between the two tests.

Terman (26) 1919 found considerable agreement in the I. Q.'s of 46 children tested three or more times. He says, p. 147: "It is possible that feebleminded children testing below 60 are less likely to hold their own than those of milder degree of defect. . . . On the other hand the I. Q. as determined by the Stanford- Binet (or any other intelligence scale yet devised) cannot indef- initely hold its constancy in the case of children who are excep- tionally superior."

MENTAL GROWTH CURVE 21

Wallin (28) 1919 discussed the use of the I. Q. in classification without data from retests. His article has been critically re- viewed by Rosenow (20) 1920, who presents experimental evi- dence of approximate stability of the I. Q. from retests of 69 cases examined at about 10 months interval.

Wallin (29) 1921 reported re-examinations on 153 children by different revisions of the Binet tests.

Kuhlmann (17) (18) who had discussed the intelligence of the feeble-minded is also reported by Hollingworth (15) p. 105 in 1920 to have found that ' ' On the whole the I. Q. for a given case remains constant with a slight tendency on the average to decrease after the ages of about nine or ten. ' '

Kuhlmann (18a) 1921 reported results on 639 cases ranging from idiocy to nearly normal mentality examined 2 to 5 times within a 10 year period by the Binet and Kuhlmann series. He found that the I. Q. decreased with age and more for the higher than for the lower grades.

Garrison (13) 1921 retested by the Stanford-Binet 94 children who had previously been tested by the Goddard Revision and found on the whole, a rather close correspondence.

Doll (10) 1921, from a study of numerous growth curves for feebleminded subjects who had received at least 5 annual exam- inations, believes in an age of arrest for the feebleminded beyond which the I. Q. would decrease. Terman (27) 1921 criticizes this presentation and the conclusion drawn from the data.

Freeman (12) 1921, published an important discussion on the concept of the I. Q. with reference to age scales and point scales.

Rugg and Colloton (21) 1921, have assembled the reports of other workers with Stanford-Binet tests and added data from 137 cases of their own. They find that with one exception investiga- tors have found an average difference in I. Q. on re-examination of 4.5 points, and confirm in some other respects Terman 's 1917 con- clusions.

The literature summarized above presents many interesting problems in regard to the age of arrest or the limit of mental growth. Our data do not extend far enough to permit us to spec- ulate on the age at which mental growth ceases in the normal or superior child, though there is reason to suspect that the mental age curves of some of the superior girls are beginning to flatten out with a resulting decrease in I. Q. Even so this may be merely

22 IOWA STUDIES IN CHILD WELFARE

a fictitious slowing up of mental growth due to the inevitable ''bumping" into the upper limit of the scale.

SUMMARY AND CONCLUSIONS

1. The fundamental problems concerning the general trend of the growth curve, the rate of improvement of children of different intellectual ability, variability in mental development, the pos- sibility of prediction in mental growth and the relation between physical and mental growth can be solved only through a study of consecutive reexaminations and observations of the same group of children throughout a number of years.

2. The mental growth curves presented herewith are probably the first curves for superior and average children of the develop- ment of general intelligence studied by means of repeated exam- inations on the same children.

3. The curves constructed from the corrected mental age rat- ings do not misrepresent the actual growth process as is the case when the chronological age is approximated to the nearest year.

4. It is apparent from these curves that superior and average children develop at different levels and that children of these dif- ferent intellectual levels grow increasingly dissimilar in mental age with increase in chronological age. This divergence in the growth curves of average and superior children has long been assumed as probable but has not heretofore been empirically demonstrated.

5. An analysis of the mental growth curve reveals a significant change in the trend with the approach of adolescence, which ap- pears earlier in the case of superior children. There is also an adolescent superiority of girls which is in accordance with other facts indicative of the earlier maturity of girls.

6. The mental growth curves are strikingly similar to the physical growth curves in height.

7. The I. Q. curves are approximately horizontal, confirming within limitations the constancy of the I. Q. There are fluctua- tions associated with physical development.

8. The curves of the rate of mental growth are higher for superior than for average children, and seem to diverge slightly at the adolescent years.

9. The general prepubertal increase appears earlier in the case of superior children.

MENTAL GROWTH CURVE 23

10. The mean I. Q. of each of the four groups of children in- creased with each successive examination, which is probably an effect of greater habituation or practice.

11. There is also an increase in the mean rate of improvement on successive examinations.

II. THE POSSIBILITY OF PREDICTION IN MENTAL

GROWTH

1. Intelligence Status of Individuals at Successive Examina- tions. The stability of the I. Q. is one of the most important prob- lems under discussion by psychologists at the present time. Upon the relative stability of the ratio between mental and chronolog- ical age depends to a large extent the possibility of prediction in mental growth.

Binet and Simon felt very doubtful of the possibility of using the I. Q. for prediction. Even Bobertag (5) and Stern (24), who are among the earliest advocates of the use of the I. Q., did not believe that it would remain constant for later ages.

The question of the stability of the I. Q. has been discussed in a number of theoretical articles. Some writers believe that it re- mains practically constant and others have found a tendency for the I. Q. of the feebleminded to decrease and for the I. Q. of the superior to increase. Any conclusive answer to the question of whether the I. Q. remains constant depends upon the accumula- tion of a sufficient number of long-time mental growth curves for children of different intellectual capacity.

Terman (26) 1919, p. 137, states the problem briefly thus : "By applying it [the Binet scale] repeatedly to the same children we can find out whether constancy or irregularity rules. Prediction hinges on the question whether a child who is found by the test to be a given per cent above or below the mental level normal for his age continues to be accelerated or retarded to the same degree. The answer is found in the extent to which the I. Q. remains constant."

Psychologists who have been accustomed to thinking that all that was required for a solution of the problems of mental growth was the accumulation of a sufficient number of re-examinations for long periods will find that the repetition of the intelligence scale brings up many puzzling new problems. A study of the original data, Tables VI and VII, shows just what variations in

24

IOWA STUDIES IN CHILD WELFARE

TABLE VI ORIGINAL DATA ARRANGED IN ORDER OF MEAN	I. Q. — BOYS
i.	Average I. C Examiner Chronological Terman Age I. Q	. 158.0. Age	E. V. 5-3 8-5 160	E. V. 5-10 9-1 156
2.	Average I. Q. 150.7.
	Examiner ...		E. V.	L. W.	L. I. 8.	L. I. S.
	Chronological	Age	5-11	7-0	7-11	8-6
	Terman Age		8-5	9-4	13-3	13-9
	I. Q		142	133	167	iei
3.	Average I. Q	. 143.6.
	Examiner ...		E. V.	E. V.	L. W.	L. I. S.	L. I. 8.
	Chronological	Age	5-1	6-1	7-2	8-1	8-7
	Terman Age		7-4	8-8	10-2	11-7	12-S
	I. Q		144	142	142	143	147
4.	Average I. Q	142.6.
	Examiner ...		E. V.	E. V.	L. W.	L. I. S.	L. I. S.
			»-•>	9-3	10-3	11 2	11-8
	Terman Age		11-1	12-1	15	16-11	17-8
	I. Q. -		135	130	146	151	151
5.	Average I. Q	. 138.2.
	Examiner —		E. V.	E. V.	L. W.	L. I. 8.	L. I. 8.
	Chronological	Age	5-a	6-9	7-9	8-8	9-2
	Terman Age		7-«	9-9	10-3	11-7	13-0
	I. Q		132	144	132	133	150
6.	Average I. Q	. 137.
	Examiner		L. W.	L. I. 8.
	Chronological	Age _	5-9	8-11
	Terman Age		7-8	9-9
	I. Q		133	141
7.	Average I. Q	. 134.5.
	Examiner ...		E. V.	L. W.
	Chronological	Age	6-10	9-2
	Terman Age		8-9	12-11
	I. Q		128	141
8.	Average I. Q	. 131.8.
	Examiner —		E. V.	E. V.	L. W.	L. I. S.	L. I. 8.
	Chronological	Age	10-7	12-1	12-7	13-7	14-0
	Terman Age		12-6	18-8	17-2	18-1	19-0
	I. Q -		117	136	137	133	136
9.	Average I. Q	. 129.0.
	Examiner _„		L. W.	L. I. 8.
	Chronological	Age	9-1	7-0
	Terman Age		7-4	9-7
	I. Q —		121	137
10.	Average I. Q	. 128.0.
	Examiner ___		E. V.	E. V.	L. I. 8.	L. I. S.
	Chronological	Age	6-3	7-4	9-4	9-10
	Terman Age		8-0	9-4	11-4	13-4
	I. Q		128	127	121	136
11.	Average I. Q	. 128.0.
	Examiner .„		E. V.	E. V.	L. I. S.	L. I. S.	L. I. 8.
	Chronological	Age	6-1	7-1	8-8	9-1	9-7
	Terman Age		7-6	9-2	11-3	11-6	12-9
	I. Q.		123	129	129	126	133
12.	Average I. Q	. 127.6.
	Examiner ...		E. V.	L. 8.	L. I. 8.	L. I. 8.	L. I. 8.
	Chronological	Age	10-6	12-0	13-1	13-6	14-0
	Terman Age .		12-8	15-5	17-0	17-8	18-6
	I. Q		120	128	129	129	132
13.	Average I. Q	. 127.2.
	Examiner —		E. V.	L. I. 8.	L. I. 8.	L. I. S.
	Chronological	Age	7-1	8-8	9-1	9-6
	Terman Age		8-0	11-2	12-1	12-4
	I. Q		120	129	133	127
14.	Average I. Q	. 126.0.
	Examiner		L. W.	L. I. S.
	Chronological	Age	7-3	8-1
	Terman Age .		9-2	10-2
	I. Q		126	126

