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THE RELATIONSHIP BETWEEN CONSISTENT I. Q. SCORES,
DECREASING I. Q. SCORES, AND READING SCORES
COMPARED ON A DEVELOPMENTAL BASIS

BY

Charles Martin greenshields

AN ABSTRACT

Submitted to the College of Education of Michigan State
University of Agriculture and Applied Science in
partial fulfillment of the requirements
for the degree of

MASTER OF ARTS
Department of Teacher Education

Year 1955

Q {6 49} the
f

lll'l.|‘ltlllllll.lllll.llllIll-llIIIIIII'

ABSTRACT

The purpose of this investigation was to determine if
the difference between consistent and decreasing I. Q. scores
could be accounted for by growth in reading. Although other
studies have been done in this area, no attempt has been made
to relate growth in intelligence with growth in reading on an
individual basis.

The longitudinal data needed for this investigation are
part of the Holt Study and can be found in the Child Develop-
ment Laboratory, Michigan State University, East Lansing, Mich-
igan.

A total of thirty-three cases were available which met
the criteria set up for this investigation. Seventeen cases
met the criteria for a consistent I. Q. and were designated as
Group I. Sixteen cases met the criteria for a decreasing I.Q.
and were designated as Group II.

A test of the significance of the difference of the
mean I. Q.'s was made in each of the five grades. No signif-
icant difference between Groups I and II were found in the first
or second grades. A significant difference favoring Group I
was found at the third. fourth, and fifth grade levels. The
subtests of the Kuhlmann-Anderson were then categorized in
terms of verbal and non—verbal content. A verbal and non—verbal

quotient was found for each individual by dividing his average

mental age score in each category by his chronological age. In
the first and second grade none of the subtests contained what
was considered to be verbal material. In the third, fourth,
and fifth grades, Group I was found to have significantly
higher verbal quotients than did Group II. There was no dif-
ference between the groups intflmathird and fifth grade in

terms of non-verbal performance. However, at the fourth grade
level, Group II scored significantly lower than did Group I.
The factors which underlie this are not known and future
research is needed to try to identify them.

Equations for each individuals' growth in reading and
in mental age were written, independently of each other, using
the Courtis modification of the Gompertz Function. It was
found that Group I was growing to a significantly higher maxima
in both reading and mental age than was Group II. There was
no significant difference between the mean rates or between
the mean incipiencies of the two groups.

It cannot be concluded that reading ability was the
primary cause for decreasing I. Q. scores in all cases. However,
in eight of the sixteen cases in Group II, the individuals'
inability to score on the verbal subtests at the same level
at which they scored on the non-verbal subtests did result
in a drop in their I. Q. scores.

Reading ability was bound to be either a primary or

secondary factor in all cases.

THE RELATIONSHIP BETWEEN CONSISTENT I. Q. SCORES,
DECREASING I. Q. SCORES, AND READING SCORES
COMPARED ON A DEVELOPMENTAL BASIS

By

Charles Martin Greenshields

A THESIS

Submitted to the College of Education of Michigan State
University of Agriculture and Applied Science in
partial fulfillment of the requirements
for the degree of

MASTER OF ARTS

Department of Teacher Education

Year 1955

ill-isms

ACKNOWLEDGMENT

The writer wishes to eXpress his appreciation and
thanks to all those who assisted in making this study
possible; particularly to Dr. A. R. DeLong for his interest

and suggestive criticism.

ii

TABLE OF CONTENTS
Page
LIST OF TABLES . . . . . . . . . . . . . . iv
LIST OF ILLUSTRATIONS . . . . .‘ . . . . . . . V

CHAPTER
I. INTRODUCTION . . . . . . . . . . . . 1
Statement of the Problem. . . . . . . . 4
Importance of the Study . . . . . . . . 5
Definition of Terms . . . . . . . . . 7
II. REVIEW OF THE LITERATURE . . . . . . . . 10

III. PROCEDURE . . . . . . ,. . . . . . . 16

Data 0 o o o o o o o o o o o o o 16
MethOd. c o o o o o o o o o o o o 17

IV. ANALYSIS OF THE DATA. . . . . . . . . . 20
V. SUMMARY, CONCLUSIONS AND IMPLICATIONS . . . . 28

Conclusions . . . . . . . . . . . . 29
Implications. . . . . . . . . . . . 30

APPENDICES O O O o O O O O O O O O I O O O 31
BIBLIOGRAPHY . . . . . . . . . . . . . . . 39

iii

LIST OF TABLES
Table Page

I. Tests of Significance of the Difference of the
Mean I. Q. Scores for Groups I and II . . . 24

II. Test of Significance of the Difference of the
Mean Verbal Subtests Quotients Between Group
I and II C 0 O O O I 0 O O O O O O 26

III. Test of Significance of the Difference of the

Mean Non—Verbal Subtests Quotients Between
Group I and II . . . . . . . . . . . 26

iv

LIST OF ILLUSTRATIONS

Figure Page

1. Curve of Constants . . ,, . . . . . . . . 22

CHAPTER I
INTRODUCTION

Since ancient times, man has observed a difference in
man's mental abilities. Quintilian, born in the year 35 A.D.,
made the observation that there are as many forms of mind as
there are individuals.1 But it wasn't until the days of
Galton that any significant headway was made in the selecting-
out of man's differences in mental ability. The next major
advancement in mental measurement was contributed by Binet.
At the turn of the century Binet constructed the first
successful test designed to discriminate between the mentally
deficient and the individual with enough intelligence to be
self-sufficient. Since Binet's original work, theairea of
mental testing has grown rapidly. There has been constant
work to improve and devise better instruments for the
measurement of individuals. Mental tests have now reached
the point where they are considered to be useful tools for

2,3.

research.

 

1George D. Stoddard, The Meaning_of Intelligence, New
York: The MacMillan Co., 1943, p. 79.

2H. A. Greene and A. N. Jorgensen, The Use and Inter-
pretation of Elementary School Tests, New York: Longmans,
Green and Co., 1938, p. “.

3Rudolf Pintner, et.al., Educational Psychology, New
York: Barnes and Noble, Inc., 1951, p. 118.

