AN WALLEANQN OF 'E‘HE COURTIS METHOD IN THE
STUDY OF GROWTH WTEONSHIPS

“hosts for flu Degree of DH. D.
MiCHIGAN STATE UNIVERSITY
Gerald H. Wohlferd

1957

3' L1 1-. NS-

This is to certify that the
thesis entitled
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"‘ A " 7 " ’ ‘ '1 ’ f "”3

presented by

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has been accepted towards fulfillment
of the requirements for

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" 7"” :.'«‘\1
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Major professor

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0-169

 

AN EVALUATION OF THE COURTIS METHOD IN THE
STUDY OF GROWTH RELATIONSHIPS

by
Gerald H. Wohlferd

AN ABS TR AC T

Submitted to the School of Graduate Studies of Michigan
State University of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

School of Education

1957

Approved: (3,¢;A,.t/, :huJLQH/g;\:“_fi

2
GERALD H. WOHLFERD ABSTRACT

This study was conducted to test the accuracy with
which the Courtis method described height and weight growth,
to test the use of correlative procedures on derivations of
this technique, and to use extrapolation to arrive at new
insights into growth.

All cases used in this study were selected from the
Dearborn Data which is available at the Michigan State Uni-
versity. All cases selected met the criteria that, measures
must be included in a span of from ninety-six months through
180 months, and each pre-adolescent and adolescent cycle
must contain at least three measures of both height and
weight. The measures of twenty-six boys and eighteen girls.
met the above criteria.

Height and weight growth equations were written for
each case by use of the Courtis method. Predicted measures
were fitted as closely as possible to actual measures.

Cyclic starting and ending times were obtained by
substituting the isocronic values for one per cent and
99 per cent respectively, for 'y' in the above equations
and solving for 't‘. Values attained at one per cent of
the adolescent cycle were obtained by substituting age at
one per cent for 't' in the pre-adolescent equation and
solving for 'y'. Percentages of development were obtained

by dividing derived scores by proper maxima.

3
GERALD H. WOLFERD ABSTRACT

The Courtis method describes growth in height and
weight well within a two per cent average deviation. Height
growth was described more accurately than weight growth.
The Courtis method describes height and weight growth so
accurately that it may be used to test for growth relation-
ships through various statistical techniques.

Correlations between rates, maxima, ages at one per
cent of adolescent growth, 99 per cent of pre-adolescent
growth, 99 per cent of adolescent growth, and percentages
of development at the beginning of the adolescent cycles
were generally positive, but too low for predictive use.

Negative correlations obtained when pre-adolescent
height and weight maxima were correlated with respective
adolescent height and weight maxima seemed to indicate that
large pre—adolescent maxima are followed by smaller adoles-
cent maxima and vice versa.

Correlations derived between values of height and
weight attained at one per cent of the adolescent cycle and
corresponding total maxima tended to verify the above
conclusion.

The use of the Courtis method to find growth rela-
tionships through correlative techniques did not produce
outstanding results. Correlations obtained between final
maxima were no better than those noted in the Review of

Literature.

Lt
GERALD H. WOHLFERD ABSTRACT

Curves of constants revealed the earlier maturing
of girls, while curves of percentages of development dis-
closed similarities of adolescent starting ages and per-
centages of total development at the beginning of adolescent
growth.

Means of starting times, of pre-adolescent height
growth attained when the adolescent cycle began, and of
percentages of total growth attained at the beginning of
adolescent growth, showed great similarities between height
and weight values of each sex. The probability of the
existence of equal height and weight adolescent cycle begin-
ning points is evidenced by the small deviations of the

above means.

AN EVALUATION OF THE COURTIS METHOD IN THE

STUDY OF GROWTH RELATIONSHIPS

by
Gerald H. Wohlferd

A THESIS

Submitted to the School of Graduate Studies of Michigan
State University of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

School of Education

1957

TABLE OF CONTENTS

CHAPTER PAGE
I. INTRODUCTION. . . . . . . . . . . . 1
Statement of the problem. 2
Importance of the study . 5
Definition of terms 6
II. REVIEW OF THE LITERATURE. . . . . . . . 10
III. PROCEDURE. . . . . . . . . . . . . 26
Data . . . . . . . . . . . . . 26
Method. . . . . . . . . . . . . 28
IV. ANALYSIS OF THE DATA AND DISCUSSION OF THE
RESULTS. . . . . . . . . . . . . 33
V. SUMMARY, CONCLUSIONS, AND IMPLICATIONS . . . 69
BIBLIOGRAPHY . . . . . . . . . . . . . . 75
APPENDICES . . . . . . . . . . . . . . . 84
APPENDIX A. Frequency and Range of Measures--
Boys . . . . . . . . . . 85
APPENDIX B. Frequency and Range of Measures--
Girls. . . . . . . . . . 86

APPENDIX C. Individual Intelligence Quotients 87

APPENDIX D. Height Formulas-~Boys . . . . 88
APPENDIX E. Weight Formulas--Boys . . . . 89
APPENDIX F. Height Formulas--Girls . . . . 90

APPENDIX G. Weight Formulas-~Girls . . . . 91

iii

CHAPTER PAGE
APPENDIX Hr'l. Deviation of Measured Height
Scores from Predicted Height
Scores[Boys]. . . . . . . 92
H--2. Deviation of Measured Height
Scores from Predicted Height
Scores[Girls] . . . . . . 102
H--3. Deviation of Predicted Weight
Score from Actual Weight
Score[Boys] . . . . . . . 109
H--u. Deviation of Predicted Weight
Score from Actual Weight
Score[Girls]. . . . . . . 115

APPENDIX I. Curve of Constants Tabulation . . 119

TABLE

II.
III.

IV.

VI.

LIST OF TABLES

Rate Correlations.

Maxima Correlations

Correlations of Ages at Specific Per Cents
of Development . .

Correlations of Values Attained

Reversals of Height Growth Patterns.

Correlations of Percentages of Growth at

Beginning of Adolescent Cycle

Page
. A5
M6

47
’49

. 50

. 51

Figure

10.