MENTAL GROWTH CURVE

25

TABLE VI — CONTINUED ORIGINAL DATA ARRANGED IN ORDER OF MEAN I.	Q. — BOYS
15.	Average I. Q. 124.5.
	Examiner _	E. V.	L. W.	L. I. 8.	L. I. S.
	Chronological Age	9-1	10-5	11-0	11-7
	Terman Age _ _	10-8	12-6	14-6	14-11
	I. Q. -— -	117	120	132	129
18.	Average I. Q. 124.2.
	Examiner	E. V.	L. W.	L. I. 8.	L. I. 8.
	Chronological Age	8-4	10-4	11-3	11-10
	Terman Age -	10-9	11-10	14-1	15-4
	I. Q -	129	114	125	129
17.	Average I. Q. 124.0.
	Examiner	E. V.	E. V.	L. W.	L. I. 8.	L. I. 8.
	Chronological Age	8-3	9-6	io-e	11-2	11-8
		10-1	11 11	13-1	13—11	14-7
	I. Q -	122	125	124	124	125
18.	Average I. Q. 123.5.
	Examiner	L. W.	L. I. S.
	Chronological Age —	6-11	7-10
	Terman Age	8-8	9-7
	I. Q -	125	122
19.	Average I. Q. 123.5.
	Examiner	L. W.	L. I. S.
	Chronological Age	8-7	9-3
	Terman Age	10-4	11-9
	I. Q	120	127
20.	Average I. Q. 123.0.
	Examiner	E. V.	E. V.	L. W.	L. I. 8.	L. I. 8.
	Chronological Age	10-4	11-11	12-11	13-6	13-10
	Terman Age	12-8	15-0	15-5	16-3	16-8
	I. Q.	122	125	119	121	128
21.	Average I. Q. 122.
	Examiner	E. V.	L. I. S.
	Chronological Age	5-4	8-3
	Terman Age	0-2	10-7
	I. Q -	lie	128
22.	Average I. Q. 121.7.
	Examiner	E. V.	E. V.	L. I. S.	L I. S.
	Chronological Age	9-8	11-3	12-9	13-3
	Terman Age	11-4	14-1	15-3	16-8
	I. Q	117	125	119	126
23.	Average I. Q. 121.2.
	Examiner	E. V.	L. W.	L. I. S.	I. I. 8.
	Chronological Age	5-2	6-6	7-3	7-10
	Terman Age „	5-3	7-6	9-5	10-4
	I- Q	109	115	129	132
24.	Average I. Q. 121.0.
	Examiner _	E. V.	E. V.
	Chronological Age	10-9	12-4
	Terman Age	11-9	16-5
	I. Q	109	133
26.	Average I. Q. 120.8.
	Examiner	E. V.	E. V.	L. W.	L I. 8.	L. I. 8.
	Chronological Age	8-6	9-7	10-10	11-7	12-0
	Terman Age	9-11	11-4	13-3	14-4	14-11
	I. Q	lie	118	122	124	124
20.	Average I. Q. 120.2.
	Examiner	E. V.	E. V.	L. W.	L. I. S.	L. I. 8.
	Chronological Age	5-1	5-8	7-0	7-8	8-3
	Terman Age	6-10	7-0	7-10	9-6	10-8
	I. Q	114	123	111	124	129
27.	Average I. Q. 120.0.
	Examiner	E. V.	E. V.	L. W.
	Chronological Age	9-0	10-0	11-8
	Terman Age —	10-8	12-1	13-0
	I. Q	118	120	122
28.	Average I. Q. 120.0.
	Examiner	L. W.	L. I. S.
	Chronological Age —	5-9	M
	Terman Age	e-e	8-2
	I. Q	113	127

26

IOWA STUDIES IN CHILD WELFARE

TABLE VI — CONTINUED ORIGINAL DATA ARRANGED IN ORDER OF MEAN I.	Q. — BOYS
29.	Average I. Q. 119.7.
	Examiner	E. V.	E. V.	L. I. 8.	L I. S.
	Chronological Age	8-10	8-4	9-11	10-5
	Terman Age	7-4	9-4	12-0	14-5
	I. Q.	107	112	122	138
30.	Average I. Q. 119.2.
	Examiner .	E. V.	L. W.	L. I. S.	L. I. S.
	Chronological Age ...	.. . 5-0	6-«	7-2	7-8
		e_ 0	1 11	8-7	9-3
	I. Q.	115	122	119	121
31.	Average I. Q. 119.0.
	Examiner	E. V.	E. V.
	Chronological Age —	7-8	9-1
	Terman Age —	9-2	10-6
	I. Q	120	118
32.	Average I. Q. 118.5.
	Examiner	E. V.	L. W.
	Chronological Age —	6-0	7-3
	Terman Age —	6-10	8-11
	I. Q -	114	123
33.	Average I. Q. 118.0.
	Examiner	E. V.	E. V.	L. W.	L. I. S.	L. I. 8.
	/-(r- 1 f | A			1 9	7 1ft	8-5
	Terman Age —	6-2	7-0	8-2	9-5	10-1
	I. Q	117	120	114	120	119
34.	Average I. Q. 118.0.
	Examiner	E. V.	E. V.	L. W.	L. I. S.	L. I. S.
	Chronological Age _._	10-1	11-2	12-8	13-2	13-7
	Terman Age	10-4	12-8	15-5	16-6	17-4
	I. Q.	102	113	122	125	128
35.	Average I. Q. 117.8.
	Examiner	E. V.	E. V.	L. W.	L. I. S.	L. I. S
	Chronological Age	9-2	10-3	11-5	12-3	12-8
	Terman Age	10-3	11-11	14-0	14-10	14-10
	I. Q.	112	lift	122	121	117
36.	Average I. Q. 117.5.
	Examiner	— L.S.&E.V.	L. I. S.
	Chronological Age	11-8	14-3
	Terman Age	14-3	16-2
	I. Q -	122	113
37.	Average I. Q. 117.5.
	Examiner	. E. V.	E. V.
	Chronological Age	8-10	9-11
	Terman Age	10-4	11-9
	I. Q -	117	118
38.	Average I. Q. 117.0.
	Examiner	.„. L. W.	L. I. 8.
	Chronological Age	6-1	6-10
	Terman Age	6-10	8-4
	I. Q	112	122
39.	Average I. Q. 116.6.
	Examiner	E. V.	E. V.	L. W.	L. I. S.	L. I. S.
	Chronological Age	7-9	9-0	10-0	10-8	11-3
	Terman Age	9-6	10-6	10-9	12-7	13-6
	I. Q.	122	116	107	118	120
40.	Average I. Q. 116.5.
	Examiner	E. V.	E. V.	L. I. S.	L. I. 8.
	Chronological Age —	8-3	9-3	11-4	11-10
	Terman Age	8-11	10-9	13-3	14-10
	I. Q.	108	116	117	125
41.	Average I. Q. 116.2.
	Examiner	E. V.	E. V.	L. I. S.	L. I. S.
	Chronological Age	10-2	11-9	13-3	13-9
		11 11	14 1	14—10	16-1
	I. Q.	117	119	112	117
42.	Average I. Q. 116.0.
	Examiner	— . E. V.	E. V.
	Chronological Age	8-11	9-11
	Terman Age	10-2	11-8
	I. Q. -	114	118

MENTAL GROWTH CURVE

27

TABLE VI — CONTINUKD ORIGINAL DATA ARRANGED IN ORDER OF MEAN I.	Q.— BOYS
43.	Average I. Q. 115.5. Examiner Chronological Age Terman Age I. Q.	E. V. 6-10 7-8 .- . 112	E. V. 7-10 9-4 119
44.	Average I. Q. 114.6.
	Examiner	E. V.	E. V.	L. W.	L. I. 8.	L. I. 8.
	Chronological Age ...	5-4	5-11	7-3	7-11	8-6
	Terman Age	5-8	7-0	8-6	8-10	10-4
	I. Q	106	118	117	111	121
45.	Average I. Q. 113.6.
	Examiner	E. V.	E. V.	L. W.
	Chronological Age ...	9-2	10-2	11-6
	Terman Age	9-8	10-10	15-0
	I. Q	105	ioa	130
46.	Average I. Q. 113.4.
	Examiner	E. V.	E. V.	L. I. S.	L. I. S.	L. I. S.
	Chronological Age ...	5-6	6-6	8-1	8-7	9-1
	Terman Age	5-10	7-4	9-0	10-2	10-11
	I. Q. —	106	112	111	118	120
47.	Average I. Q. 113.0.
	Examiner	E. V. 8-9	E. V. 9-9	L. W. 11 1	L. I. S. 11-8	L. I. 8.
	Terman Age	9-7	10-6	12-9	13-4	14-8
	I. Q.	109	107	115	114	120
48.	Average I. Q. 112.7.
	Examiner	E. V.	E. V.	L. I. S.	L. I. S.
	Chronological Age —	11-0	12-7	14-1	14-7
	Terman Age	11-3	14-10	16-8	16-8
	I. Q.	102	117	118	114
49.	Average I. Q. 111.6.
	Examiner	E. V.	E. V.	L. W.
	Chronological Age —	6-3	7-3	8-7
	Terman Age	7-2	8-0	9-6
	I. Q. -	114	110	111
50.	Average I. Q. 111.5.
	Examiner	L. W.	L. I. 8.
	Chronological Age ...	7-4	8-2
	Tennan Age	8-4	9-0
	I. Q.	113	110
51.	Average I. Q. 111.0.
	Examiner	M.	L. I. 8.
	Chronological Age —	5-4	6-7
	Terman Age	5-8	7-8
	I. Q —	106	118
52.	Average I. Q. 110.5.
	Examiner	L. W.	L. I. 8.
	Chronological Age —	7-4	8-6
	Terman Age ..	7-8	9-10
	I. Q. — -	105	lie
53.	Average I. Q. 110.0.
	Examiner	E. V.	E. V.	L. I. 8.
	Chronological Age —	6-8	7-8	9-3
	Terman Age —	7-0	8-4	10-10
	I. Q	105	108	117
54.	Average I. Q. 110.0.
	Examiner	L. W.	L. I. S.
	Chronological Age —	6-4	7-2
	Terman Age	7-2	7-8
	I. Q	113	107
56.	Average I. Q. 108.7.
	Examiner	E. V.	L. W.	L. I. S.	L. I. S.
	Chronological Age —	6-4	7-10	8-5	8-11
	Terman Age	7-0	8-0	9-2	10-2
	I. Q	110	102	109	114
56.	Average I. Q. 107.5.
	Examiner	E. V. fi-">	E. V. 7-1
	Terman Age	6-6	7-10
	I. Q.	106	110