1

Assuming that growth is continuous and individual by
nature, the method of research to be followed must reflect
both its continuity and individuality. In comparatively
recent times there has been a shift of emphasis to the longi-
tudinal approach to show the continuity and individuality of

‘ 4

growth. Scammon is frequently given credit as being one of
the first to recognize some of the advantages of the longi-
tudinal approach. He was one of the first to conclude that
the pattern of grOWth, as shown by mass data, had little
relationship to the pattern of individual growth. To quote
Freeman and Flory:

. . . . since different children are tested at suc-

cessive ages, it is impossible to be sure that the

selection of cases at each successive age is a

similar sample of the population as that at the

other ages. In fact, we may go farther and say that

the successive gge groups are not similar samples of

the population.
It seems logical and scientifically sound then that it is
necessary to study the individual in order to learn the
patterns of growth.

The determination of the approach provides only the

frame of reference. An accurate descrfption of the data is

necessary to assure the validity of the conclusions. The

 

”R. E. Scammon,"Developmental Anatomy," Morris'
Anatom , 10th, ed. by J. P. Schaeffer, Philadelphia: Blakiston,
1952. _

5Frank N. Freeman and Charles D. Flory, "Growth In
Intellectual Ability as Measured by Repeated Tests," Monographs
of the Society for Research in Child Deve10pment, Vol. II,
No. 2, Washington, D.C., 1937. PP. 2-3.

Courtis6 modification of the Gompertz Function is a method

which should accurately describe the process of growth in all
its phases. The Courtis technique has been shown to be useful
in describing the patterns of growth as well as the relation-

ships between various aSpects of grOWth by a number of

7.8.9.10.11
researchers.

6S. A. Courtis, Maturation Units_gnd How to Use Them,
Ann Arbor, Michigan: (Litho-printed) Edwards Brothers, 1950.

7Thomas P. F. Nally, "The Relationship Between Achieved
Growth in Height and the Beginning of Growth in Reading."
Unpublished Ph.D. thesis, Department of Education, Michigan
State College, 1953.

8Gerald T. Kowitz, ”An EXploration Into the Relation-
ship of Physical Growth Pattern and Classroom Behavior in
Elementary School Children.I Unpublished Ph. D. thesis,
Department of Education, Michigan State College, l95h.

9Reuben R. Rusch, "The Relationship Between Growth
in Height and Growth in Weight," Unpublished Master's
thesis, Michigan State College, 1954.

10
Ekanen (Benson) Udoh, “Relationship of Menarche to
Achieved Growth in Height." Unpublished Ph. D. thesis,
Department of Education, Michigan State University, 1955.

11
Lillian Larner, "A Comparison of Growth in Height
with Growth in Achievement.” Unpublished manuscript; Child
GrOWtheInd Development Laboratory, Michigan State University,

1955.

Statement of the Problem
There are many theories on the nature and deveIOpment
of intelligence. There is for every theory, either stated
or assumed, a definition of What ”intelligence” tests measure.
There has been a lot of controversy over the terms in which
the results of the tests have been stated, namely, mental age
or the intelligence quotient, etc. Most of the controversy

12

has been over the intelligence quotient. There are those

who claim the I. Q. to be ”constant",13 those who claim that
it "increases“lu and others who claim that the I. Q. "de-

«15:16 with age. These opinions have been based

creases
primarily on results from their own tests.
Kuhlmann and Anderson, in their manual for the

Kuhlmann-Anderson Intelligence tests17 predict the decreasing

 

2
1 Henry E. Garrett, "A Developmental Theory of Intelli-
gence,” American Psychologist, I, 19H6, pp. 372- 377.

13L. M. Terman, The Measurement of Intelligence,
Cambridge: Houghton Mifflin Company, The Riverside Press, 1916.

luH. E. Garrett, loc cit.

1
5F. Kuhlmann, Tests of Mental Development, Minneapolis:
Educational Publishers, Inc., May, 1957.

16H. Heines, "A Personal Constant," Journal of Education
Psychology, Vol. XVII, March, 1926, pp. 163—18.

17F. Kuhlmann and R. Anderson, Kuhlmann-Anderson Intelli-
ggnce Test - Instructions Manual, (5th ed.) Educational Test
Bureau, 19Ll'2’ p. 170

I. Q. pattern. They have said that this is due to the
fallacy of the I. Q. The writer, in analyzing some of the
data being collected by the Child Growth and DeveIOpment
Laboratory at Michigan State University, found that there
were some individuals who seemed to have a “decreasing“I. Q.
and some who seemed to have a "consistent" I. Q. There were
none with an "increasing" I.Q. when the results of the
Kuhlmann-Anderson tests were analyzed. This writer hypothe-
sized that, among the many possibilities which might cause
the I. Q. to decrease or to be rather consistent, reading
might be an important factor. The purpose of this investi-
gation then is to determine if the difference between con-
sistent and decreasing I. Q.'s can be accounted for by

growth in reading.

Importance of the Study
In order to avoid confounding of an experiment, it
is necessary to test one particular variable with one "yard-
stick". Introduction of other tools designed to measure the
same variable may yield results that are not comparable to
those obtained by the initially used instrument.18 It was
assumed at the start of the current Holt Study19 that the

Kuhlmann-Anderson Intelligence Tests were sufficiently

 

18
W. F. Dearborn and J. W. M. Rothney, Predicting
Ehe Child's Development, Cambridge, Mass.: Science-Art
Publishers, l9hl, p. 59.

1
9A. R. DeLong, "A Longitudinal Study of Individual
Children,“ Michigan Education Journal, November, 1951.

validated and reliablezo

for the purpose of measuring mental
growth.21 When results from the tests failed to follow pre-
dicted patterns, the question of the validity of the results
again arose. An attempt is being made. therefore, to account
for them.

The problem was one in which it was necessary to
examine each individual's pattern of mental growth. Probably
the most accurate method for doing this was the technique

22,23 2” 25 26.27.28

developed by Courtis. Rusch, Kowitz and others,

 

20O. K. Euros, The Fourth Mental Measurement Yearbook,
Highland Park, N. J.: Gryphon Press, 1953, p. 302.

21
L. W. Webb and A. M. Shotwell, Testing in the
Elementary School, New York: Fanner and Rhinehard, Inc., 1939.

 

22
op, cit.

2
3T. J. Nally and A. R. DeLong, ”An Appraisal of a
Method of Predicting Growth,“ Child Development Laboratory
Publication,Series I, No. 1, East Lansing, 1952.