11.
12.
13.
14.
15.
16.
17.
18.
19.

\OCIDNQU'IL‘UOM

LIST OF FIGURES

Number of Measures Including Both Sexes and

Distribution of Intelligence Quotients

83M Height . . .
83M Weight

118F Height.

118F Weight.

176M Height.

176M Weight.

Predicted Scores

Distribution of Weight Predicted Scores

Both Cycles.
Closeness of Fit--Case
Closeness of Fit--Case
Closeness of Fit-~Case
Closeness of Fit--Case
Closeness of Fit--Case
Closeness of Fit--Case
Distribution of Height

from Actual Measures.

from Actual Measures.
Height Curve Comparison
Weight Curve Comparison
Curves of
Curves of
Curves of
Curves of
Curves of
Curves of
Age at

Total Maturity-~Girls'

Constants--Height Measures
Constants--Weight Measures
Total Maturity-~Height Percentages
Total Maturity--Weight Percentages

Total Maturity--Boys' Percentages.

Percentages

which Adolescent Cycle Began . -. .

Page

28
29
35
36
37
38

39
A0

42

1+3
53
524
56
57
58
59
61
62
614

vi

Figure Page
20. Per Cent of Pre-Adolescent Cycle Attained
when Adolescent Cycle Began. . . . . . . 66
21. Per Cent of Total Development Attained at

Beginning of Adolescent Cycle . . . _. . . 67

CHAPTER I

PROBLEM AND DEFINITION OF TERMS

Introduction

 

The relationships between height and weight are
interesting to many people. Parents discuss the progress
their off-spring are, or have been making. They compare
them with siblings and other children. They even recall
and use as a yardstick their own progress as children.
The children, themselves, in their society compare them-
selves with their peers. Who has not heard the derisive,
"Pick on someone your own size"? Young adolescent girls
often complain that boys of similar chronological age
are "too short for me."

The business world is interested in the size of
humans. Ever since the industrial revolution and the
beginning of mass production of clothing, sizes have been
attached to facilitate sales.1 Penny weight scales have
norms for height and weight prominently displayed.

Telephone booths, car,2 train, bus, and airplane seats,

 

lMargaret Dana, Behind the Label (Boston: Little,
Brown and Company, 19387, p. 127.

aEdwin C. Pickard, Ford Motor Com any Engineer,

A Passenger Car Comfort and Seat Design paper presented

at SAE meeting, 1956).

 

 

2
theatre seats,3 doorways, step heights, and hosts of other
manufactured items are constructed according to norms
established by careful research.“

Advertising companies day after day announce the
nutritional growth producing values of breakfast cereals,
breads, candies, drinks and a wide range of pills, vitamins,
and various sundry nostrums.

School desks, chairs and tables are now adjustable
and scaled to fit different grade levels. -Blackboards,
sinks, toilets, pencil Sharpeners, and drinking fountains
are installed within reach of desired grade ranges.

Scientists, too, are interested in height-weight
relationships, and have suggested numerous ways of

describing and predicting growth.5
I. STATEMENT OF THE PROBLEM

General Statement

 

Courtis6 postulates the idea that growth can be-

accurately described by the mathematical equation

 

3American Seating Company, Better Seating for America
Through Research, Testing, InspectIEn, Grand“Rapids, Michi-

gan, 1953.

u"Basic Body Measurements of School Age Children,"
U. S. Department of Health, Education and Welfare, June,

1953.

 

 

 

 

5See'"Review of the Literature" Chapter II.

6S. A. Courtis, Towards A Science of Education (Ann

Arbor, Michigan: Edwards Bros.7 19515,ppT—13-16.

 

3

y = k I rt i i],and that different elements, or constants,

of the equation lend themselves to mathematical comparison.
The purpose of this study is (1) to evaluate the

accuracy with which height and weight growth is described

by the Courtis method, (2) to test the application of

correlative procedures to Courtis equation derivations,

and (3) to show the extent to which extrapolation may be

used to arrive at new insights into growth.

Specific Statement

 

Specifically, this investigation has the following
major objectives:

1. To determine the deviation of predicted measures
from actual measures.

2. To obtain correlations between like constants,
as below, for each sex:
a. r1 height with r1 weight
b. r2 height with re weight
c. r1 height with r2 height
d. r1 weight with re weight

e. k1 height with kl weight

p...)
x.
[U

height with kg weight
k3 height with k3 weight
kl height with k2 height
k1 height with k3 weight

k2 height with k3 height

x Lb re 3 a:

. kl weight With kg weight

1. k1
m. k2
n. bl
0. t1
p. t2
q. t1
r. t1
8. c1
t. c1
u. cl
v. c1
w. cl
x. d1
y. d2
2. d1
* d1
To use
a. To

of
b. To

weight
weight
height
height
height
height
weight
height
height
weight
height
weight
height
height
height

weight

with
with
with
with
with
with
with
with
with
with
with
with
with
with
with

with

extrapolation:

weight
weight
weight
weight
weight
height
weight
weight
height
weight
height
weight
weight
weight
height

weight

determine curves of constants for measures
height and weight, for each sex.

determine curves of constants for per-

centages of total maturity of height and

weight,

TO

for each sex.

determine the mean age at which the

adolescent height and weight cycles begin

for each sex.

(1) To determine the deviations from the

mean of the above beginning ages.

d. To determine the mean percents of pre-
adolescent height and weight development
attained when the adolescent cycle begins
for each sex.

(1) To determine the deviations from the
mean of the above beginning percentages.

e. To determine the mean per cent of total
height and weight maturity attained when
the adolescent cycle begins.