28

IOWA STUDIES IN CHILD WELFARE

TABLE VI — CONTINUED ORIGINAL DATA ARRANGED IN ORDEB OF MEAN I. Q. — BOYS
57.	Average I. Q. 106.7.
	Examiner	E. V.	L. W.	L. I. 8.	L. I. 8.
	Chronological Age	5-11	7-5	8-1	8-7
	Tennan Age	8-2	7-10	8-8	9-6
	I. Q	104	106	107	110
58.	Average I. Q. 106.7.
	Examiner ...	— . E. V.	L. W.	L. I. 8.	L. I. 8.
	Chronological Age	11-0	12-2	13-O	13-6
	Tennan Age	12-0	12-11	14-1	14-1
	I. Q	109	106	108	104
59.	Average I. Q. 106.0.
	Examiner	. E. V.	E. V.
	Chronological Age	11-1	12-8
	Terman Age	11-6	13-5
	I. Q -	104	108
30.	Average I. Q. 105.7.
	Examiner	—. E. V.	E. V.	L. I. 8.	L. I. S.
	Chronological Age —	11-2	12-3	14-2	14-8
	Terman Age	11-1	13-7	14-11	16-0
	I. Q. — - -	99	110	106	109
61.	Average I. Q. 105.6.
	Examiner	E. V.	E. V.	L. W.	L. I. S. L. I. 8.
	Chronological Age	12-5	13-11	14-11	15-4 15-10
	Terman Age	12-2	14-8	15-3	17-2 17-8
	I. Q	97	105	102	112 112
82.	Average I. Q. 105.5.
	Examiner	E. V.	L. W.	L. I. 8.	L. I. S.
	Chronological Age —	5-4	6-6	7-6	8-0
	Terman Age	5-6	6-fl	7-8	9-3
	I. Q -	103	100	103	116
63.	Average I. Q. 105.5.
	Examiner	E. V.	L. I. S.
	Chronological Age ...	9-7	12-0
	Terman Age	10-1	12-fl
	I. Q	105	106
64.	Average I. Q. 108.0.
	Examiner	E. V.	L. I. 8.
	Chronological Age	.. . 8-8	11-2
	Terman Age	9-0	11-5
	I. Q. — -	104	102
65.	Average I. Q. 103.0.
	Examiner	L. W.	L. I. 8.
	Chronological Age ...	10-4	11-1
	Terman Age	10-5	11-8
	I. Q	101	105
66.	Average I. Q. 102.7.
	Examiner	E. V.	E. V.	L. I. 8.	L. I. S.
	Chronological Age —	11-8	13-3	14-9	15-3
	Terman Age	11-7	14-1	15-0	15-10
	I. Q -	99	106	102	104
67.	Average I. Q. 102.5.
	Examiner	E. V.	L. W.	L. I. 8.	L. I. S.
	Chronological Age ...	5-5	8-11	7-6	8-0
	Terman Age	5-6	7-3	7-7	8-5
	I. Q	100	104	101	106
68.	Average I. Q. 99.5.
	Examiner	E. V.	L. I. 8.
	Chronological Age ...	6-7	8-10
	Terman Age	6-8	8-8
	I. Q	101	98
69.	Average I. Q. 97.5.
	Examiner	E. V.	L. I. S.	L. I. 8.	L. I. i.
	Chronological Age ...	7-3	8-10	9-3	9-10
	Terman Age	7-2	8-4	9-2	9-8
	I. Q	99	94	99	98
70.	Average I. Q. 97.5.
	Examiner	E. V.	E. V.	L. I. 8.	L. I. 8.
	Chronological Age ...	10-0	12-0	13-10	14-4
	Terman Age	10-8	11-8	13-1	14-3
	I. Q	99	97	96	90

MENTAL GROWTH CURVE 29

TABLE VI — CONTINUED ORIGINAL DATA ARRANGED IN ORDER OF MEAN I.	Q. — BOYS
71. 72.	Average I. Q. 96.0. Examiner Chronological Age Terman Age I. Q. Average I, Q. 95.0. Examiner Chronological Age . Terman Age — I. Q.	E. V. 12-2 , . . 11-8 ... 96 E. V. 11-2 10-1 90	E. V. 13-fl 13-3 90 E. V. 12-9 12-9 100
73.	Average I. Q. 98.2.
	Examiner	E. V.	E. V.	L. I. 8.	L. I. S. L. I. 8.
	Chronological Age ...	12-6	14-1	15-1	15-fl 16-0
	Terman Age	11-0	13-1	14-7	14-7 15-5
	I. Q.	83	92	96	94 96
74.	Average I. Q. 93.2.
	Examiner	E. V.	L. W.	L. I. 8.	L. I. 8.
	Chronological Age ...	8-7	10-O	10-8	11-2
	Terman Age	8-3	9-3	9-8	10-7
	I. Q	95	92	91	96
75.	Average I. Q. 92.0.
	Examiner	L. W.	L. I. 8.
	Chronological Age ...	- . 10-8	11-6
	Terman Age	10-2	10-2
	I. Q	95	89
76.	Average I. Q. 92.0.
	Examiner	E. V.	L. I. S.
	OhiYinAln^lpftl A trt*	9-5	11 11
		8-6	11 2
	I. Q	90	91

the I. Q. occur. In order to illustrate this more completely the 36 children of the Five Examination Group were arranged in the order of merit on the basis of the I. Q. for the first examination. For all of the children the first I. Q. was plotted, Chart Via and b, and the points connected by a solid line to show this array of children in the original order of increasing I. Q. The vertical scale represents the range of I. Q.'s from 80 to 100. The numbers running horizontally across the chart are the identification num- bers of the children in the tables of original data. The four suc- ceeding I. Q.'s for each child were plotted on the same vertical axis as the point for the first I. Q. and different kinds of lines drawn in order to make it possible to identify the I. Q.'s of dif- ferent children at the 2d, 3d, 4th and 5th examinations. The heavy horizontal lines indicate the conventional classifications of I. Q. level, 90 to 110 being considered average ability; 110 to 120 superior, with an additional classification of very superior for 120 to 140. In this study the very superior cases were not suf- ficiently numerous to permit of the last classification. Accord- ingly, all children with a mean I. Q. of 110 or above are classed as superior.

30

IOWA STUDIES IN CHILD WELFARE

TABLE VII
ORIGINAL DATA	ARRANGED IN	ORDER	OF MEAN	I. Q. — GIRLS
1. Average I. Q. 148.0.
	E V	E V	L W	LIB	L. I. S.
Chronological	8-3	9-4	10-4	11-4 ni	11-10 17 7
I. Q	139	143	158	151	149
2. Average I. Q. 146.8.
Examiner	E. V.	E. V.	L. W.	L. I. S.	L. I. 8.
Chronological	8-11	10-0	11-0	12-0	12-5
Terman	12-6	13-11	16-7	18-7	18-7
I. Q. -	140	139	150	155	149
3. Average I. Q. 140.5.
Examiner	. L. I. S.	L. I. S.
Chronological —	8-10	9-7
Terman —	12-7	13-4
I. Q.	142	139
4. Average I. Q. 131.7.
Examiner	E. V.	L. I. S.	L. I. S.	L. I. S.
Chronological	7-0	8-2	8-8	9-3
Terman	8-8	10-5	11-3	13-6
I. Q.	123	128	130	146
5. Average I. Q. 130.7.
Examiner	E. V.	E. V.	L. I. S.	L. I. S.
Chronological	9-1	10-2	11-8	12-2
Terman —	11-3	12-10	15-10	17-8
I. Q — -	123	126	136	138
6. Average I. Q. 130.5.
Examiner	L. W.	L. I. 8.
fliTnTinlniyinRl	6-4	7-2
Terman	7-6	10-3
I. Q. — - -	118	143
7. Average I. Q. 130.2.
Examiner	E. V.	E. V.	L. I. S.	L. I. S.	L. I. S.
Chronological	9-6	10-7	12-1	12-7	13-0
Terman „	11-0	13-7	15-11	17-8	17-8
I. Q	115	128	132	140	136
8. Average I. Q. 130.0.
Examiner	E. V.	E. V.
Chronological	7-0	8-1
Terman	9-2	10-5
I. Q.	131	129
9. Average I. Q. 128.8.
Examiner	E. V.	E. V.	L. W.	L. I. S.	L. I. 8.
Chronological	8-10	9-10	11-1	11-10	12-4
				lfi-7	17 1
I. Q	111	lie	139	140	138
iO. Average I. Q. 127.8.
Examiner	E. V,	E. V.	L. I. S.	L. I. 8.	L. I. S.
Chronological	. .. 6-6	7-5	9-0	9-6	9-11
Terman	8-2	9-2	10-8	12-9	13-8
I. Q.	125	123	119	134	138
.1. Average I. Q. 125.5.
Examiner	E. V.	L. W.	L. I. S.	L. I. S.
«-!L_^_ l * I	o_a	10-8	11 3	11 10
Terman	10-3	13-4	15-1	16-3
I. Q - -	106	125	134	137
12. Average I. Q. 125.0.
Examiner	— . E. V.	E. V.
Chronological	. . 8-9	9-9
Terman	10-8	12-6
I. Q. — -	122	128
3. Average I. Q. 124.7.
Examiner	E. V.	L. W.	L. I. S.	L. I. 8.
Chronological	4-11	5-6	6-6	7-0
Terman	6-4	6-10	8-0	8-8
I. Q	128	124	123	124
14. Average I. Q. 124.6.
Examiner	— . E. V.	L. S.	L. I. 8.
Chronological	10-9	12-3	13-3
Terman	12-4	15-6	17-8
I. Q.	115	126	133

MENTAL GROWTH CURVE

31

	ORIGINAL DATA	TABLE VII — CONTINUED ARRANGED IN ORDER OF MEAN I	. Q. — GIRLS
15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.	Average I. Q. 124.0. Kxaniiner . __	L. W.	L. I. S. 6-7 8-0 121 L. I. S. 6-9 8-10 131 L. W. 11-2 12 11	L. I. S. 11-11 15-7 130 L. I. S. 11-4 12-3 108 L. I. S. 14-1 18-O 128 L. I. S. 8-8 10-10 125 L. W. 10-5 12-0 115 L. I. S. 12-6 14-9 118 L. I. S. 13-0 15-5 118 L. I. 8. 10-0 12-2 121 L. I. S. 9-7 10-11 114	L. I. 8. 12-5 16-11 136 L. I. S. L. I. S. 11-9 12-3 15-3 17-8 129 144 L. I. S. 14-8 18-6 123 L. I. S. 9-3 11-3 122 L. I. S. L. I. 8. 13-0 13-6 16-5 17-8 126 127 L. I. S. L. I. S. 13-5 13-11 17-2 17-2 127 123 L. I. 8. 10-7 13-0 123 L. I. S. 10-2 12-2 119
Chronological	5-9
Term an	7-4
I. Q	127
Average I. Q. 123.5. Examiner	L. W.
Chronological	5-7
Term an	6-6
I. Q. .	. . 116
Average I. Q. 123.2. Examiner	E. V.
Chronological	9-11
Terman	11-0
I. Q	Ill	116 L. I. S. 6-4 7-6 118 E. V. 9-10 11 1
Average I. Q. 122.5. Examiner	L. W.
Chronological	5-1
Terman	6-6
I. Q.	.. . 127
Average I. Q. 122.4. Examiner	E. V.
Chronological	8-9
Terman	10-5
I. Q.	119	112 L. W. 13-1 16-4 124 E. V. 7-6 8-11 119 L. I. S. 8-3 9-6 115 L. I. S. 7-1 9-0 127 E. V. 8-11 10-9 120 E. V. 11-1 12-3 110 E. V. 11-6 13-1 113 L. I. S. 9-8 11-2 115 L. I. 8. 9-2 10-S 116
Average I. Q. 122.0. Examiner	L. I. S.
Chronological	11-5
Terman	13-0
I. Q	113
Average I. Q. 121.0. Examiner	E. V.
Chronological	6-1
Terman	7-6
I. Q	123
Average I. Q. 120.5. Examiner .	E. V.
Chronological	e-8
Terman	8-0
I. Q	120
Average I. Q. 120.0. Examiner	L. W.
Chronological	5-11
Terman -	6-8
I. Q.	113
Average I. Q. 119.0. Examiner	E. V.
Chronological	7-10
Terman	9-7
I. Q.	...1. 122
Average I. Q. 118.6. Examiner	E. V.
Chronological	10-0
Terman	11-3
I. Q	112
Average I. Q. 118.0. Examiner	E. V.
Chronological	10-5
Terman	11-5
I. Q ;	109
Average I. Q. 117.2. Examiner	E. V.
Chronological	8-0
Terman .	8-10
I. Q. .	110
Average I. Q. 117.2. Examiner	E. V.
Chronological	7-7
Terman	„ . 9-1
I. Q	. - 120