S. A. Courtis, Maturation Units and How to Use Them,

2“Reuben R. Rusch, op. cit.

25
T. P. F. Nally, op. cit.

26Lillian Larner, op. cit.

27E. Kanen (Benson) Udoh, op. cit.

28G. T. Kowitz, op. cit.

» ——-“ 4.-‘—‘1'

using this technique, have shown scientifically the relation-

ships between various aspects of growth. Their work is added

support for the theory of organismic growth,29'30 which holds

that all aspects of development are-related.31 The relation-
ship between reading and intelligence, however, has not yet

been investigated in this manner.

Definition of Terms

1. Consistent I.QL Scores: Those scores, that at
individual has achieved over a period of five years on the
Kuhlmann-Anderson Intelligence Tests, which have a difference
of ten I. Q. points or less between the highest and lowest
I. Q. score.

2. Decreasing IL.Q. Scores: Those scores,that an
individual has achieved on the Kuhlmann-Anderson Intelligence
Tests which have lessened over a period of.four years, each
I. Q. score being less than the I. Q. score of the previous
year.

3. Rgading Scores: Those scores,that an individual
has achieved on the Stanford Achievement Tests beginning with
the second grade. The Reading Score is found by averaging
the paragraph meaning scores and word meaning scores and con-

verting this score to age units.

 

29
D. C. Heath and Co., 1951, p. 3.

30Willard C. Olson, Child Developmepp, Boston: D. C.
Heath and Co., 1949. p. 8.

31Millard, loc. cit.

C. V. Millard, Child Growth and Development, Boston:

 

A. Development: "The progress toward maturity
brought about in an immature organism by the action of appro-
priate environmental forces under constant conditions."32
"In actual practises, growth, development, and maturation are
used interchangeably, depending upon the emphasis desired."33

5. Growth Cycle: "A period of specific maturation
during which all the elements and forces acting are constant

within allowable errors of control and measurement."3)4

 

 

at t .36
6. ‘gpe Gompertz Fppction:35 y=Kece or y=Kir ‘Where°
y = achieved develOpment at the time "t“
k 2 maximum towards which development is progressing.

6°: incipiency (i) or the degree of development
at the beginning of the period of growth.

ea: rate (r) of growth eXpressed in isochrons.

 

 

, 323. A. Courtis, Towards a Science of Education, Ann
Arbor: Edwards Brothers, 1951, p. 9.

333. A. Courtis, Maturation Units and How to Uge Them,
0p3 cit., p. 22.

3“S. A. Courtis, "What is a Growth Cycle?" Growth,
V01. I, NC. 39 May, 1937, p. 1714'.

35Benjamin Compertz, Philosophical Transactions of
phe Royal Society of Lungpn for the Year MDCCCXVL Part I.
Printed by N. Nicol, St. James, Pall Mall, Printers to the
Royal Society, MDCCCXXV.

36S. A. Courtis, Maturation Units and How to Use
Them, pp. cit., pp. 23-2b.

 

7. Growth Constants: Maximum, rate, and incipiency.

8. Maximum: The ultimate state or condition within
a Specific cycle.

9. Rppg: Magnitude of change per unit of time.

10. lpochrons: One per cent of the total time required

 

for a growth curve to change from a deveIOpment of 0.000000189
per cent to a deveIOpment of 99.90917 per cent.

11. Verbal Tests: In the Kuhlmann-Anderson Intelli-
gence Tests subtests 18, 21, 22, 23, 25, 26, 27, and 28 are
considered to be verbal tests in this study.

12. Non-Ve§p§1_Subtests: Kuhlmann~Anderson Tests

1 through 17, 19, 20 and 2h.

CHAPTER II
REVIEW OF THE LITERATURE

The literature available on intelligence is so
voluminous that only a brief selected review will be pre-
sented here. Goodenough37 states that a listing of titles
would require a book. She cites Hildreth's (1939) bibli-

ography which covers 251 pages and lists over h,000 titles.

In describing growth it is necessary to do so in

terms of the individual. The only way to study the individ~
38
ual is by using a longitudinal approach. In using a cross-
sectional approach conventional measures and mass statistics
have to be applied. These methods not only do not permit
the analysis of the individual's growth pattern, they make
#0

it impossible.39' The longitudinal approach is not some-

thing new. Dearborn.and.Rothney cite the work of H. P.

 

37

F. L. Goodenough, “The Measurement of Mental Growth
in Childhood,” Mgpual of Child Psychology, Leonard Carmichael,
ed., New York: John Wiley and Sons, Inc., 1946, p. h5h.

388. A. Courtis, "The Element Concept in Psychology,"
from paper delivered at the Michigan Academy of Sciences, Art
and Letters, March, 1955.

39S. A. Courtis, "Validation of Statistical Procedures,"
Journal of Educational Research, Vol. XII, June, 1925, pp.31-40.

”0L. K. Frank, ”Research In Child Psychology: History
and PrOSpect,' Child Behavior and Development, New York: Mc-
Grew-Hill, 1943. p. 3.

10

ll

Bowditch done at Harvard in 1872.“1 While the approach is

not new, there are few studies which utilize longitudinal

data.u2,u3.uu.45.46
Had the instruments of achievement been used more

rigorously, the controversy of the constant I. Q. might not

exist.“7 The constant I. Q. implies a linear relationship

between mental age and chronological age.“8

 

ulDearborn and Rothney, Predicting the Child's Develop-
ment, op. cit., p. 33.

”Z'Harvard Growth Study Data," Monographs of the
Society for Research in Child Developmepp, Vol. 3, Ser. No.
174', NO. 1' 19380

“BB. T. Baldwin, "Physical Growth of Children from
Birth to Maturity," University of Iowa Studies in Child
Welfare, Vols 1, No. 1, 1921.

44
H. E. Jones and N. Bayley, "Growth, Development,

and Decline," Anppal Review of Psychology, 1:1—8, 1950.

u5Jean W. McFarlane, "Studies of Child Guidance. 1.
Methodology of Data, Collection and Organization," Monographs
of the Society for Research in Child Development, Vol. III,
Ser. No. 19, No. 6, 1938.