(1) To determine the deviations from the

mean of the above percentages.
II. IMPORTANCE OF THE STUDY

Courtis postulates a natural law, and asserts that
all living matter follows such a law. He maintains that
all living things grow in a cyclic fashion according to
predictable rules. His mathematical description of the
universal law of growth is Y = kir , a function of the
Gompertz curve. He has tested this formula on the growth
patterns of living organisms of many kinds and feels that
such studies have borne out its validity.7

He suggests that interrelationships exist between

the constants of the equations. Furthermore, he states

 

78. A. Courtis, Maturation Units and How 22 Use
Them (Ann Arbor, Michigan: Litho-printed, Edwards Bros.,
1950), Appendix C.

 

that these constants can be computed from three reliably
determined points on a maturation curve, and that the
equation so derived will describe a curve which deviates
less than two per cent from the actual measurements.

Courtis feels that many past educational studies
are unscientific, and debunks them as having "the dry rot
of meaningless Juggling of statistical symbols." He then
states:

The glory of science is that it isman' s only

way to determine, objectively, whether a given

idea is true or false.

On the basis of scientific truth man is able to
predict and control. That is true "which works;"9

If his method "works," then it is worthwhile using
his technique to search for growth relationships or other

insights into the developmental pattern of human growth.
III. DEFINITION OF TERMS USED

Development. The progress towards maturity brought

 

about in an immature organism by the action of appropriate

environmental forces under constant conditions.10 In

 

8

Courtis, Toward A Science 9: Education, op. cit.,p.l.

9Courtis, Maturation Units and How £9 Use Them,
op. cit., p. 129. ""

loCourtis, Towards A Science gf Education, op. cit.,
p. 9.

actual practice, growth, development and maturation are

used interchangeably depending upon the emphasis desired.ll

Growth cycle. A well marked period of maturation

 

during which the organism, forces, and end products are

constant.12

Maximum. The ultimate state or condition within

a specific cycle.l3

Maturity. The maximum of development related to a
specific growth and situation; e.g., physical maturity is

factor "k" of the Gompertz function.14

Pre-adolescence and adolescence. There are two

 

periods of rapid growth, with one period between of slower
growth. The periods of rapid growth are early infancy and
adolescence. The period of less rapid growth is late

childhood or . . . . (pre-adolescence).15

 

llCourtis, Maturation Units and How to Use Them,
op. cit., p. 129.

 

12Courtis, Towards 5 Science of Education, op. cit.,
p. 13.

l3Rueben R. Rusch, "The Relationship Between Growth
in Height and Growth in Weight" (unpublished M.A. thesis,
Department of Education, Michigan State College, 1954).

 

14Ekanem A. Udoh, "Relationship of Menarch to
Achieved Growth in Height" (unpublished Ph.D. thesis, De-
partment of Education, Michigan State College, 1955).

150. v. Millard, Child Growth and Development (Boston:
D. C. Heath and Company, 1951), p. 65.

 

The term adolescence is . . . . a period during

which the growing person makes the transition from child-

hood to adulthood.16

l at
The Gompertz functions. 7 y = kece or

 

t
y = kir where:

y = achieved development at time "t."
k = maximum towards which development is
progressing.
eC = incipiency (i) or the degree of development at
the beginning of the period of growth.
ea = rate (r) of growth expressed in isochrons.
Isochron.18 One per cent of the time necessary

for the generation of the Gompertz Function from

0.000000189 per cent to 99.90917 per cent.

Constants. Maximum, rate and incipiency.

 

 

1
6Arthur T. Jersild, The Psycholo y'gf Adolescence
(New York: The Macmillan Company, 1957), p. 4.

17Gerald T. Kowitz, "An Exploration into the
Relationship of Physical Growth Pattern and Classroom
Behavior in Elementary School Children" (unpublished Ph.D.
thezis, Department of Education, Michigan State College,
195 .

l8

Courtis, Maturation Units and How £9 Use Them,

op. cit., p. 140.

 

-. talks.

 

 

Symbols employed.

 

rate of pre-adolescent cycle.

rate of adolescent cycle.

maximum.of pre-adolescent cycle.
maximum of adolescent cycle.

total maturity.

age at 1 per cent of adolescent cycle.
age at 99 per cent of pre-adolescent cycle.
age at 99 per cent of adolescent cycle.
value at 1 per cent of adolescent cycle.

per cent of pre-adolescent cycle attained
at the beginning of the adolescent cycle.

per cent of total maturity attained at the
beginning of the adolescent cycle.

CHAPTER II
REVIEW OF THE LITERATURE

The study of the human body is no new fad. Physical
growth was of early scientific interest. Buffon,19 in 1837
reported studies conducted during 1759-1776. Measuring
instruments and techniques, however, were crude. Queteletf-BO
who is also credited with origination of the term 'anthro-
pometry', first standardized a method for studying physical
growth. Since then, due to the efforts of Hrdlicka21 and

22,23,24,25,26,27

others, measurement of the human body

has become common.

 

19Count de Buffon, "Sur l‘accroissement successif
des enfants, Gueneau de Montbeillard mesure de 1759 a 1776,"
Oeuvres Completes (Paris: Furne and Pie, 1837), Vol. III,
pp. 174-176.

 

2OA. Quetelet, Anthropometrie (Bruxelles: Muquardt,

 

1871).

21Ales Hrdlicka, Practical Anthropometry (Philadel-
phia: Wister Institute of Anatomy and Biology, 1920), pp.
x-230.

 

22M. P. Baum, and V. S. Vickers, "Anthropometric
and Ortho edic Examinations: A Technique for Use with
Children,‘ Child Develgpment Monographs, 1941, Vol. 12,

No. 4, pp. 339-345-

 

23L. M. Bayer and N. Bayley, "Directions for
Measures and Radiographs Used in Predicting Height," Child
Develgpment Monographs, 1947, Vol. 18, No. 3, pp. 85-87.

 

 

11
Studies of physical growth became so numerous in the
following years that in 1921 Baldwin28 met the pressing
need for syntheses by publishing a summary of previous

works. Many other bibliographieseg’30’31’32’33 have

 

2D'W. F. Dearborn and J. W. M. Rothney, Predicting
the Child's Development (Cambridge, Mass.: Sci-Art Pub.,
I941), Chapter 4.