32

IOWA STUDIES IN CHILD WELFARE

TABLE VII — CONTINUED
	ORIGINAL	DATA	ARRANGED	IN OBDEB	OF MEAN	I. Q. — GlKLS
29.	Average I. Q.	117.0.
	Examiner	,_-__	E. V.	L. w.	L. I. S.	L. I. S.
	Chronological _		5-7	8-9	7-8	8-2
	Terman		6-8	7-8	9-0	10-0
	I. Q.		us	113	117	122
30.	Average I. Q.	118.8.
	Examiner		. E. V.	E. V.	L. W.	L. I. 8. L	. I. 8.
	Chronological .		8-11	•10-3	11-4	11-11	12-*
	Terman		10-7	11-9	12-1	14-4	15-8
	I. Q -		118	114	108	120	126
31.	Average I. Q.	iie.2.
	Examiner		E. V.	E. V.	L. I. S.	L. I. S.
	Chronological .		9-3	10-9	12-4	12-10
	Term an		10-9	12-5	14-1	15-5
	I. Q.		118	115	114	120
32.	Average I. Q.	116.0.
	Examiner		.... L. W.	L. I. 8
	Chronological .		5-11	7-2
	Terman		8-2	9-2
	I. Q -		104	128
33.	Average I. Q.	115.6.
	Examiner . ._		E. V.	L. S.	L. I. S.	L. I. S. L	. I. S.
			5-1	8-1	7 7	8-1	o_7
	TermftrK , ,		5-0	7-4	9-2	9-10	10-2
	I. Q.		. - 98	120	121	121	118
34.	Average I. Q.	115.5.
	Examiner		.... L. W.	L. I. 8
	Chronological -		5-4	6-7
	Terman		8-8	7-2
	I. Q. -		122	109
35.	Average I. Q.	114.5.
	Examiner		.— E. V.	L. W.	L. I. 8.	L. I. S.
	Chronological _		9-4	10-6	11-4	11-11
	Terman		10-10	11-11	12-10	13-9
	I. Q		118	114	113	115
36.	Average I. Q.	113.5.
	Examiner		.— E. V.	L. W.	L. I. 8.	L. I. S.
	Chronological .		11-8	12-5	13-1	13-9
	Terman		12-8	13-9	15-1	16-7
	I. Q		108	110	115	121
37.	Average I. Q.	113.5.
	Examiner		.— E. V.	E. V.
	Chronological .		8-1	7-1
	Terman		8-10	8-2
	I. Q		112	115
38.	Average I. Q.	113.4.
	Examiner		... E. V.	L. S.	L. W.	L. I. S. L	I. S.
	Chronological -		6-2	7-1	8-9	9-3	9-8
	Terman		7-8	8-4	9-8	10-3	10-7
	I. Q		121	117	110	110	109
39.	Average I. Q.	112.0.
	Examiner		E. V.	E. V.	L. I. 8.	L. I. 8. L	I. S.
	Chronological ..		11-4	12-11	14-0	14-4	14-10
	Terman		11-8	14-10	14-10	17-7	17-7
	I. Q. .		101	114	106	122	118
0.	Average I. Q.	112.0.
	Examiner		E. V.	E. V.	L. W.	L. I. S. L	I. 8.
	fiK—rt nrtl /•» &\ no!		a_9		1ft-7	11 2	11-8
			9-4		11 2	12-0	14—7
	I. Q		114	109	105	107	125
41.	Average I. Q.	110.5.
	Examiner		— L. W.	L. I. S.
	Chronological .		6-8	7-6
	Terman		7-4	8-4
	I. Q		110	111
42.	Average I. Q.	110.0.
	Examiner		— E. V.	L. I. 8.	L. I. S.	L. I. S.
	Chronological —		9-4	10-7	10-11	11-8
	Terman		9-7	10-8	12-3	14-7
	I. Q		102	99	112	127

MENTAL GROWTH CURVE

	ORIGIN AL	TABLE VII — CONHNUED DATA ARRANGED IN ORDER OF MEAN I. Q. — GIRLS
43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 50.	Average I. Q. Examiner _	100.0.	E. V. 7-6 8-4 111 L. W. 6-5 6-8 104 E. V. 8-8 9-7 110 L. 8. 12-7 13-8 108 E. V. 8-11 10-2 114 E. V. 9-3 7-0 112 E. V. 9-9 10-4 106 E. V. 6-7 7-0 108 L. 8. 15-7 15-3 97 L. W. 6-0 6-6 108 L. W. 6-e 6-10 105 L. W. 5-1 5-8 111 E. V. 11-3 11-1 98 L. I. 8. 9-0 9-2 103	E. V. 8-10 9-8 109 L. I. 8. 7-7 8-7 113 E. V. 9-9 10-4 105 L. W. 14-2 15-9 100 L. I. 8. 10-3 10-8 104 L. I. 8. 9^ 10-1 103 E. V. 11-3 12-* 109 L. W. 7 11	L. I. 8. L. I. 8. L. I. 8. 10-1 10-6 11-0 10-T 11-10 11-10
Chronological _
Term an
I. Q.		104 113 108 L. W. 11-0 12-1 109 L. I. 8. L. I. 8. 19-3 15-9 16-8 19-8 109 109 L. I. 8. L. I. 8. 10-8 11-2 11-9 11-9 108 105 L. I. S. L. I. 8. 8-8 9-9 9-9 9-0 112 105 L. I. 8.
Average I. Q. Examiner	108.5.
Chronological _
Terman _
I. Q
Average I. Q. Examiner	108.0.
Chronological _
Terman
I. Q
Average I. Q. Examiner	108.0.
Chronological -
Terman
I. Q.
Average I. Q. Examiner -	107.7.
Chronological _
Tpirmnn
I. Q.
Average I. Q. Examiner	107.5.
Chronological . Terman
I. Q. - .. .
Average I. Q. Examiner	107.5.
Chronological _
TflTtnan ,
I. Q.
Average I. Q. Examined .	107.0.
Chronological -
Terman __		8-4 105 E. V.
I. Q.
Average I. Q. Examiner	107.0.
Chronological _		16-9 18-0 112 L. I. 8. 7-4 7-8 105 L. I. 8. 7-4 7 10	17-8 18-0 118 L. I. 8. 13-10 15-10 114
Terman
I. Q. .
Average I. Q. Examiner _ „	108.5.
Chronological _
Terman
I. Q.
Average I. Q. Examiner	106.0.
Chronological -
Terman
I. Q		107 L. I. 8. 9-4 9-4 100 E. V. 12-6 13-0 104 L. I. 8. 9-0 7-2 100
Average I. Q. Examiner _	105.5.
Chronological _
Terman _
I. Q. _.
Average I. Q. Examiner	105.3.
Chronological -
Terman .
I. Q
Average I. Q. Examiner	104.5.
Chronological .
Terman .
I. Q _

34

IOWA STUDIES IN CHILD WELFARE

TABLE VII — CONTINUED
	ORIGINAL DATA	ARRANGED IN	ORDER OF	MEAN I.	Q. — GlBLS
57.	Average I. Q. 103.5.
	Examiner	E. V.	E. V.	L. I. S.	L. I. S.
	Chronological	8-8	9-8	11-8	12-3
	Terman	9-8	10-6	11-4	12-2
	I. Q.	111	107	97	99
58.	Average I. Q. 102.7.
	Examiner	— . E. V.	E. V.	L. I. 8.	L. I. S.
	Chronological	9-2	10-3	12-3	12-9
	Terman	9-8	10-9	12-0	13-3
	I. Q -	105	104	98	104
59.	Average I. Q. 102.6.
	Examiner _„ „	E. V.	E. V.	L. I. 8.	L. I. S. L	I. 8.
	Chronological __	7-11	9-0	10-7	10-11	11-5
	Terman	8-2	9-9	10-3	10-9	12-4
	I. Q. — ~.	108	108	98	98	108
60.	Average I. Q. 102.5.
	Examiner _._	— . E. V.	L. I. S.
	Chronological	12-6	14-10
	Terman>	13-0	14-11
	I. Q.	104	101
61.	Average I. Q. 102.5.
	Examiner	.... L. W.	L. I. 8.
	Chronological	8-3	9-3
	Terman .	8-4	9-7
	I. Q	101	104
62.	Average I. Q. 98.5.
	Examiner	L. W.	L. I. S.
	Chronological	5-4	8-6
	Terman _	5-2	6-6
	I. Q	97	100
33.	Average I. Q. 93.8.
	Examiner	E. V.	E. V.	L. I. 8.	L. I. S. L	I. S.
	Chronological	9-6	10-4	11-6	11-11	12-6
	Terman	8-8	10-4	10-7	10-10	11-10
	I. Q. —	91	100	92	91	95
64.	Average I. Q. 93.5.
	Examiner	— - E. V.	E. V.
	Chronological	9-8	10-7
	Terman	8-10	10-2
	I. Q.	91	90
65.	Average I. Q. 92.7.
	Examiner .	E. V.	L. W.	L. I. S.	L. I. S.
	Ohronological	6-4	7-7	8-4	8-11
		5-10	9-n	7 Q	R-K
	I. Q -	92	92	93	94
86.	Average I. Q. 91.7.
	Examiner	— . E. V.	L. W.	L. I. 8.	L. I. S.
	Chronological	9-3	10-8	11-0	11-6
	Terman	9-4	9-6	9-9	10-2
	I. Q. — -	100	90	89	88
67.	Average I. Q. 91.5.
	Examiner	L. W.	L. I. 8.
	Chronological —	11-2	12-3
	Terman	9-8	11-9
	I. Q	87	96

It is apparent that these class names have very little real sig- nificance, as almost all of the children vary from their original classfiication on re-examination. A variation of only a few points in the I. Q. measuring actual mental growth or occurring as a chance error of examination would be sufficient to transfer a child from the average to the superior class. The same amount of vari- ation might keep a child within its class if the original I. Q. has been sufficiently low. This fallacy in the use of type names has

MENTAL GROWTH CURVE 35

long been recognized by careful students of individual differences, but it needs to be emphasized again because of the loose use of these terms by "Binet testers."