46Katherine Simmons, "The Brush Foundation Study of
Child Growth and Development, II, Physical Growth and Develop-
ment,“ Monographs of Society for Research in Child Development,
Vol. IX, Ser. No. 37. No. 1, 19332 .

u70mar C. Held, "Constancy ~of—the—I.Q. Controversy,"
School and Society, July-December, 1939, 805—806.

Frank N. Freeman and Others, "The Influence of
Environment on the Intelligence, School Achievement,£nd
Conduct of Foster Childre," National Society for the Study
of Education, Yearbook XVII, Part I, 1928, pp. 103-217.

 

12

(According to Courtis?9

mental age is a maturation process and
it is cyclic in nature. This means that mental age is
curvilinear, as are other aspects of growth such as height
and weight.

There is an abundance of literature on the variations
of I. Q.'s.50’51'52’53’5u'55 Dearborn and Rothney,56 using

Harvard data, found wide variations in intelligence test per~

formance. This they said was either a function of the test

 

49$. A. Courtis, "The Element Concept in Psychology,"
op. cit.

50Nancy Bayley, "Consistency and Variability in the
Growth of Intelligence from Birth to Eighteen Years," Peda-
logicatheming§_and Journg; of Genetic Psychology. 75: 155-
19 D 19 9.

51Garrett, 0p. cit.

52Arnold H. Hilden, ”A Longitudinal Study of Intellec-
tual DeveIOpment," Journal of Psychology, 28:187-21u, July, 19h9.

53A. M. Leahy, "Nature-Nurture and Intelligence! Genetic
Psyghology Monographs, Vol. XVII, No.b, August, 1935, 235-308.

5“Louis P. Thorpe, Child Psychology and Development,

New York: The Ronald Press Company, 19h6.

55David Wechsler, “Intellectual Changes With Age,"
in thside Reading in Psychology, E. Hartley, H. Birch and
H. Hartley, Editors, New York: Thomas Y. Cromwell Company,

1950.

56Dearborn and Rothney, op, cit.

13

or the testing situation. Many have described the mental
grthh curve using mass statistics. But mass statistics do
not describe the pattern of growth for the individual.57’58
For example, if there is a Wide variation between individuals'
rate of growth or between their final.achieved height, they
are concealed by mass statistics. Bayley,59 Dearborn and

61 and Shuttleworth62 are some

Rothney,60 Freeman and Flory,
of the peOple who have studied the mental growth curve of
the individual. Their work has been based on the results of
several different tests. None or these peOple have used the
Courtis technique, although Dearborn and Rothney did employ
the Gompertz curve to describe mental growth.

There has not been a study done which shows the

relationships between mental growth and any other aspect of

growth using the Courtis technique. Millard has described

57George D. Stoddard, The Meaninggof Intelligence,
op. cit., p. 177.

8
5 5- A- Courtis, "Validation of Statistical Procedures,"
Journal of Educational Research, 0p. cit.

59Nancy Bayley, "Mental and Motor Deve10pment from
Two to Twelve Years," Review of Educational Research, 9:18—37,

11u—125, 1939.

6oDearbornand Rothney, op. cit.

61Freeman and Flory, op. cit., pp. 2—3.

62F. K. Shuttleworth, "The Physical and Mental Growth
of Girls and Boys Age Six to Nineteen in Relation to Age at
Maximum Growth," Monographs of the Society for Research in
Child Develonment, Vol. IV, No. 3, Ser. No. 22, 1939.

14

growth in reading using the I. Q.:for comparison.63 Using
over a hundred cases, Millard found that the more intelligent
children were growing toward higher maxima in reading achieve—
ment. Several studies have shown a fairly high correlation

6u,65,66,67,68 69

between reading and intelligence. Allen,

investigating the relationship between Kuhlmann-Anderson7o

 

630. V. Millard, "The Nature and Character of Pre-
Adolescent Growth in Reading Achievement," Child Development,
Vol. II. NO. 2’ pp. 71"114, 19140.

6“Edward C. Abbott, “Relationship Between Variations

in Silent Reading Ability and Mental Ability," Journal of
Educational Research, Vol. 39. pp. BID-316, December, 1935.
Abstract of Doctor's Dissertation.

65Donald D. Durrell, “The Influence of Reading
Ability in Group Intelligence Measures," Journal of Educational
Psychology. 2h: 412-“46, 1933.

66
Karl C. Garrison, Growth and Development, New York:

Longmans, Green and Company, 1952. 54“.

67Pintner, Rudolph and Others, Educational Psychology,
op cit., 178.

68Ruth Strang, "Variability in Reading Scores on a
Given Level of Intelligence Test Scores,” Journal of Educational
Research, 38:4ho-u46, 1945.

69Mildred M. Allen, "Relationship Between Kuhlmann—
Anderson Intelligence Tests and Academic Achievement in
Grade IV," Journal of Educational Research, Vol. 39. PD. 229-
239. 19“#.

7OKuhlmann-Anderson, op. cit.

15

Intelligence Tests and Stanford Achievement Tests found that
any one of the following three Kuhlmann-Anderson Verbal sub-
tests, 21, 22, 23, were Just as good an indicator of achieve-
ment as was the total battery. In the same study Allen also
found that the reading age obtained on the Stanford Achieve-
ment Test had a correlation of .71 with the Kuhlmann-
Anderson mental age. These results, along with the Kuhlmann-
Anderson's prediction of a decreasing I. Q. pattern, bring
up some interesting hypotheses, the most promising being that
the I. Q.£1nd reading ability are related and that even
though mental functioning were constant, a person with.a low
reading ability would show a decreasing I. Q.a1s the verbal

content of the test increased.

CHAPTER III
PROCEDURE

Data

The data used in this investigation were taken from
the Holt Study, which can be found in the Child DevelOpment
Laboratory, Michigan State University, East Lansing, Michigan.

The Holt Study was begun in 1950, and is currently
in progress. Some of the types of data being collected cover
five areas: [1] Physical Development, [2] Mental Development,
[3] Subject Matter Development, [4] General Development, and

[5] Social Status.71

This present investigation is concerned with the area
of Mental Development,<iata for Which was obtained from the
Kuhlmann-Anderson Intelligence Tests. These tests were
administered once each year, in the winter, by a trained
graduate student or staff member. Standard scoring proced—
ures were followed. All tests were scored at least twice by
different individuals. The results were stated in terms of
mental age, grade age, and I. Q.