 

 

25V. B. Knott, "Physical Measurement of Young
Children," University of Iowa Studies: Studies in Child
Welfare, 1941,IV01. 18, No. 3.

 

 

 

26W. M. Krogman, "A Handbook of the Measurement and
Interpretation of Height and Weight in the Growing Child,"
Mono ra h of the Society for Research in Child Development,
1958. VoIJ_T3. No. 3} pp. ix-68. .

 

 

27H. C. Stuart and Staff, "The Center for Research
in Child Health and Development, School of Public Health,
Harvard University, I," Monograph 9f the Society for
Research in Child Development, 1939, Vol. 4, No. 1, pp. xiv-
261.

 

 

 

28B. T. Baldwin,"The Physical Growth of Children
from Birth to Maturity," University 2: Iowa Studies gf
Child Welfare, 1921, Vol. 1, NO. 1.

 

 

 

29Children‘s Bureau of the United States Department
of Labor, References on the Physical Growth and Development
9; the Normal Child. I927, No. 179.

 

 

 

3OHoward v. Meredith, "Physical Growth of White

Children, A Review of American Research Prior to 1900,"
Mono raph of the Society for Research in Child Development,
, o .‘I, No. 2, pp. I283.

 

 

31H. E. Jones, "Relationships in Physical and
Mental Development," Review 9: Educational Research, 1933,
No. 3, pp. 150-162.

 

32H. V. Meredith and G. Stoddard, "Physical Growth
from Birth to Maturity," Review of Educational Research,
1936, Vol. 6, pp. 54-84.

 

12
subsequently been published and references are now kept
current through ‘Child Development Abstracts,‘ which began
publication in 1927.

Child development as a scientific endeavor began
in the 1920's with the establishment of research centers
in America, whose purpose was the collection and processing
of data concerning all phases of human development. Some
of the more important of these are: Harvard University
Center for Research in Child Health and Development, 1922;
University of California Institute of Child Welfare, 1922;
University of Minnesota Institute of Child Welfare, 1922;
Yale Institute of Human Development, 1925; Fels Institute,
Antioch College, 1929;2um1Brush Foundation, Western Reserve
College, 1931.

As child development research increased in volume,
the method of study changed. Pioneers in the field of
human growth wrote biographical accounts of individual

34

children, usually their own. From these early sketches,

developmental studies resolved into a type of study known

as the ‘cross-sectional' method. This procedure utilized

the collection of data on large groups of children

 

33W. M. Krogman, "The Physical Growth of Children:
An Appraisal of Studies 1950-1955," Monographs of the
Society for Research l2 Child Development, Inc., 19‘6, Vol.
20, No.60, pp. 111191.

34L. K. Frank, Child Behavior and Development,
edited by Barker, Kounin and wright.(New York: ‘McGraw-Hill
Book Company, Inc., 1943), p. l.

 

 

 

 

 

13
of different age periods and aggregating the observations
and measurements of this large array of subjects.35

Cross-sectional data lends itself particularly well
to the use of statistical techniques and those doing
research in child development made use of these in analysis.
Many valuable generalities have been arrived at through
this type of study.36’37'38’39’40

The publication of height-weight norms in both non-

professional“1 and scientific,u2’u3:u4 Journals is an

 

35Ibid., pp. 10.

36Arnold Gesell and Catherine S. Amatruda, Develo -
mental Diagnosis (New York: Paul B. Hoeber, Inc., I952),

p. 496.

37Norman L. Munn, The Evolution and Growth of Human
Behavior (New York: Houghton Mifflin Company, l9557,p.525.

38Hilde Bruch, "Obesity in Childhood: I. Physical
Growth and Development of Obese Children," American Journal
of Diseases of Children, Vol. 58, No. 3, pp. 457-484.

 

 

 

39Ethel M. Abernethy, "Relationships Between Mental
and Physical Growth," Monographs of the Society for Research
lg Child Development, Vol. I, No. 7, pp. vii-80.

 

 

 

“ORuth Strang, An Introduction £2 Child Study (New
York: The Macmillan Company, 1951), p. 705.

AllAndrew Hamilton, "You Can Tell Now How Tall Your
Child Will Grow," Colliers, August 9, 1952.

nZMaury Massler, "Calculation of Normal Weight,"

Child Development Monographs, 1945, Vol. 16, Nos. 1 and 2.

 

 

 

43Helen B. Pryor, "Width-Weight Tables (Revised),"
American Journal of Diseases of Children, Vol. 61, pp. 300-
304. "“‘ "-‘————-

 

14
expression of the universal interest in height-weight
relationships.

Wood45 published in 1910 the first height-weight norms
to receive general attention. In 1914 Baldwin“6 was able to
report on two hundred height-weight relationship studies.
Baldwin, Wood and Woodbury)47 published a revised table in

1940; Steggerdau8

constructed tables using Navaho Indians
and Holland (Michigan) whites in 1936. Simmons and Todd“9

used Cleveland children in their study in 1938. Todd,50

 

44W.Kornfie1d, "Technical Aspects of the Analysis
of Bodily Conformation in Children," American Journal of
Diseases of Children, Vol. 55, pp. 835.

 

45T. D. Wood, "Health Examination," Ninth Yearbook,
National Society for the Study of Education, 1910, Vol. 9,
Part 1, pp. 34- 35.

 

 

“6B. T. Baldwin, "Physical Growth and Progress,"
Bulletin 19; H;.§; Burgag of Education, Washington, D. C.,
l 1

 

1”B. T. Baldwin, at al, Height-Weight Age Tables
(New York: American Child HEalth Association, 1923)

 

48M. Steggerda, "A Height-Weight-Age Table for
Navahoes 6-18 Years; a Height-Weight-Age Table for Dutch
Whites, 6-15 Years, Measured in Holland, Mich.," (Washington,
D.C.: Carnegie Institute, 1936).

“9K. Simmons and T. W. Todd, "Grthh of Well Children.
Analysis of Stature and Weight, Three Months to Thirteen
Years," Growth, 1938, Vol. 2, p. 130.