Inspection of the variations in each child's I. Q. as shown in Chart VI shows that the original I. Q. is only approximately con- stant upon successive examinations. In two cases the second, third, fourth and fifth I. Q.'s are actually below the first I. Q. ; in five cases one of the later I. Q.'s is below the original one and in ten cases two or more of the later I. Q.'s are below the first. The remaining 19 cases show a general increase in I. Q., though each succeeding examination does not always give a higher I. Q. than the one preceding.

The uniform and homogeneous nature of the mean I. Q. curves in Chart IV tends to give a false impression of the individual child's successive I. Q.'s. For this reason the individual curves of the 36 children who had the largest number of examinations were plotted in Charts VII and VIII in order to show the actual variations in I. Q. that occur. A comparison of the charts for boys and girls shows a greater irregularity of development in girls, together with a tendency toward greater decrease in I. Q. at the later ages, probably due to the fact that the girls, who are more advanced in their development, can not maintain their orig- inal rates because of having passed so many of the tests at the upper limit of the scale. The fairly consistent and uniform curve which would correspond to an absolutely stable I. Q. is not ex- emplified in any of the girls' curves and in only two of the boys' curves, Nos.1 3 and 17. A gradual steady increase in I. Q. is observable in some instances, as for example in the curves of boys Nos. 25, 34 and 61 and girl No. 5. Examples of curves show- ing a steady rise followed by a decrease in I. Q. are: for boys Nos. 11 and 8 and for girls Nos. 1, 7 and 26. Curves showing marked irregularities with the I. Q. alternately increasing and de- creasing are : for girls Nos. 63 and 39, and for boys Nos. 47 and 33.

"While many of these changes are well within the 5 point limit of safety, a sufficient number show deviations of such magnitude2 that extreme care should be exercised about making any dogmatic statements in regard to what a child's future status will be. For

'These numbers correspond to the numbers assigned the children in the tables of original data.

*Cf. Root, W. T. Two Cases Showing Marked Change in I. Q., /. of Appl. Ptychol., (5) 1921, 156-158.

36

SUCCESSIVE I.Q.'S 3

Bi6i G|J4 Gp» 8jJ* Gi59 8j-»6 &44 8|4? <S26 0:4i G>4 Bj« Gti5 G)40 8iib 0.7

example, Girl No. 9 (Chart VIb) whose I. Q. in the first test was 111, obtained on four subsequent tests 116, 139, 140 and 138. A careful study of this case showed no difference in the method of examination and no unusual physical condition aside from the adolescent physiological acceleration.

No doubt these fluctuations in general mental achievement were modified more or less by such factors as time of day, health con- ditions at the time of the examination, fatigue, interest of the child in a particular examination, and changes in the home and school environment. Similarly conditioned changes in attitude on the part of the examiner might also have their effect.

2. Deviations of Individuals from their Mean I. Q, Level. In order to determine other causes of the variability that is apparent from an inspection of the individual I. Q. curves, each child's deviation in I. Q. for every examination was calculated from his mean I. Q. in all of his examinations. For example, one boy of very superior general intelligence showed on 5 examinations, deviations of +.4, — 1.6, — 1.6 and +3.4 ; another boy of average ability showed very different deviations. It is possible that these deviations are influenced by chance errors of examination. Never- theless it is apparent that the size of these deviations depends not only on the real (inherent) variability of the child, but also upon the size of his mean I. Q. A large deviation on a high I. Q. may

MENTAL GROWTH CURVE CHART VIb

37

1 ' ' ' A	i \ ,so
r 77 ~—"" A >,. /V A,	><J^ 140

130

100

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B|23 8(JJ 0|8 CjJO G-19 B|I2 6(38 B|39 B|20 ftl? Bill 6|5 GilO &5 ft4 6il Oi2 BiJ II I I I I I I .1 I 1 I I I I I I I 80

not be very different from a small deviation on a low I. Q. In order to make all deviations comparable they were expressed as percentages of each child's mean I. Q. These percentages were then averaged for each child and the mean of the individual

TABLE VIII MEAN OF INDIVIDUAL DEVIATIONS FROM INTELLIGENCE QUOTIENT	LEVEL
	Mean	Boys P. E.	Girls Mean P. E.
Superior I. Q. 110+ Average I. Q. 90-110 Total Under 10 at last exami- nation Over 10 at first exami- nation	4.48 2.65 3.99 3.60 4.85	.53 .23 .38 .31 1.26	6.92 3.80 5.95 5.14 7.09	.78 .29 .57 1.19 1.36

variabilities obtained for various classes of subjects (Table VIII). The mean for all the boys was 3.99 ± .38; for all of the girls 5.95 ± .57. The mean for the superior boys was 4.48 ± .53, for superior girls 6.92 ± .78. The mean for average boys was 2.65 ± .23 ; for average girls 3.80 ± .29.

To determine whether chronological age was also a factor tend- ing to make the individual vary from his I. Q. level, means were obtained for boys and girls who were under 10 years of age at

38

IOWA STUDIES IN CHILD WELFARE CHART VII

1 I T

1 — r — r

ICO

INDIVIDUAL I.Q.

100

iU .

the last examination and for those over 10 at the first examina- tion. The mean for the boys who were under 10 years of age at their last measurement was 3.60 ± .31; for boys who were over 10 at their first measurement was 4.85 ± 1.26. The mean for girls who were under 10 years of age at their last measurement was

CHART VIII

ACF IN YFABS

MENTAL GROWTH CURVE

39

5.14 ± 1.19 and for those over 10 at their first measurement was 7.09 ± 1.36.

The P. E. of all these means is sufficiently large to obscure the difference between the means for the group under comparison. There is, nevertheless, a constant tendency in all the groups for the girls to be more variable than the boys, for the superior chil- dren to be more variable than the average children and for the older children to be more variable than the younger.

3. Differences in I. Q. at Successive Examinations. One method of studying the stability of the I. Q. is that of direct observation of the changes that take place on re-examination. For every pos- sible combination of examinations in the four groups the differ- ences of I. Q. for each child were computed and the increases in I. Q. tabulated as positive and the decreases as negative. These positive and negative variations were then grouped by class in- tervals of 5 point differences in I. Q. and the per cent of cases showing each amount of difference calculated. For example, 16 of the 74 boys who had two examinations showed a decrease of 0 to 5 points on the second examination; i. e., 21.6% showed this amount of negative difference. The percentage distribution of the differences, exclusive of the cases showing no differences, is shown for boys and girls in Table IX and Chart IX.

Between the first and second examination the percentage dis- tribution of differences approximates the normal frequency curve with the greatest number of cases showing a positive change within the 5 point range. As the interval between examinations increases the effect of the repeated examinations intervening be- comes apparent in a shift toward the positive end of the scale. Although there is no large ser difference, the girls have a wider range of deviation, particularly those of the Four and Five Exam- ination Groups, where the last examination fell for the majority of the children within the period of adolescence.

The mean change in I. Q. was found to be

Examination	1-2	2-3	3-4	4-5
Deviation	__ i	— +	— +	, i
Boys Girls	4.61 7.39 4.53 7.32	5.12 7.60 5.17 8.00	3.42 7.27 3.75 6.79	2.50 5.14 3.44 7.75

Here there is evident a shift in the relation between negative and positive changes as the number of examinations children have taken grows larger.

40

IOWA STUDIES IN CHILD WELFARE

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IOWA STUDIES IN CHILD WELFARE

These I. Q. changes cannot, however, be taken at their face value, since a large change on a high I. Q. may not be more signif- icant than a small change on a low I. Q. In order to make all changes comparable, the mean gains and losses from the first to second, second to third, third to fourth, and fourth to fifth examinations were expressed as per cents of the mean I. Q. at the 1st, the 2d, the 3d or the 4th examination, depending on the com- parison being made. The material was also arranged to give a separate mean for average and superior children. The per cents of change in I. Q. follow :

Examination	1-2	2-3	3-4	4-5
Deviation %	+	— +	— +	+ —
Superior Boys Girls	4.3 7.0 3.5 8.5	5.1 6.5 3.5 7.1	3.1 7.5 4.1 5.8	2.0 4.2 2.5 6.3
Average Boys Girls	3.9 5.0 5.0 5.5	3.0 6.5 6.8 6.3	2.3 4.8 2.9 5.7	0 1.9 5.0 7.0

This tabulation shows a slightly greater per cent of change, especially in the positive direction, for superior children, due probably to the fact that superior children profit more readily by practice.

It would be of great interest to know what is the effect of chronological age upon the change in I. Q., but the writers have been unable to devise any reliable method of determining the facts from the data available. The computation of the mean I. Q. change at each chronological age is not permissible because of the varying amounts of practice. For example, at age 8 there are the first examinations for some children, and also the second, third, fourth and fifth for others. Such tabulation of cases with reference to the age at the first test would, moreover, class the children whose second examination was given after a consider- able time, with those who had been re-examined at a shorter in- terval, and would tend to obscure any characteristic chronological changes occurring. It would seem that the question of whether older children show a different amount of I. Q. change than younger children could be solved only by a special experi- ment with a series of examinations beginning at a uniform age, on children of equal intelligence, and applied at uniform intervals.

No determination can be made in this study of the effect of the interval separating the examinations. The change from the 1st to

MENTAL GROWTH CURVE 43

the 5th I. Q. cannot be compared with the change at other intervals because of the different amounts of practice intervening.

Terman (26) 1919, p. 138, used the method of I. Q. comparison described as follows :

"Tests have been given to 315 children in the vicinity of Stan- ford University. To 46 of these children, three or more tests have been given. In case of a child tested several times each test has been compared with each of the others, for example, the first test with the second, third, and fourth, separately, the second test with the third and fourth separately, and the third test with the fourth. This gives in all 435 I. Q. comparisons."