The sampling for this study was extremely small due

to the criteria set up for case selections. The criteria were:

71A. R. DeLong, "A Longitudinal Study of Individual
Children," op. cit.

l6

17

[1] Each case was to have been tested serially
five times with the Kuhlmann-Anderson Intelli-
gence Test.

[2] Each case was to have been tested serially
four times with the Stanford Achievement
Test, beginning with the second grade.

[3] Those cases considered to have a consistent
I. Q., which had a variability of ten points
or less.

[a] Those cases considered to have a decreasing
I. Q., which had three successively decreasing
I. Q. '8.

Method
Since there is a method available which will describe,
mathematically, individual growth.according to the "Law of
Growth,"72'73 the method, known as the Courtis technique,

was selected for this investigation.

 

72$. A. Courtis, "Growth and Development in Children,"
Advance in Health Education, Proceedings of Seventh Health
Education Conference, Ann AnobrL Michigan, 1933. New York:
Herman Child Health Association, 1931», pp. 180-206.

738. A. Courtis, "Prediction of GrOWth," Journal of
Egycational Research, Vol. XXVI, pp. bSl-h92, March, 1933

18

The Courtis equation was solved by the following
procedure:

[1] Data was plotted on logarithmic paper.

[2] Those points obviously out of the pattern
were discarded for purposes of determining
the maximum. The points were included when
determining the error of the equation.

[3] Each measurement was divided by the estimated
maximum, and the percentage of development
was thus determined.

[u] The results were plotted on isochronic paper.
The correct maximum was assured when the
plotted per cent of development approached a
straight line. The equationuwaB written from
the trial maximum that produced the nearest
approximation to a straight line.

[5] Mental growth equations and reading growth
equations were written independently.

Most of these equations are in the pro—adolescent cycles.

In some cases, the individuals appear to have entered theaido-
1escent cycle. Theneitsinsufficient data to confirm or negate
this hypothesis.

The means of the three parameters (rate, incipiency,
and maxima) were determined for each group in mental growth
and growth reading. From these, a curve of constants was
drawn to demonstrate, graphically, the relationships between

growth and growth in reading. (See Figure l.)

19

The Student "t” test was used to determine the signi-

L;

ficance of the differences between the means7 of Groups I

and II on:

[1] The I. Q. from year to year for the five year

period.

[2] The scores on the verbal subtests of the

Kuhlmann-Anderson.
[3] The scores on the non-verbal subtests of the
Kuhlmann—Anderson.

[h] The maxima of mental growth as determined by

the Courtis equation.

[5] The maxima of growth in reading as determined

by the Courtis equation.

In some cases it was possible to match individuals
from both groups on either reading maxima or mental age maxima
and compare their rates of growth in both areas, as well as the
maxima to which they were growing in the area on Which they
were not matched.

A ratio between the scores achieved on the verbal
subtest and chronological age was computed, also a ratio between
the scores achieved on the non-verbal subtest and chronological
age. It Was assumed that this would be a limited quotient of
verbal and non-verbal ability. A test of the difference of
the mean was then computed for the verbal scores and the non-

verbal scores between the two groups.

 

7“ O. L. Lacey, Statistical Methods in Experimentation,
New York: MacMillan Company, 1953. p. 2A9.

—q.-- m wen-f
s.

CHAPTER IV
ANALYSIS OF THE DATA

In the writing of the equations using the Courtis
technique it is necessary to have at least three measurements.75
While three are necessary, more measurements generally yield
more accurate equations as errors in measurement are then less
likely to influence the results.

With more measurements available for this investigation,
it would have been possible to determine whether or not any
of the individuals who appeared to enter adolescence, did so
or not. At this time, it is not possible to confirm or negate
this hypothesis and the measures have, therefore, been included.

For mental growth in Group I (consistent I. Q. scores)
the rate ranged from .10593 isochrons to .35780 isochrons. The
mean rate is .19961 isochrons. The range of incipiencies was
from 10.25 isochrons to 22.n3 isochrons. For the maxima the
range was from 110 months to 230 months with a mean of 175.71
months.

In Group II (decreasing I. Q. scores) the rates ranged

from .07000 isochrons to .32221 isochrons with a mean of .19678

isochrons. Incipiencies ranged from 11.68 isochrons to 31.91

 

758. A. Courtis, Maturation Units and How to Use

Them, op. cit.

20

21

isochrons with a mean of 22.29 isochrons. The range of the
maxima was from 105 months to 200 months. The mean was 13h.81
months.

The individual equations showing the differences in
rates, incipiencies, and maxima are found according to group
in Appendices A and B. At the end of each of the Appendices
is found the mean rates, incipiencies, and maxima for that
group. From these mean rate, incipiency, and maxima the curves
of constants for growth in reading and mentaltage have been
drawn. These are shown in Figure 1.

It was found that the average deviation for describing
mental growth for a period of five years in Group I Was 1.69
and 1.99 months for Group II. The average deviation for des-
cribing growth in reading was 1.62 months for Group I and 2.79
months for Group II. Since Group II individuals were more
variable, their variations are probably described less pre—
cisely. Such variation also is indicative that additional
factors are Operating, and that further research is needed
to discover their nature.

The mean rates of growth between the two groups in
mental age and reading were not significantly different.
However, it was found that Group I's mean mental age maximum
was significantly higher, at the .01 level of confidence,
than the mean mental age maximum of Group II. In terms of
growth in reading, the mean maximum for Group I Was signifi-

cantly higher, at the .01 level of confidence, than was the

READING AND MENTAL AGE IN MONTHS

 

22

 

200‘“
18019
160 “”32“
t- /.
x'.’
,z’
/
[K
1140“- / /
‘0'."
. ‘/./..—-
120_L / ./0/
./ ,/a-""' I..-’
.A/" r’
// /./’
100" 1” ,I Group I M.A.
‘ /' _ _ ____R.A.
. ,l/ Group II . . .M.A.
/ / / -—_-_.o- _RoAn
80.L , ’1
/ /
’ /
6 Z i;_ L 'L __L 1 __1.
0 so 100 120 iuo 186 186 200

Fig. l.

CHRONOLOGICAL AGE

Curves of Constants

23

mean for Group II. This is consistent with the data in

Table I which shows the mean I. Q. scores, the differences
between the groups in Grades One and Two. At this level

there are no verbal subtest in the Kuhlmann-Anderson Tests.
The first verbal subtests appear in the Grade III tests.