50Ibid., pp. 93-134.

15
Meredith,51 Shuttleworth,52 and other853’5u have also
worked with physical growth norms.

A definite relationship between different types of
human growth has been long and ardently sought. Corre-
lation studies abound in past and current literature, and
the areas of height and weight have received considerable
attention. Though Simmons55 found some fairly high
correlations (ranging from .399 to .814) between height
and weight, McCloy56 (r = .587), Jackson57 (r = .52),

 

51Howard V. Meredith and Matilda E. Meredith, "Annual
Increment Norms for Ten Measures of Physical Growth on
Children Four to Eight Years of Age," Child Development
Monographs, Vol. 21, No. 33.

 

 

52Frank K. Shuttleworth,'"Standard of Development
in Terms of Increments," Child Development Monographs, 1934,
No. 1, pp. 89-91.

53Medora B. Grandprey, "Range of Variability in
Weight and Height of Children Under Six Years of Age,"
Child Development Monographs, 1933, No. 1, pp. 26-35.

 

54Susan P. Souther, a; El: "A Comparison of Indices
Used in Judging the Physical Fitness of School Children,"
American Journal of Public Health, 1939, Vol. 29, pp.434-438.

 

 

55Katherine Simmons, "The Brush Foundation Study of
Child Growth and Development: II. Physical Growth and
Development," Monograph of the Society for Research in
Child Development, 1944, Vol. 9, No. 1, p. 53. ""

 

 

 

56Charles H. McCloy, "Appraising the Physical
Status--The Selection of Measurements,‘ University of Iowa
Studies, Vol. 12, No. 2, p. 59.

57C. M. Jackson, "Normal and Abnormal Human Types,"
Measurement of Man (Minneapolis, Minnesota: University
of MinnesotaFPress, 1930), Vol. 86.

 

 

16
Miller58 (r = .63), and Dearborn and Rothney59 (r = .68)
60

bear out Millard's statement that correlations are

.11

positive . but too low to indicate much relationship."
But, many scientists felt that the ‘normal‘ person

is a non-entity, and that cross-sectional methods used to

find the hypothetical normal person actually hide individual

traits.6l’6‘2’63 They, therefore, proposed that each

individual included in a study be observed over a period

of time. This technique-—the longitudinal method-~immedi-

ately proved of value. The theory that a growth pattern

 

58R. Bretney Miller, "Physique, Personality and
Scholarship, A Comparative Study of School Children,"
Mono ra h of the Society for Research 1p Child Development,
1 , ol{FVIIIT No. 1, p. 57.

 

 

 

59W. F. Dearborn and J. W. M. Rothney, Predicting
the Child's Development (Cambridge, Massachusetts: SciiArt
Publishers, 1941), p. 293.

 

 

6OMillard, op. cit., p. 31.

61William W. Greulich, "Some Observations on the
Growth and Development of Adolescent Children," The Journal
.2: Pediatrics, 1941, Vol. 19, pp. 302-314.

62Franz Boaz, "Observations on the Growth of
Children," Science, July, 1930, Vol. 72, pp. 44-48.

 

 

63A. R. DeLong, "The Relative Usefulness of
Longitudinal and Cross-Sectional Data," (paper presented
to the Michigan Academy of Science, Arts, and Letters,
March 26, 1955).

17
is not a single cycle phenomena was soon to be chal-
lenged.6u’65’66’67’68 Courtis,69 Millard,7O Bayley,71
and Gray72 suggest that growth in height and weight is
multi-cyclic in pattern.

No real ultimate in the education and understanding
of children can be reached, however, until the growth of

children in all facets of life may be predicted accurately.

 

6LLMeredith, op. cit., pp. 1-83.

65Ruth S. Wallis, "How Children Grow, An Anthrop-
ometric Study of Private School Children From Two to
Eight Years of Age," Universipy pf Iowa Studies ip Child
Welfare, Vol. 5, No. 1, p. 73.

 

 

 

66George Wolff, "A Study of Height in White School
Children from 1937 to 1940 and a Comparison of Different
Height-Weight Indices," Child Development Monographs,
Vol 13, No. 1, pp. 65-77.

 

67Howard V. Meredith, "The Rhythm of Physical
Growth," University pf Iowa Studies, 1935, Vol. 11, No. 3,
p. 232.

68C. B. Davenport,'"Human Growth Curve, Journal
‘pf General Physiology, 1926, Vol. 10, pp. 205-216.

698. A. Courtis, "Maturation as a Factor in
Diagnosis," The 34th Yearbook pf the Society for the Study
p3 Education, 1935,pp.169-187.

 

 

.ll

 

 

 

 

 

70A. J. Huggett and c. v. Millard, Growth and
Learning pp the Elementary School (Boston: D. C. Heath
and Company, 1946), p. 39.

 

 

71Nancy Bayley, Studies 1p the Development pi
Young Children (Berkeley, CaIifornia: University of
California Press, 1940), p. 13.

72H. Gray, "Individual Growth-Rates: From Birth to
Maturity for Fifteen Physical Traits," Human Biology, 1941,

Vol. 13, No. 3, pp. 306-333.

 

 

 

18

Numerous procedures have been offered to this end, though
most are of interest only to the scientist and are im-
practical for classroom use. Todd,73 Flory,74 Bayley,75
and Greulich76 have published detailed descriptions of the
development of bone in the skeleton (principally the wrist
Joint). Wetzel77 constructed an easy to use graphical
presentation of growth from which he claimed to be able

to determine physical fitness.78’79

 

73Wingate T. Todd, Atlas pf Skeletal Maturation
(St. Louis, Missouri: Mosby Publishing Co., 1937).

 

740. D. Flory, "Osseos Development in the Hand as
an Index of Skeletal Development," Monographs of the

Society for Research 1p Child Development,7VolT_1, No. 3,
pp. x-lEI.

 

 

75Nancy Bayley, "Tables for Predicting Adult Height
from Skeletal Age and Present Height," Journal pg Pediatrics,
Vol. 28, 1946, pp. 49-64.