Terman (26) p. 140, reports that his comparisons show: "that it makes little difference whether the child was bright, average or dull, how long an interval separated the tests or what the age of the child was at the earlier test. The majority of the changes are for all groups relatively small ....

"The central tendency of change is represented by an increase of 1.7 in I. Q. : the middle 50% of change lies between the limits of 3.3 decrease and 5.7 increase; the probable error of a predic- tion based on the first test is 4.5 points in terms of I. Q."

The method of I. Q. comparison as used by Terman is open to the objections stated above. The I. Q.'s obtained after repeated examinations are pooled with those from a first examination, and the average tendency of change computed on the basis of these data. It seems to us that the differences in practice would make it inadvisable to pool these examinations.

Such a tabulation of change in I. Q. with reference to the age at the first test would, moreover, afford no opportunity for the special characteristics of the adolescent period to show them- selves if they existed. As has been demonstrated in connection with the mental growth curves, and the physical growth curves, boys and girls have a period of adolescent acceleration at differ- ent chronological ages, and children of superior and average mental and physical status show a similar difference. A pooled classification of these different classes of data tends to destroy any characteristic chronological age changes in I. Q.

We have felt that the solution of these problems would not be obtained by the use of this method. The 695 separate I. Q. com- parisons afforded by the data in this study would have been re- duced to a very small number if the comparisons had been made only with children of the same chronological age, sex, I. Q. level, and physical status.

4. Intercorrelations. The stability of the I. Q. can be investi-

44 IOWA STUDIES IN CHILD WELFAKE

gated by another means than that of noting the size of the differ- ences in I. Q. and calculating the central tendency of change. The similarity in the relative rankings of children on successive examinations can best be studied by means of the method of cor- relation. Although several writers have reported correlations between two examinations no data have so far been presented in the literature to show the intercorrelations of several examina- tions given on the same group of children for several years. From such an array of correlations one can determine whether the ma- jority of children maintain at a later examination their relative position above or below the mean of their group and tend to deviate from this mean by approximately the same amount after several years interval. The accuracy of the prediction is condi- tioned by the size of the correlations. A high correlation between the I. Q.'s obtained by a group of children on two examinations would mean considerable stability in I. Q. and the possibility of predicting with a high degree of accuracy the future status of children of any I. Q. level.

For this method of investigating the evenness of the mental growth there were calculated Pearson coefficients of correlation for four groups of children. One group consisted of 56 children who had been examined twice; the coefficient of correlation for the two examinations was +.81±.03. Another group consisted of 51 children who had been examined three times ; the coefficient for the first and second was +.76^04; for the first and third +.69 ± .05 ; for the second and third +.83 ± .03.

It was possible to give a fourth examination to all but 9 of this group. The coefficients for this smaller group were, for the first and second examinations +.79±.04, for the second and third +.86 ± .03, for the third and fourth +.93 ± .02, for the first and third +.77 ± .04, for the second and fourth +.82 ± .03, and for the first and fourth +.72 ± .05.

The last group of 36 children was given five examinations. The correlation between the first and second was +.85±.03, between the second and third +.85±.03, between the third and fourth +.91±.02, between the fourth and fifth +.92±.02, be- tween the first and third +.74±.05, between the first and fourth +.78±.04, between the first and fifth +.82±.04, between the second and fourth +.80±.04, between the second and fifth +.82±.04, and between the third and fifth +.84±.03.

MENTAL GROWTH CURVE

45

TABLE X
INTEBCOBBELATIONS OF INTELLIGENCE QUOTIENTS FOB Two, THREE, FOUB AND FIVE EXAMINATION GBOTTPS
Examination	1 and 2	1 and 3	2 and 3	1 and 4	2 and 4	3 and 4	1 and 5	2 and 5	3 and 5	4 and 5
5 Exam. Group.-JCoel. {P. E	+ .85 ±.03	+.74 ±.05	+ .85 ±.03	+ .78 ±.04	+ .80 ±.04	+ .91 ±.02	+ .82 ±.04	+ .82 ±.04	+ .84 ±.03	+ .92 ±.02
4 Exam. Group— JCoel. (P. E	+ .79 ±.04	+.77 ±.04	+ .86 ±.03	+.72 ±.05	+ .82 ±.03	+ .93 ±.02
S Exam. Group-.JCoef. IP. E	+ .76 ±.04	+ .69 ±.05	+.83 ±.03
i Exam. Group..$Coel (P. E	+.81 ±.03

The coefficients (Table X) are uniformly high and reliable with low probable errors, ranging from +.72 ± .05 to +.93 ± .02. The coefficients of correlation for near-lying examinations, that is, two examinations with none intervening, are highest, the mean being +.88. For three correlations with one intervening exam- ination the mean is +.79. For the two with two intervening examinations the mean is +.80, and for the one with three interven- ing examinations the correlation is +.82. Although the coefficient is highest for near-lying examinations there is no tendency for the correlation to decrease with increase of interval.

TABLE XI PEBCENTAQE OF CHILDREN TESTED BY SAME EXAMINEE
Group	Examiner	M£ •o os a x «w	cog T3 OS !*	eo g •a GO a x *w M	"S 59 a M <spq H	*a "a os a H *w M	* 3 v * a M «W co	IB g •c «e §M H	10 S •a os a * «w M	usg >a os 33 c«	10 S •O OS a x «H •*<
5 Exam.	E. V	91.4% 0 0 0 s.e 32.2 0 0 0 99.8 77.8 0 0 0 22.2 28.0 0 0 3.5 67.8	0% 0 0 0 100 0 0 0 0 100 0 0 0 0 100	0% 0 0 0 100 0 0 0 18.6 81.4 0 0 0 0 100	0% 0 0 0 100 0 0 0 0 100	0% 0 0 0 100 0 0 0 18.8 Sl.i	0% 0 0 40 eo 0 0 0 100 0	0% 0 0 0 100	0% 0 0 0 100	0% 0 0 40 60	0% 0 0 100 0
4 Exam. 3 Exam. 9 Exam.	L. 8
L. W.
L. I. 8
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L. W.
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Misc
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L. I. 8
Misc
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	L. 8
L. W
L. I. 8
Misc

46 IOWA STUDIES IN CHILD WELFAEE

It is possible that the size of the correlation might be influenced by the fact that a number of children were examined on both oc- casions by the same examiner. A study of Table XI shows that although for the two highest coefficients +.93 and +.92, 100% of the examinations were made by the same examiner, the next highest coefficient, +.91, showed only 40% by the same examiner. Other high coefficients are +.86 with 18.6% of the examinations and +.85 with 91.4% of the examinations by the same examiner. A correlation of +.85 was also found where no child had been examined twice by the same examiner and a coefficient as low as +.76 was obtained with 77.8% of the examinations made by the same examiner. It would appear then that the personal equation of the examiner although of some influence is not the important factor in the size of the correlation.

In general it is not justifiable to compute correlations for a group with such a wide range in chronological age. Such a procedure would tend to raise the correlation. The correlations between I. Q.'s are probably not subject to criticism from this point of view, since the I. Q. compensates for the difference in the chronological ages.

Considerable doubt has been thrown by K. Pearson (Proc. Roy. Soc., 1897 (60) 489.) on the justifiability of correlating ratios. From this point of view the calculation of correlations between I. Q.'s may result in spurious correlation. This method is, however, the only feasible one at this stage in the development of the problem.

In each group the highest correlations occur between near-lying examinations at the end of the series of examinations where the children were better adjusted to the situation and had apparently reached a certain stability of position within the group.

For comparison it is of interest to note the size of the correla- tions obtained by other examiners. These were : Bobertag, +.95 (Binet) ; Terman, +.93 (Stanford) ; Cuneo and Terman, +.95, +.94, +.85 (Stanford) ; Rosenow, +.82 (Binet and Stanford) ; Rugg and Colloton, +.84 (Stanford).

5. Probable Error of Estimate. Knowing the value of the coefficient of correlation between the first and any succeeding test, we can predict what any future I. Q. would be and compute the difference between the I. Q. as predicted and as actually obtained, or the error of estimate.

MENTAL GROWTH CURVE

47

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48

IOWA STUDIES IN CHILD WELFARE

Our data for five consecutive examinations of 36 children have been used to make a comparison of the I. Q.'s actually obtained and the I. Q. 's predicted by means of the regression equation :

where y1 = the I. Q. to be predicted, y = the mean of the obtained (later) I. Q.'s, x = the mean of the obtained first I. Q.'s, xt = the individual I. Q. on the first test, and a = the standard devia- tion of the x or y series.

The equation can more conveniently be used in the simplified form:

The quantity r -^ is a constant through a whole prediction *

series, a different constant being used for each of the four pre- diction series (second, third, fourth and fifth I. Q.'s from first

I. Q.'s). The quantity y — . r -f- ^ is also a constant in each of

"•

these four prediction series, which reduces the formula to y^~ k(xi)-\-kl. For example, by substituting the constants for the prediction of the second I. Q. one obtains y1=.78(x1)-}-29.5. For the prediction of the third from the first I. Q. : i/1=.90(a;1)-}-15.9.

TABLE XIII
DISTBIBUTION OF DIFFEBENCES BETWEEN OBTAINED AND PREDICTED I. Q.'s (Errors of Estimate)
Examination	2345
Amount of I. Q. Difference	Number of Cases
0-5	—9	+12	—6	+6	—7	+4	—10	+7
5-10	—4	+ 7	—6	+5	—7	+8	— 6	+7
10-15	—2	+ 1	—2	+5	—3	+3	— 2	+2
15-20	1	0	—3	+2	—1	+2	— 1	0
20-25	0	0	—1	0	—1	0	0	+ 1

MENTAL GROWTH CURVE CHART X

	DISTRIBUTION OF DIFFERENCES BETWEEN OBTAINED AND PREDICTED 7<pV
•5th. Exam.
4th Exam,					••MBM
3 rd Exam
ind Exam.,

-30 -<S5 -XO -/5 -/O -S C +5 +10 +15 +86 +15 +3O

Amount of Difference

For the prediction of the fourth from the first I. Q. : yt= .90(2^) +20.1. For the prediction of the fifth from the first I. Q. :

By the use of this formula the second, third, fourth and fifth I. Q.'s for each child were predicted and the differences between

4

50 IOWA STUDIES IN CHILD WELFARE

the predicted I. Q.'s and the I. Q.'s actually obtained at each of these examinations (the errors of estimate) calculated, together with the mean of the differences for the group as a whole. The I. Q.'s as actually obtained and as predicted are shown in Table XII. The distribution of the differences between obtained and predicted I. Q. 's is shown in Table XIII and Chart X.