Here the difference in I. Q. between the two groups is signif-
icant at the .01 level of confidence. This also holds true

at the Fourth and Fifth Grade level.

When the equations for growth in reading and mental
age were analyzed on an individual basis, it was found that
twelve of the sixteen individuals of Group II were growing
toward higher maxima in mental age. Only two cases were
growing toward higher maxima in reading than in mental age.
Two cases had the same maxima in both areas. In Group I,
ten cases were found to be growing to a higher maxima in
mental age, whileseven were growing to higher maxima in
reading age.

Appendix C shows eleven individuals matched in terms
of mental growth maxima. Five of the six Group II individuals
were growing toward a lower maxima in reading than were the
Group I individuals. .

Appendix D shows ten individuals matched in terms
of reading maxima. Six of the seven Group II are growing
toward a lower mental age maxima than those of Group I.

Appendix E shows individual scores on the verbal and

non-verbal subtests. These scores are in mental age quotients

24

TABLE I

TESTS OF SIGNIFICANCE OF THE DIFFERENCE OF THE

MEAN I.Q. SCORES FOR GROUPS I AND II

 

 

 

Mean 1. Q. Mean I. Q. S '— "t" evel of
Grade of Group I of Group II. D BfDMgzns Value Confidence
1 105.18 104.06 2.16 1.12 .51 Not sig.
2 , 103.82 101.63 2.n2 2.19 .905 Not sig.

3 102.88 96.56 2.17 6.32 2.91 .01

4 103.12 89.56 2.84 13.56 b.77 .01

5 102.65 85.19 3.35 17.46 5.21 .01

 

 

 

 

 

 

 

which are found by dividing the average score of the verbal

and non-verbal subtests by the chronological age of the individ-

ual.

In Group II the majority of the individuals scored higher

on the non-verbal test.

Eleven of the sixteen individuals in

Group II scored higher on the non-verbal tests and five scored

higher on the verbal tests at the third grade level.

At the

fourth grade level, fifteen of the sixteen individuals scored

higher on the non—verbal and only one individual scored higher

on the verbal

subtests.

In the Fifth Grade, the results were

the same, fifteen out of the sixteen scored higher on the non-

verbal subtests and only one individual scored higher on the

verbal subtests.

When looked at from an individual rather than

a group standpoint, nine of the Group II individuals scored

consistently higher on the non-verbal tests.

That

is, their

scores on the non-verbal tests were always higher than their

scores on the verbal subtests.

None of the individuals in

Group II scored consistently higher on the verbal subtests.

25

This would lead one to believe that there was a difference
between the verbal and non-verbal ability of this group.

In the Third Grade there are two verbal and eight
non-verbal tests. Twelve of the seventeen individuals from
Group I scored higher on the non-verbal tests and four scored
higher on the verbal tests. One individual had the same
quotient for both groups of subtests. At the Fourth Grade
level Where the loading is about the same, four verbal and
six non-verbal subtests, nine of the seventeen casesmored higher
on the non-verbal tests. In the Fifth Grade where the loading
changes to one of a high verbal nature, eleven of the seventeen
individual scored higher on the verbal tests and five scored
higher on the non-verbal tests. When analysed on an individual
basis, two individuals scored consistently higher on the non—
verbal subtests and two scored consistently higher on the
verbal subtests. This Would indicate that individuals in
Group I perform about the same on the verbal and non-verbal
subtests. It is born out by the mean scores of the group snown
in Table I. At the Third Grade level there is a difference
of 9.u7 points, a difference of .h2 at the Fourth Grade level,
and a difference of 2.53 points at the Fifth Grade level.

Tables II and III show the results of the "t" tests
between the difference of the means on the verbal and non—
verbal subtests between the two groups. In the Third Grade,
Group I's verbal quotient was significantly higher than the

verbal quotient of Group II. The difference between the groups

26
TABLE II

TEST OF SIGNIFICANCE OF THE DIFFERENCE OF THE MEAN
VERBAL SUBTESTS QUOTIENTS BETWEEN GROUPS I AND II

 

 

 

 

 

 

 

 

 

 

 

 

 

Mean I. Q. Mean I} Q. S, 'D—Diff. "t" Level of
Grade of Group I or Group II D of Means Value Confidence
3 94.29 73.50 7.92 20.79 2.625 .05
u 103.” 69.81 5.93 33.59 5.66 .01
5 102.59 71.86 6.58 30.73 b.67 .01
TABLE III
TEST OF SIGNIFICANCE OF THE DIFFERENCE OF THE MEAN NON-
VERBAL SUBTESTS QUOTIENTS BETWEEN GROUPS I AND II
Mean I. Q. Mean I. Q. S, 'D Diff. “t" Level of
Grade of Group I of Group II D of Means Value Confidence
3 103.76 96.43 0.01 7.33 1.83 Not sig.
a 102.82 88.50 8.32 15.32 3.55 .01
5 100.06 95.13 8.17 8.93 1.18 Not sig.

 

 

 

 

 

 

 

on the non-verbal subtests was not significantly different. In
the Fourth Grade, Group II scored significantly lower on both
the verbal and non-verbal subtests. Since all calculations were
rechecked and no error was found, this difference then, must be
attributed to an unknown factor(s). It was beyond the scope of
this investigation to determine the factor or factors that
underlie this difference. Further research is planned to try

to account for it.

27

In the Fifth Grade, there was a shift back. At this
level, Group I's quotient on the verbal subtest was significantly
higher than Group II's. There was no significant difference
between the scores on the non-verbal subtests.

There is a significant difference between the two
groups in terms of maxima in reading and mental age but not in
terms of rate and incipiency. This means that the two groups
have similar starting points and proceed toward their maxima
at approximately the same rate. The maxima then, becomes the
significant characteristic of difference between the two groups.
There is, however, some overlapping between the individuals of
Group I with relatively low maxima and some individuals of
Group II With relatively higher maxima. It appears that those
individuals in Group I growing toward a low maxima in reading
are able to score better on the verbal subtests than those
individuals of Group II growing toward similar maxima. In some
cases, then, there seems to be another factor operating, other
than reading ability, which underlies the decreasing I. Q.
score. In other cases, it can be shown, however, that inability
to read is the primary factor in the decreasing I. Q. score.
While reading ability appears to be a primary factor in some
cases and a secondary factor in others, the significant thing

is that it is a factor of degree in all cases.