 

76W. W. Greulich. "The Rationale of Assessing the
Developmental Status of Children from Roentgenograms of
the Hand and Wrist," Child Development, 1950, Vol. 21,

pp. 33-44.

 

77Norman C. Wetzel, Tho Treatment pf Growth Failure
1p Children (Cleveland, Ohio: NEA Service, Inc., 1948).

78H. J. Leeson, pp al, "The Value of the Wetzel
Grid in the Examination of_School Children," Canadian
Journal pf Public Health, 1947, Vol. 38, pp. 491-495.

 

 

 

798. M. Garn, "Individual and Group Deviations
from 'Channelwise' Grid Progression in Girls," Child
Development, Monographs, Vol. 23, No. 3, September, 1952,
pp. 193-206.

 

 

19

Meredith80

made a ‘T' score graph from data
collected on Americans of North European parentage that
he feels offers a reasonably refined instrument for pre—
dicting the stature of public school children of white

81

North European ancestry. Sheldon divided the human

physique into three body types: mesomorphic, ectomorphic,
82

and endomorphic. Stolz and Stolz used these divisions
in studying physical development of boys. Jens and Bayley83
reported on a mathematical equation developed by L. S.
Reed of Johns Hopkins University for the description of
growth, and found it could be used to compare several
characteristics of growth in children.

A technique for predicting body weight has been
worked out by Dearborn and Rothney,8h which they claim to be

twenty per cent more effective than ordinary height-weight

 

80H. V. Meredith, "The Prediction of Stature of
North European Males Throughout the Elementary School

Years," Human Biology,1938, Vol. 8, No. 2, pp. 279-283.

 

81W. H. Sheldon, p£_agj The Varieties 2: Human
Physique (New York: Harper Brothers, 1940), p. 5.

 

 

82Herbert R. Stolz and Lois M. Stolz, Somatic 23-
velopment of Adolescent Boys (New York: The Macmillan

Company, 1951), pp. xxxiv-557.

 

 

83R. N. Jens and Nancy Bayley, "A Mathematical
Method for Studying the Growth of a Child," Human Biology,

19373 V01. 9) pp- 556-563-

8”'W. F. Dearborn and J. W. M. Rothney, "Basing
Wei ht Standards Upon Linear Bodily Dimensions," Growth,
193 , Vol. 2, No. 2, pp. 197-212.

 

20
tables. Through the use of their method, they obtained
a correlation of .676 between height and weight.85 Other
methods of description and prediction of growth are
reviewed by Shock.86

Olson and Hughes87 have devised a method by which

various types of growth are converted to comparable age
units, thus making simple the comparison of growth patterns.
The "Organismic Age" concept of growth, as advanced by them
suggests that all types of growth are related.
88

Bloomers after studying the "Organismic Age"
theory, and applying it to selected data, agreed that
"there is some relatedness in rate of growth among various
physical measures." A correlation of .57 was obtained by
him between height age and weight age.

Tyler89 in 1953 attacked the organismic age theory

on the basis of the variability of the rates, and starting

 

85Dearborn, Predicting the Child Development, pp.
cit., p. 270.

 

86N. S. Shock, "Growth Curves," Handbook of Ex eri-
mental Psychology (New York: John Wiley, I95I),_Chapger 10.

 

87W. C. Olson and B. 0. Hughes, "Growth of the Child
as a Whole," Child Behavior and Development, edited by
Barker, Kounin, and Wright (New York: McGraw-Hill Book
Company, 1943), Chapter 8.

88F. Bloomers, et al,'"The Organismic Age Concept,"
Journal pf Educational—Psychology, 1955, Vol. 46, pp.142-148.

 

 

89Fred T. Tyler, "Concepts of Organismic Growth: A
Critique," Journal pf Educational Psychology, 1953, Vol. 44,
pp. 321-342.

 

21
and ending points of the various converted growth ages.
Yet, a few years later he writes:

No doubt there are important relationships among
growth of testes and certain other aspects of growth
or development or learning. These related character-
istics are more likely to be in the realm of physical
growth, and possibly in social and emotional learning
rather than in acedemic learning. . . . O

Stroud,91 too, felt there is a relationship between

various factors of growth. He suggests this is probably
due to heredity and possibly to a fairly constant environ-
ment.

It remained for Courtis92’93’9",95 to advance to a

more accurate description of growth. By using a function

 

90Fred T. Tyler, "Organismic Growth: Sexual Maturity
and Progress in Reading," Journal 23 Educational Psychology,

1955, Vol. 46, pp. 85-93.

 

91J. B. Stroud, Psycholo y ip_Education (New York:
Longmans, Green and Company, I966), pp. 24I-257.

92S. A. Courtis, The Measurement of Growth (Ann
Arbor, Michigan: Brumfield and Brumfield: 1932), pp. 155-
162.

 

933. A. Courtis, "What Is A Growth Cycle?," Growth,
1937, Vol. 1, No. 4, pp. 155-174. '"““'

948. A. Courtis, "Maturation Units for the Measure-
ment of Growth," School and Society, 1929, Vol. 30, pp.
683-690.

 

95Courtis, Maturation Units and How pp Use Them,

op. cit., pp. 1-95.

 

22
of the Gompertz equation,96’97’98 Courtis was able to
mathematically describe growth of all types. Milland§9!1oo
early experimented with the accuracy of this method, and
has offered convincing evidence of the applicability of
this method.

Some authors have raised questions about the
accuracy and application of the Courtis technique.

lOl

Flanagan offers the following observations about the

Courtis method:

These units (isocrons) appear to offer simplicity
and comparability. The principal disadvantage is
the complexity of the functions to be measured in
education. . . . Another very serious practical
limitation is the difficulty in identifying the
upper limit to be used in defining complete maturity.

 

96C. P. Winsor, "The Gompertz Curve as a Growth
Curve," Proceedingp pi the National Academy pf Sciences,
1932, Vol. 18, No. 1, pp. 138.