On the average the prophesied second I. Q. differs from the obtained second I. Q. by 4.7 points, P. E. ± .5, i. e., the chances are equal that the average for the differences between the pre- dicted and obtained I. Q.'s will not be less than 4.2 or greater than 5.4. The average difference between the predicted and ob- tained third I. Q. or the average of the errors of estimate is 8.5 ; between the predicted and obtained fourth I. Q. is 7.7 and be- tween the predicted and obtained fifth I. Q. is 6.3. The mean interval between the second and first examination was approxi- mately 13 months; between the third and first was 28 months; between the fourth and first was 36 months and between the fifth and first 41 months.

While Table XII shows for each prediction series the most prob- able predicted I. Q. for each child, a better sampling from a larger number of cases might have resulted in another predicted I. Q. In other words, while 137.9 is the proper estimate for the second I. Q. for case 1, the probable error of estimate gives the number of points variation above or below this estimate that will take in 50% of all the other possible estimates. Knowing the value of the 4 coefficients of correlation involved, one can calculate the probable error of estimate for each of the prediction series by means of the formula P. E. = .6745 X « var. V 1— r2. This for- mula gives as a probable error of estimate for the prediction of the second from the first I. Q. ±4.2, for the prediction of the third from the first I. Q. ±7.0 ; for the prediction of the fourth from the first I. Q. ±6.2 ; for the prediction of the fifth from the first I. Q. ±5.5. The P. E. of estimate of the second from the first is ±4.2 as previously stated, i. e., the chances are equal that the true predicted second I. Q. will not vary from the calculated I. Q. by more than ±4.2. The chances that the true predicted I. Q. will not vary from the calculated I. Q. by more than ±8.4 (or 2 P. E.) are 1802 in 10,000 or 1 chance in every 4.5. The chances that the true predicted I. Q. will not vary from the calculated by more than ±12.6 are 434 in 10,000 or the chances that a deviation greater than ±12.6 would occur are 1 in 22. The same chances of

MENTAL GROWTH CURVE 51

error per 10,000 on 2 P. E. and 3 P. E. exist for the other predic- tion series, the only difference in each case being the size of the P. E. The P. E. of estimate for the second examination is very nearly the same as that reported by Rosenow (20) which was 3.988.

The size of the P. E. obviously depends on the size of the co- efficient of correlation for the particular comparison involved. At first thought one might expect that an increase of interval be- tween the examinations would result in a larger error of estimate. An increase in the probable error of estimate was, in fact, ob- served to take place in the prediction of the third from the first, where the interval was lengthened by one year. As was noted in connection with the correlations, however, the coefficient does not decrease regularly with an increase of the interval, but re- flects the general habituation and improvement that has taken place and the tendency for each individual to find and remain at his characteristic level.

The calculation of the regressions and of the probable errors of estimate is of no special significance for this particular group, since the later I. Q.'s are already known. The real value of the procedure lies in utilizing the knowledge in regard to the corre- lation between earlier and later examinations for predicting the later I. Q. of other children who have received only the earlier examination. Chart X shows there is a conspicuous increase in the positive and a decrease in the negative differences observable where the group has had considerable opportunity for becoming adjusted to the examinations. It is not possible from the data at hand to make an exact determination of the amount of error of prediction for various intervals of examination since all of the children in this group have had repeated measurements in be- tween, which influences the size of the correlations for the longer intervals. In order to determine how accurately one may pre- dict a child's I. Q. one year later, two years later, etc., the corre- lations will have to be obtained on a sufficient number of children at each examination interval without intervening practice. In the absence of such long-time data, one can say that it is possible to predict a child's I. Q. with a probable error of from 4 to 7 points. Larger amounts of error would of course occur at the extremes of distribution. That such extreme variations do occur is shown by numerous cases in Table XII; for example in the

52 IOWA STUDIES IN CHILD WELFARE

case of number 10, a difference of 23.2 exists between the pre- dicted and obtained third I. Q.

The concept of a stable I. Q. involves a supplementary concept of a sort of initial acceleration or impetus of mental growth which predetermines the rate and level at which mental progress takes place and results in an approximately constant I. Q. The intelligence quotient could not, however, remain constant if serious fluctuations in the individual's rate of mental growth occurred.

If it should be proven that at certain ages children normally grow at an increased rate, the usefulness of the I. Q. would be considerably limited. It would always be of value still in de- termining the relative mental status of children of the same age but it would lose much of its prestige as a convenient diagnostic instrument for predicting the status of a child at later stages of its mental growth. In a previous chapter we have shown that considerable fluctuation in the rate of mental growth occurs, notably a sharp rise in the mental age curve at the approach of adolescence. This general intellectual renaissance is apparently a function of physiological age, occurring earlier in girls than in boys and earlier in children of superior intellectual endowment than in those of merely average ability. The inevitable result of this phenomenon is an increased I. Q. which in many cases could not have been predicted from the child's intellectual status at an earlier age and which would be a very unsafe basis in certain instances for inferring at the age of puberty what his earlier I. Q. had been. Prediction would still be possible, however, if one had a complete knowledge of the normal irregularities in mental growth at different ages.

SUMMARY AND CONCLUSIONS

1. The tabulated results of individual cases show that the I. Q. is only approximately constant during successive examinations.

2. Considering each child's deviation from his mean I. Q. ex- pressed as a per cent of his mean I. Q. there is a tendency for the girls to be more variable than the boys, for the superior chil- dren to be more variable than the average children, and for the older children to be more variable than the younger.

3. Considering the difference between the first and second ex- amination the larger number of cases show a difference of less than five points ( — or -}-) in I. Q-; between the first and other

MENTAL GROWTH CURVE 53

later examinations with intervening practice, many more cases show greater amounts of difference, the positive differences be- coming more and more marked.

4. With the change expressed as a per cent of the previous I. Q. there is a slightly greater change in the positive direction for superior children, due probably to the fact that these profit more readily by practice.

5. No final determination can be made of the effect of chrono- logical age or of the interval between examinations on the change in I. Q.'s.

6. The coefficients of correlation between all examinations within the four groups are high and reliable, ranging from -{-.12, ±.05 to -f .93 ±.02, showing that they may be used as a basis for prediction. The correlations are probably only slightly modified by the personal equation of the examiners.

7. The value of the probable error of prediction lies in utiliz- ing the knowledge in regard to the correlation between earlier and later examinations for predicting the later I. Q. of other chil- dren who have received only the earlier examinations. The P. E.'s of estimate range between 4.2 and 7.0 for the prediction of the second, third, fourth and fifth examination from the first. (

III. THE RELATION BETWEEN PHYSICAL AND MENTAL

GROWTH

1. Data. During the time that the psychological examinations were being made, physical measurements and x-ray photographs were taken with a view to analyzing the physical status and de- velopment of the children. A description has been given in an earlier study of the technique of taking the height and weight measurements and determining the area of the exposed surface of the carpal bones which serves as an index of anatomical de- velopment and is closely related to the physiological changes with their accompanying physical and mental phenomena. Mental measurements were also available for the children, some made on the same day as the physical examinations and others at vary- ing intervals with a few separated by as long a time as six months.

2. Resemblances in the Mental and Physical Development of Brothers and Sisters. Among the children measured in the school in which our data were collected there happened to be a number

54

IOWA STUDIES IN CHILD WELFARE CHART XI

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who were related to each other. Chart1 XI shows the individual mental growth curves of two families in each of which three members had been given repeated measurements. Family A in- cludes a boy No.2 3, and two girls, Nos. 2 and 20, two of whom are superior to the mean for the superior children of this study. Family B includes two boys, Nos. 10 and 40, and one girl, No. 39. These children are closer to the mean, and the girl is below it for a considerable part of its course. The members of Family A show a certain resemblance in the smooth and even rise of their growth curves, whereas the curves for Family B are more irregu- lar and L. B. even shows periods of no measureable mental growth. There will be noted a similarity in the general trend

"The norms on this chart are the mean for the superior and average children in this study.

2These numbers correspond to those assigned to individuals in the tables of original data.

MENTAL GROWTH CURVE

55

of the mental growth curves of the brothers in Family B, and also of the sisters in Family A.

3. Mean Mental Age of Physiologically Accelerated and Re- tarded Children. The children included in this study were di- vided into 4 groups on the basis of general physical development. Group 1 consisted of the boys whose height and weight were above the norms for their age, and Group 2 of the boys whose height and weight were below the norms, or very close to the norms in one or the other of these two measurements. Group 1 consisted then of physiologically accelerated boys and Group 2 of physiologically retarded boys, since it has been shown by Bald- win (1) and (3), that height and weight are closely correlated with physiological maturation. This division was made on the basis of the physical measurements without knowledge of the mental age of the child. A similar division into two groups was made for the girls.

The corrected mental ages of the children in each of the four groups were then averaged for each chronological age as shown in Table XIV. The mean mental age of physiologically acceler-

TABLE XIV
MEAN MENTAL AGE IN MONTHS OF PHYSIOLOGICALLY ACCELERATED AND
RETARDED BOYS AND GIRLS
Chronological	Boys	Girls
Age	Accelerated	Retarded	Accelerated	Retarded
5	72.0	62.8	74.4	57.6
6	89.4	83.2	81.3	79.0
7	101.3	97.1	99.9	95.0
8	118.2	110.8	114.6	107.0
9	131.1	120.3	128.6	119.1
10	142.4	131.0	141.1	131.0
11	155.3	137.6	151.2	144.3
12	171.1	150.1	176.7	168.2
13	179.0	158.4	(182.5)	189.2
14	194.2	166.2	194.9	183.7

ated boys is uniformly higher than the mean mental age of re- tarded boys. For the girls the same holds true with the exception of age 13, where the mean (printed in parenthesis) is too low because of the inclusion of the measurements of some girls who were of superior intellectual ability but of the very tall, thin type. This table confirms the findings of other investigators summar- ized in (2), who in general agree that superior mental develop- ment accompanies superior physical development as a rule. The first investigation to trace the correspondence between pedagog-

56 IOWA STUDIES IN CHILD WELFARE

ical acceleration and physical development by means of consecu- tive school marks and physical measurements was made by Bald- win (1) in 1914. The present study is the first to determine for the same individuals the relation between general physical status and mental growth as indicated by consecutive intelligence examinations.

