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
tao
709
tro
669
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472.
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433
•
GROW T
// CURVES
HEIGHT
(Baldwin)
2 -Short
vidual Curves,
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IN
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S 6 7 S 9 10 li 12 13 A* IS '6 ir It
Aye >n Y€or*
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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Examina
tion
d o
_" f ,
so
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W o
c?o«3«3«5
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
90
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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MENTAL GROWTH CURVE
CHART IX
41
PERCfNTAse DISTRIBUTION
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DIFFERENCES IN I Q
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42
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
Mlsc
E. V
L. 8
L. W.
L. I. 8
Misc
E. V
L. 8.
L. W. . .
L. I. 8
Misc
E. V...
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
<
»-O» »e 1
§
i-i ic 0
oo « N w oo •
•» H us «o •<<• •<* ^ us
*
.Q t-H
O
I
a/-i
o
•« IH ic 00 M •«<• «
c- 06 ^« eo o r-c ee •* t~<« us
Ti
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
#99
22*
S06
I9Z
ITS
w
"c 160
I
^ 144
§>
^ '26
^
|//2
96
80
64
j
INDIVIDUAL HENTAL d
or
BROTHERS AND
Mental Growth Curve
for Superior Boyi
for Superior Girlt
family A Family £
towTH CURVES /
SISTERS /
/
J*VI
r*
A.
.&
£
r
\-c* «•-
\
— — i
p
C/LJi
*'~ >
/
^
r-— ^
\
Git /» * * 6irfo— - ^—
^
/
IB
A
i/j
M
57
^
x/
/£
*f&A./
/
t
/
^
^
^ A
ao
/
/
x?
4'^
^/
r
/
//
ffl</'
2
?
)
£4
2
^Xj
g
«
tf
n
16
\
9 10 II
i in Years,
15 16
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
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of Educ., Bulletin No. 10, 1914, Whole No. 581. Pp. 215.
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Studies in Education, No. 3, 1920. Pp. 75.
3. BALDWIN, B. T., Physical Growth of Children from Birth to Maturity.
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4. BERRY, C. S., Eighty-two Children Retested by the Binet Tests of
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5. BLOCH, E., tfber Wiederholung der Binet-Simonschen Intelligenz-prii-
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9. DESCOEUDRES, A., Les tests de Binet-Simon comme mesure de d6velopp-
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11. FERMON, M. L., Validity of I. Q. as Established "by Retests. M. A.
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12. FREEMAN, F. N., The Interpretation and Application of the Intelligence
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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
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60
MENTAL GROWTH CURVE 61
19. POTJLL, L. E., Constancy of I. Q. in Mental Defectives According to
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21. RTJGG, H. ATJB COLLOTON, C., Constancy of the Stanford-Binet I. Q. as
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22. STENQUIST, J. L., Unreliability of Individual and Group Intelligence
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23. STEBN, W., The Psychological Methods of Testing Intelligence. Trans.
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25. TERMAN, L. M., The Stanford Revision and Extension of the Binet-
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