 

 

97R. D. Prescott, "Law of Growth in Forecasting
Demand," Journal pf the American Statistical Association,
1922, Vol. 18, No. 140, pp. 471-479.

98F. E. Croxton and D. J. Cowder, Applied General
Statistics (New York: Prentice-Hall, Inc., 1939), pp.
447;452.

 

990. V. Millard, "The Nature and Character of Pre-
Adolescent Growth in Reading Achievement," Child Develop-
ment, Monographs, Vol. 11, No. 2, 1940, pp. 71-114.

 

 

100C. V. Millard,"An Analysis of Factors Conditioning
Performance in Spelling" (unpublished Ph.D. thesis, School
of Education, University of Michigan, 1937).

101J. C. Flanagan, "Units, Scores, and Norms," Edu-
cational Measurement, ed. E. F. Lindquist (Washington, D.C.:
American CCunciI of Education, 1951), p. 722.

 

 

If! Alt lull-.i

23
There are very few areas in which any one ever
attains complete maturity. It is also extremely
difficult to place the zero point in a practical
situation. Therefore, although learning expressed
in equal time units appearszn;first consideration
to be an excellent idea, it does not seem practical
for the typical kinds of educational measurement
in current use.

Tyler102 discusses the Courtis method indirectly
in a critique on Millard's work with height and reading
relationships. One of his objections has to do with the
difficulty of obtaining in our present schools, the nec-
essary measurements from which to base the determination
of the age at which the child would begin to read. Another
deals with the use of "extrapolation" in determining
beginning and ending points of cycles.

The use of extrapolation, from derived Courtis
equations to obtain figures, which are not obtainable by
direct measurement, is upheld by Dearborn and Rothney103
in their exhaustive study of the prediction of development
in children. The foregoing authors offered another method
for obtaining the maxima, which they felt to be a more
accurate, though more time consuming procedure.

Meredith104 attempted to apply the Courtis method

to test its usefulness on Six selected cases using only

 

102Tylep, "Concepts of Organismic Growth," op. cit.,
pp. 321-342.

 

103Dearborn and Rothney, Predicting the Child‘s
Develppment, pp. cit., pp. 213-237. '

 

104Meredith,-"The Rhythm of Physical Growth," pp.
cit., p. 120.

*

24
three measures each, between the ages of seven years and
nine years, nine months. He reported his results as
follows:

Critical evaluation is made of the . . . Courtis

‘"universal law" method of prediction individual
growth . . . (and) is considered unsuited to the
prediction of individual growth in stature for white
males between six and eleven years.

Nally and DeLonglO5 reworked Meredith's data and
found errors of computation which caused him to find
erroneous maxima. From the results of their study, Nally
and DeLong concluded, "that Courtis' law of growth is
applicable for the prediction of growth in stature with
an accuracy that is within rigorous scientific limits. . "

Doctoral candidates at Michigan State University
have used the Courtis method. Nally106 employed this
technique in suggesting that reading achievement and height
of children have a definite relationship. Kowitz107

applied this method to social ranking and developmental

 

105T. P. Nally and A. R. DeLong, "An Appraisal of
a Method of Predicting Growth," Series II, No. 1 (East
Lansing, Mich.: Child Development Laboratory, 1952).

106T. 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).

107Kowitz, op. cit.

25
height and weight to demonstrate its use still further.
Rusch108 also established broad relationships between
height and weight. Udoh109 found relationships between

maturity in height growth and advent of menarche in girls.

 

108Rusch, op. cit.

109Udoh, op; cit.

CHAPTER III

PROCEDURE

Data

 

The data used in this study were taken from
material available in the Child Development Laboratory
at Michigan State University. The forty-four cases,
twenty-six boys and eighteen girls, are part of approxi-
mately three hundred children of the Dearborn, Michigan
study. Data on these children were obtained by teachers
trained in techniques of proper measurement, under the
directon of Dr. C. V. Millard.

Cases used in this study were selected to fit the
following criteria: (1) Measures to include a span of
from 96 months through 180 months. This age range was
chosen so that the material would encompass two cycles
of growth.110 (2) When plotted upon logarithmic graph
paper each cycle must have contained three measures of
both height and weight in both the pre-adolescent and the
adolescent cycles of growth. No attempt was made to

obtain a random sample.

 

 

llOMillard, Child Growth and Development ip the
Elementary School, op. cit., p. 65.

 

27

Figure 1 shows a summary of the magnitude of
measures of height and weight. A detailed tabulation of
each individual case, including the range of the measures,
may be found in Appendices A and B.

The boys of this study have an average I.Q. of 106.7,
and the girls an average I.Q. of 107.1; resulting in a
combined average I.Q. of 106.8. Figure 2 is a frequenCy
histogram showing the distribution of I.Q.‘s. Individual
I.Q.‘s may be found in Appendix C. The standard deviation
for the total I.Q.‘s is 9.2, which shows a close grouping
within the ranges of average intelligence.

The parents of the children of the Dearborn study
were found to fit the Class IV grouping of the Sims111
socio-economic rating scale which was administered'to
them. This grouping, which consists of skilled laborers
working for someone else, building trades, transportation
trades, and manufacturing trades involving skilled labor,

coincides with Terman's112

rating of Class III. Forty-five
per cent of our national population falls within this

classification according to Terman.113 The Terman Class III

 

111Verner M. Sims, The Measurement 93 Socio-Economic
Status (Bloomington, Illinois: Bloomington Public Schools
PuBlIshing Company, 1928), passim.

 

 

112Lewis M. Terman and Maud A. Merrill, Measurin
Intelligence (Boston: Houghton Mifflin CompanyT—I9397jgi
p.*H8.

 

113Ibid.