4. The Relation between Physical Traits and Mental Age. A correlation between height and mental age previously reported by Baldwin (2) was +.71±.04 for boys and +.62±.05 for girls. In the present study the particular mental age selected for each child was the one which had been determined nearest to the time of physical measurement. In no case was there more than a few months interval between the physical and mental measurement. The correlations obtained between height and mental age are for 72 boys +.84 ±02, and for 61 girls +.89 ±.02. The correlation between weight and mental age by Baldwin (2) was for boys +.68 ±.04 and for girls +.56 ±.06. In the present study the cor- relations for weight and mental age are higher, that is, for boys +.86±.02 and for girls +.77±.04.

The significance of the growth of the carpal bones in rela- tion to general physical development was first emphasized by Kotch in 1910 and is summarized by Baldwin (3). In order to determine the relationship between anatomical age as indicated by the comparative development of the carpal bones and mental development as shown by the mental age rating, Pearson coef- ficients of correlation have been worked out by us. These coef- ficients give the first determination of the interdependence of these physical and mental traits. The coefficient of correlation between mental age and an index of anatomical age, (exposed area of the carpal bones of the right wrist) was for 54 boys +.873 ±.021 ; for 50 girls +.869 ±.023.

Earlier correlations between height and weight and the exposed area of carpal bones for a group of children were reported by Bald- win (3). The correlations between height and total exposed area of carpal bones of the right wrist were for boys +.88 ±.03 and for girls +.73 ±.05. The correlation between weight and area of carpal bones was for boys +.76 ±.05 and for girls +.77 ±.05. For this study the correlations between height and weight for boys was +.92 ±.01, and for girls +.89 ±.02.

As has previously been pointed out by Baldwin (2) the size of these coefficients is increased by the wide range of ages. It is

MENTAL GROWTH CURVE

57

possible to gain some knowledge of the influence of the age factor by the method of partial correlation. The results for 49 girls selected because of the completeness of the data, show the follow- ing intercorrelations of height, weight, X-Rays, mental and chrono- logical age. / /

TABLE XV INTEBCORRELATIONS BETWEEN PHYSICAL TRAITS, CHRONOLOGICAL AND MENTAL AGE
	Chr. Age	Weight	Height	Mental Age
Age Weight Height Mental Age X-Ray	.84 .88 .88 .92	.86 .71 .88	.89 .92	.83

The partial correlations with one factor constant for these same girls are given in Table XVI.

TABLE XVI PARTIAL CORRELATIONS BETWEEN PHYSICAL TRAITS, CHRONOLOGICAL AND MENTAL AGE
Traits	Constants
Chron. Age	Mental Age	Height	Weight	X-Ray
Height-Weight Height-Car. Age Height-Ment. Age Height-X-Ray Weight-Chr. Age Weight-Ment. Age Weight-X-Ray X-Ray-Chr. Age X-Ray-Ment. Age Chr.-Ment. Age	.57 .53 .62 —.15 .52 .09	.80 .41 .73 .66 .76 .72	.30 —.40 .37 .62 .04 .47	.52 .81 .65 .71 .63 .76	.38 .16 .59 .14 —.11 .54

The influence of chronological age is more important with some traits than others. For example the correlations between physical traits are very little influenced by keeping chronological age con- stant (+.89 to -f.53). Although there is no correlation between weight or X-Rays and mental age for this group when chronolog- ical age is kept constant, there is a positive correlation between height and mental age.

58 IOWA STUDIES IN CHILD WELFARE

SUMMARY AND CONCLUSIONS

1. There is a similarity in the mental growth curves of broth- ers and sisters. The resemblance between brothers and sisters is further shown in physical traits by the correlation of the height X-Eay and weight quotients and in mental traits by the corre- lation between the I. Q.'s. The correlations are higher for the physical traits than for the mental.

2. The mean mental age of physiologically accelerated is higher than the mean mental age of physiologically retarded chil- dren. This study is the first to determine for the same individuals the relation between general physical status and mental growth as determined by consecutive intelligence examinations.

3. The coefficients of correlation between height and mental age are high even when the influence of chronological age is elim- inated.

IV. GENERAL CONCLUSIONS

For years the literature has been full of statements in regard to the desirability of obtaining repeated measurements on the same children in order to study the process of mental develop- ment. The use of the Stanford Revision of the Binet scale even for the relatively short period of four years shows the unsuita- bility of this scale in its present form as a means for measuring mental growth. The limited number of alternative tests results in a certain practice effect on repeated examinations. Another defect of the present system of tests is the lack of a sufficient number of tests at the higher levels to measure the mental growth that apparently goes on in a bright young child even after the exhaustion of the 16 or 18 year old tests. It is commonplace in clinical psychology that a gifted child has more opportunity to gain a high I. Q. if measured early in his life where he has a greater range of tests in which to succeed. Theoretically it would seem to be a better measure of mental growth to use a combina- tion of point scales for specific mental traits, each scale to be suf- ficiently extended to measure whatever ability exists and the whole system to include a sufficient variety of traits to afford a general measure of the development of the individual.

The findings of this study have been summarized in detail at the end of each section. A survey of these results show the im- portance of many factors influencing mental growth processes,

MENTAL GROWTH CURVE 59

and producing differences in the mental growth curves of boys and girls, and of children of superior and average ability.

An analysis of the individual growth curves shows that the I. Q. is only approximately constant during successive examinations. The amount of difference between I. Q.'s obtained at various ex- aminations is sufficiently small, and the correlations between the examinations are sufficiently high with small probable errors of estimate, to permit of predicting from an earlier examination what the individual's later development will be.

The most significant outcome of this study is the empirical de- termination of the mental growth curve and the establishment of the close interrelation between mental and physical development as shown by the general similarity between growth in height and in mental age, the rise in the mental age curve at the adolescent years, the superior mental development of physiologically accel- erated children, and the high correlation between mental age and height.

It is evident that mental age ratings by the present scale are the result not only of native intelligence but also of the degree of physiological acceleration over that which is normal for the age. This latter factor is of extreme importance in any educational or social treatment of the individual. A high I. Q. reflects this fac- tor as well as the general intelligence that it is designed to measure.

REFERENCES

1. BALDWIN, B. T., Physical Growth and School Progress. U. S. Bureau

of Educ., Bulletin No. 10, 1914, Whole No. 581. Pp. 215.

2. BALDWIN, B. T., Studies in Experimental Education. Johns Hopkins

Studies in Education, No. 3, 1920. Pp. 75.

3. BALDWIN, B. T., Physical Growth of Children from Birth to Maturity.

Univ. of la. Studies in Child Welfare, No. 1, 1921. Pp. 412.

4. BERRY, C. S., Eighty-two Children Retested by the Binet Tests of

Intelligence. Psychol. Bull., 1913, (10), 77-78.

5. BLOCH, E., tfber Wiederholung der Binet-Simonschen Intelligenz-prii-

fung an denselben schwachsinnigen Kindern nach Ablauf eines Jahres. Zsch. f. d. ges. Neur. u. Psychiat., 1915, (28), 445-455. Also Bloch, E. and Lippa, H. Zsch. f. angew. Psychol., 1915, (9), 512-515.

6. BOBERTAG, O., tJber Intelligenzprtifungen. Zschr. f. angew. Psychol.,

1912, (6), 495-538.

7. CHOTZEN, F. AND NICOLATTER, M., Die Intelligenzpriifungsmethode von

Binet-Simon bei schwachsinnigen Kindern. Zsch. f. angew. Psychol.,

1912, (6), 411-494.

8. CUNEO, I. AND TERMAN, L. M., Stanford-Binet Tests of 112 Kinder-

garten Children and 77 Repeated Tests. Pea. Sem., 1918, (25), 414- 428.

9. DESCOEUDRES, A., Les tests de Binet-Simon comme mesure de d6velopp-

ment des enfants anormaux. Arch, de psychol., 1915, (15), 59.

10. DOLL, E. A., The Growth of Intelligence. Psychol. Monog, 1921, (29),

Pp. 130.

11. FERMON, M. L., Validity of I. Q. as Established "by Retests. M. A.

Thesis, Columbia University, May, 1921.

12. FREEMAN, F. N., The Interpretation and Application of the Intelligence

Quotient. J. of Educ. Psychol., 1921, (12), 3-13.

13. GARRISON, S. C., Fluctuation of Intelligence Quotient. School and

Society, June, 1921, 647-649.

14. GODDARD, H. H., Three Annual Testings of 400 Feeble-Minded Chil-

dren and 500 Normal Children. Psychol. Bull., 1913, (10), 75-77.

15. HOLLINGWOHTH, L. S., The Psychology of Subnormal Children. New

York: Macmillan, 1920. Pp. 285.

16. KRAMER, Die Intelligenzpriifung bei kriminellen und psychopathischen

Kindern. Bericht iiber den 1. Kongress fur Jugendbildung zu Dresden, (11), 1911.

17. KTTHLMANN, F., The Degree of Mental Deficiency in Children as Ex-

pressed by the Relation of Age to Mental Age. J. of Psycho-Asthen.,

1913, (17), 132-143.

18. KTTHLMANN, F., What Constitutes Feeble-Mindedness? J. of Psycho-

Asthen., 1915, (19), 214-236.

60

MENTAL GROWTH CURVE 61

19. POTJLL, L. E., Constancy of I. Q. in Mental Defectives According to

the Stanford Revision of Binet Tests. J. of Educ. Psychol., 1921, (12), 323-324.

20. ROSENOW, C., The Stability of the Intelligence Quotient. J. of Delinq.,

1920, (5), 160-173.

21. RTJGG, H. ATJB COLLOTON, C., Constancy of the Stanford-Binet I. Q. as

Shown by Retests. J. of Educ. Psychol., 1921, (12), 315-322.

22. STENQUIST, J. L., Unreliability of Individual and Group Intelligence

Tests in Grades 1, 2, 3. Unpublished.

23. STEBN, W., The Psychological Methods of Testing Intelligence. Trans.

by G. M. Whipple. Baltimore: Warick and York, 1914. Pp. 158.

24. STEBN, W., Der Intelligenzquotient als Mass der kindlichen Intel-

ligenz, insbesondere der unternormalen. Zsch. f. angew. Psychol., 1916, (11), 1-18.

25. TERMAN, L. M., The Stanford Revision and Extension of the Binet-

Simon Scale for Measuring Intelligence. Baltimore: Warwick and York, 1917, Chapter 3, 51-61.

26. TEBMAN, L. M., The Intelligence of School Children. New York:

Houghton Mifflin Co., 1919, Chapter 9, 134-164.

27. TEBMAN, L. M., Mental Growth and the I. Q. J. of Educ. Psychol.,

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