CHAPTER V
SUMMARX, CONCLUSIONS, AND IMPLICATIONS

This investigation was carried out to determine whether
or not reading ability was a factor that might cause I. Q.
scores of some individuals to decrease.
In the sampling criteria employed, the cases had to
have a minimum of five I. Q. measures on the Kuhlmann-Anderson
Tests and four Stanford Achievement measures. Those placed in
the consistent I. Q. group (Group I) were to have a variability
of ten I. Q. points or less and those placed in the decreasing
I. Q. group (Group II) were to have three consecutively decreasing
I. Q. scores. A total of thirty-three cases from the Holt Study
fell within the limits of the criteria.
Equations were written on both groups in reading and
mental growth using the Courtis modification of the Gompertz
function.
Tests for the significance of the differences of the
mean between Groups I and II were run on the following:
[1] I. Q. scores from year to year. I
[2] Scores on the verbal subtests of the Kuhlmann-
Anderson.

[3] Scores on the non—verbal subtests of the
Kuhlmann-Anderson.

[4] Maxima in mental growth.

[5] Maxima in reading growth.

28

29

Group I was found to have a significantly higher mean
I. Q. at the Third, Fourth, and Fifth Grade level than Group II.
The differences between the two groups at the First and Second
Grade level were not significant. Group I's mean scores on
the verbal subtests were significantly higher than those of
Group II at the Third, Fourth, and Fifth Grade level. None of
the subtests at the First and Second Grade level are considered
to be verbal.

On the non-verbal subtests there were no significant
differences until the Fourth Grade. At the Fourth Grade level,
Group I scored significantly higher than Group II. At the
Fifth Grade level there was no significant difference between
the two groups.

In terms of growth maxima, twelve of the sixteen
Group II individuals had higher mental maxima than reading
maxima. Two cases had the same maxima in both areas. In
Group I; ten of the seventeen individuals had higher mental
maxima than reading maxima.

A significant difference was found between the mean
maxima of the two groups. There was no significant difference

between the mean rates and incipiencies.

Conclusions
While it cannot be stated that reading ability was
the primary cause for decreasing I. Q.s in all cases, in eight
of the sixteen cases in Group II, the individuals' inability

to score on the verbal subtests at the same level at which they

3O

scored on the non-verbal subtests did result in a drOp of their
I. Q. scores.

It can be said that the verbal ability of Group I is
significantly higher than Group II's, although there is some
overlapping between groups.

It can be conclusively stated that maxima in growth

is the primary differentiating characteristic, between the two

groups.

Implications

Researchers need to be constantly aware of the fact
that there are many factors which may influence test results.

The classroom teacher needs to know the type of test
and other factors such as reading ability which might influence
the results. It is of necessity, then, to know something of
the individual's total development before adequate appraisal
can be made in a specific area of growth.

Reading is a more complicated process than research
designs have heretofore assumed.' For example, three parameters
(maximum, rate, and incipiency) were used to describe reading.
A difference was found between the two groups in maximum butnot
in terms of rate or incipiency. Then too, maximum did noteub-
count for the difference in all cases which indicates the
Operation of one or more other factors. It would seem, there-
fore, that an attempt to account for a difference in reading \

based upon a single test, should be expected to produce less

than accurate results.

APPENDICES

31

32

APPENDIX A

GROWTH EQUATIONS son READING AND MENTAL AGE —- GROUP I
[y=k(=rt1i)1AD]

 

 

 

k. AD
Maxims Average
Case Growth in Rats Incipiency Dev. in
In“ Months r 1 Months
H—0-106-F M 162 .21181 + 16.35 .1 2.87
R 200 .1372? + 18.25 .1 1.30
H-0-107—F M 165 .26454 + 13.99 .1 1.35
R 200 .28833 + 11.24 .1 1.60
H-0-120-F M 1U0 .31955 + 10.25 -* 1.72
s 160 .239L11 + 10.34 :1: 2.77
H—0-137-M M 200 .15628 + 19.0” .1 3.16
R 280 .14250 + 1h.23 .1 3.39
H—O-lhO-M M 230 .11086 + 20.70 .1 3.31
R 150 .21304 + 13.75 1 1.05
H-O-lh3—M M 125 .226667 + 16.83 .1 1.22
R 280 .13b09 + 14.89 .1 2.22
H-O-lhn-F M 185 .17848 + 18.97 .1 2.22
R 150 .39600 + .61 .1 1.06
H-O-th-F M 170 .21302 + 16.12 1 1.66
R 115 .77080 - 31.46 .1 .06
H-0-150-M M 210 .13590 + 19.87 .1 2.19
R 145 .32555 + 5.82 1 1.02
H-0-155-F M 190 .14272 + 20.32 .1 1.01
R 140 .20305 + 18.40 .1 1.69
H-0-159—M M 180 .18159 + 18.03 .1 .37
R 150 .35085 + 3.39 :1: .80
H-0-160-F M 200 .17171 + 17.72 .1 2.02
R 160 .36208 + .26 1 2.36

 

l

 

 

 

 

 

*M ~~ Equations for Mental Growth
R -- Equations for Reading GrOWth

33

APPENDIX A -- Continued

 

 

 

k. AD
Maxims Average
GrOWth in Rats: Incipiency Dev. in
Case In“ Months r t Months
H-0-161-F M 160 .19355 + 19.67 1 .49
R 130 .46228 - 4.04 .1 1.46
H-0-167-M M 210 .16622 + 18.54 .1 .47
R 130 .41333 + 1.11 1 1.19
H-0-177-M M 110 .3578 + 10.28 1 .63
R 130 .2040 + 18.14 .1 1.50
H—l-lOl-M M 140 .21674 + 17.85 .1 2.2
R 125 .28500 + 10.99 .1 2.16
H—1-211-M M 210 .10593 + 22.43 .1 1.75
R 220 .19729 + 12.28 .1 1.55
RANGE M 110 .10593 + 10.25 .1 .37
230 .3578 + 22.43 .1 3.31
RANGE R 115 .13409 - 31.46 .1 .06
280 .77080 + 18.40 .1 3.39
MEAN M 175.7 .19961 + 17.47 1 1.69
MEAN R 168.5 .29911 + 6.98 .1 1.62

 

 

 

 

 

 

 

34

APPENDIX B

GROWTH EQUATIONS FOR READING AND MENTAL AGE -_ GROUP 11
[y=k#rt_+_i)_tADJ

 

‘ ' k. - ‘1 AD

Maxims Average

Case Growth in Rate Incipiency 4 Dev. in
In“ Months r i Months
H—0-102-M M 140 .18222 + 21.46 1 .72
R 140 .29083 + 6.24 1 3.94
Ha0-103-F M 135 .32227 + 11.68 1 .62
R 140 .34739 + .239 .1 3.93
H—0-116-F M 130 .21333 + 21.48 1 1.05
R 105 .71304 - 23.77 .1 4.67

H—0-124-M M 170 .11857 + 24.12 1 1.306
R 110 .38833 + 5.70 1 .05
H-O-125-M M 105 .32074 + 17.56 1 4.08
R 120 .47173 - 13.32 .1 5.25
H-0-127-F M 130 .10684 + 29.95 1 .42
R 105 .28885 + 18.27 1.1.35
H-0-128-M M 130 A .25032 + 18.33 1 3.21
R 110 .35472 + 8.83 1.3.56
H-0-133-M M 125 .2000 + 22.47 1 1.62
R 110 .34222 + 11.13 1 1. 35
H-0-134-M M 120 .23781 + 20.97 1 3.44
R 115 .30722 + 12.19 1 2.12
H-0-135-M M 130 .18676 + 22.86 1 2. 58
R 115 .23285 + 17.56 1 1.55
H-0-136-M M 150 .24428 + 16.12 1 1.88
_ R 140 .24250 + 14.20 1 .79
H-0—141-M M 125 .2190u + 23.10 1 2.15
' R 115 .19388 + 23.28 1.1.69

 

 

 

 

 

 

* M -- Equations for Mental Growth
R —- Eduations for Reading Growth

35

APPENDIX B -- Continued

 

 

 

k. AD
Maxims Average
Case Growth in Rats Incipiency Dev. in
In“ Months r - t Months
H-0-158-M M 125 .15222 + 26.15 .1 2.80
R 125 .23782 + 11.71 .1 1.91
H-l-lOS-M M 127 .07000 + 31.91 .1 3.03
R 120 .54608 - 10.98 .1 5.06
H-1-117-M M 115 .19250 + 26.87 .1 1.17
R 105 .55260 - 16.81 1 5.11
H-l-146-M M 200 .13159 + 21.68 .1 1.80
‘ R 125 .36750 + 6.10 1 2.25
RANGE M 105 .07000 + 11.68 .1 .7
200 .3222? + 31.91 .1 4.08
RANGE R 105 .19388 + 23.28 .1 .05
140 .55260 - 23.77 1 5.2.5
MEAN M 134.8 .19678 + 22.29 1 1.99
MEAN R 118.8 .36172 + ' 5.78 1 2.79

 

 

 

 

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38

APPENDIX E

AVERAGE MENTAL AGE QUOTIENTS ACHIEVED ON THE
VERBAL AND NON VERBAL SUBTESTS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Verbal Tests Non-Verbal Tests
Grade Grade
Case -
3 L4 5 3 4 5
Group I
H-1-101-M 82 97 88 82 80 53
H—O-106-F 93 103 102 97 104 105
H-1-107-F 118 117 118 119 118 114
H—0-120-F 96 93 95 115 108 102
H-1-137-M 92 109 108 110 111 104
H—0-140-M 85 95 106 98 98 99
H-1—143-M 93 97 105 97 80 94
H-o-144-F 112 123 124 122 110 110
H-0-148—F 108 96 102 100 108 98
H-O-lSO-M 102 113 102 101 104 98
H-0-155-F 91 85 78 104 109 111
H-0-159-M 111 119 110 103 101 94
H-0-160-F 92 110 109 108 104 109
H-0—161-F 99 109 102 105 121 101
H-0-167-M 105 111 116 119 120 115
H-0-177-M 87 9O 88 82 89 88
H-1-211-M 97 109 102 102 92 106
Group II

H—O-lOZ-M 50 78 78 100 104 98
H-0-103-F 102 89 94 106 105 101
H-1-105-F 91 43 40 85 68 89
H-0-116-F 102 70 92 75 82 101
H-1-117-M 92 40 47 83 92 88
H-o-124—M 85 89 92 102 97 98
H-0-125-M 86 59 11 87 73 87
H-0-127-F 95 66 92 98 58 97
H-0-128-M 86 65 59 105 99 102
H-0-133-M 87 63 82 99 77 94
H-0-134-M 42 84 67 102 96 94
H-O-lBS-M 87 60 44 98 77 91
H-0-136-M 90 92 99 108 99 105
H—0-141-M 103 44 59 101 106 111
H-1-146—M 44 101 102 116 102 99
H-0-158-M 80 55 63 78 65 81

 

 

 

 

 

 

 

 

BIBLIOGRAPHY

Abbott, Edward C. "Relationship Between Variations in Silent
Reading Ability and Mental Ability," Journal of
Educational Research, Vol. 39 (December, 1945),
3I4-316. Abstract of Doctor's Dissertation.

Allen, Mildred M. "Relationship Between Kuhlmann-Anderson
Intelligence Tests and Academic Achievement in
Grade IV," Journal of Educational Psychologl,35:
229'“ 239 p 19111;.

Baldwin, B. T. "Physical Growth of Children from Birth to
Maturity," University of Iowa Studies in Child Welfare,
Vol. I, No. l, 1921.

Blair, A. w. and Burton, W. H. Growth and Deve1Opment of the
greadolescent. New York: Appleton-Century-Crofts,
Inc. 1 1951.

 

Bayley, Nancy. "Mental and Motor Deve10pment from Two to
Twelve Years," Review of Educational Research, 9:
18-37. 114-125. 1939.

"Consistency and Variability in the Growth of
Intelligence from Birth to Eighteen Years," Pedagogical
Seginar and Journal of Genetic Psychology, 753165-196,
l9 9.

 

Buros, O. K. The Fourth Mental Measurement Yearbook. Highland
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