28

Number of
Cases

22

 

 

 

 

 

 

 

 

 

 

 

o I of I ll

12 13 14 15 16 17 18 19 2O 21 22

 

Number of height measures

Number of
Cases

12 1%
lO

 

 

 

 

 

 

2 l— _

7 8 9 10 11 12* 13

 

 

0

Number of weight measures

Figure 1. Number of Measures Including
Both Sexes and Both Cycles

Number of
Cases

14
13
12

11

10

 

 

 

 

 

 

 

 

 

[—1111 I]

29

 

75 8o 85 9o 95 100 105 110 115 120 125 130
Intelligence quotients

Figure 2. Distribution of Intelligence
Quotients Including Both Sexes

30
average I.Q. of 107 and the average I.Q. of the forty-four
cases of this study (106.8) show very evident close agree-
ment, which is significant at the five per cent level of
confidence. Hollingshead would place the parents of the
children in this study in his Class III category.

Forty-two percent of the . . . . families in
Class III own small businesses, farms, or are
independent professionals. The other 58 percent
derive their livelihood from wages and salaries.11"
According to the ‘Revised Scale for Rating
115

Occupation‘ by Warner, the occupations of the fathers
of the children of this study place their families in
Class IV. This class includes proprietors and managers
of businesses valued at $2,000 to $5,000; factory fore-
men; and owners of electrical, plumbing, carpentery, and
watch repair businesses.

Each of these classifications places the children

in a mid or central position of social stratification.

Method
In order to study human growth relationships it is
necessary that unequivalent units of measures be equated

in some manner. The Courtis method, which is utilized

 

114A. B. Hollingshead, Elmtown‘s Youth (New York:
John Wiley and Sons, Inc., 1949), p. 96.

 

115W. L. Warner, et a1, Social Class in America

(Epingo: Science Resea66h_Associates, Inc., 1949), pp.

 

31
in this study, accomplishes this by converting all measures
to equal units called ‘isocrons.‘ The Courtis method, an
adaptation of the Gompertz Function y = kirt, reduces the

cyclic pattern of growth to the mathematical formula

I)

y k #rt i i] in which y = achieved growth, k = maximum,
r = rate, t = time, i = incipiency, and § ] = enclosure
of isocronic values. A detailed explanation of this

method is given in Courtis‘ manual, Maturation Units and
116

 

11211215211122-

Original measures, for each case, were processed by
the Courtis method to obtain an equation for two cycles of
height and weight growth each. As a purpose of this study
is to determine the accuracy with which the Courtis Method
describes growth, the predicted scores were calculated as
closely as possible to the actual measures. The average
deviation of predicted measures from actual measures was
calculated without consideration of sign.

All subsequent derived scores were determined from
the above equations as follows:

1. b1 -- substitute the isocronic value for 1 per
cent (14.73) for ‘y‘ in the individual equation, and solve
for ‘t‘. Omit ‘k‘ from the equation.

2. t1 and/or t2 -- substitute the isocronic value

for 99 per cent (76.00) for ‘y‘ in the individual

 

116Obtainable from S. A. Courtis, 9110 Dwight
Avenue, Detroit 14, Michigan.

32

equation of the cycle desired. Omit ‘k‘ from the
equation.

3. cl -- substitute the age of the beginning of
the adolescent cycle, as found in (1) above, into the
adolescent equation and solve for ‘y‘.

4. Per cent of pre-adolescent cycle attained at
the beginning of the adolescent cycle as follows:
bl % k1 x 100.

5. Per cent of total maturity attained at the
beginning of the adolescent cycle as follows: bl f k3 x 100.

Correlations were obtained through use of the ‘rank-

difference‘ method, for which the formula is:

r=l_ 5(1))?

n(n2 - l)

CHAPTER IV

ANALYSIS OF THE DATA AND DISCUSSION
OF RESULTS

Through the use of the Courtis method of describing
growth, disparate measures become amenable to mathematical
and graphical comparison. The reduction of seriatim
measures into a formula with the constants; rate, maximum,
and incipiency, makes possible detailed analysis of these
commonly accepted, but seldom specifically differentiated,
components of the growth cycle.

Height and weight growth was described with
gratifying accuracy by the above method. The deviation
of predicted measures from actual measures was in all
cases within the two per cent limits specified by Courtis}l7
A list of these deviations may be found in Appendix H.

The average of all boy‘s height deviations was .182 inches
with a range of .094 through .256 inches. The average
boy‘s weight deviations was .811 pounds with a range of
.143 through 1.5 pounds. The average of the girl‘s height
deviations was .2 inches with a range of .106 through .283

inches. The average of the girl‘s weight deviations was

 

117Courtis, Maturation Units and How pp Use Them,
op. cit., p. 129.

 

 

34

.885 with a range of .106 through 1.855 pounds. These
deviations are all within the acceptance limits of the
error of measurement established for the collection of
anthropometric measurements by Dearborn and Rothney.118

Three cases were chosen by chance to demonstrate
graphically the adequacy of the method employed in this
study (Figures 3 through 8).

Even a cursory inspection of deviations of pre-
dicted scores from actual measured scores would reveal
that height scores are more closely described by the Courtis
method than are weight scores. Such results are only
natural, as other studies have shown that monthly gains in
weight are more variable than gains in height.119’120
Some possible reasons for such weight variability are:
(1) weight scores are easily and suddenly alterable by

oral acquisition, or by anal elimination of liquid or solid

substances, (2) weight has been found to fluctuate with

 

118Dearborn and Rothney, Predicting the Child‘s
Development, op. cit., p. 83.

 

 

119Meinhard Robinow,'"The Variability of Weight and
Height Increments from Birth to Six Years," Child Develpp-
ment, June, 1942, Vol. 13, No. 2, pp. 159-164.

 

120C. E. Palmer, et a1, "Anthropometric Studies
of Individual Growth. IIT'_Age, Weight, and Rate of
Growth in Weight, Elementary School Children," Child
Development, Vol. 8, No. l.

 

 

[I.IIl-Iiltllflinillll) .. .IJ. .lllllllll.

35

 

 

Inches

63-

60 h-

55F

50"
{ Actual ---—-
' Predicted

45 | J J .L i

O 100 120 140 160 180

 

Chronological Age (months)

Figure 3. Case 83M Height

120 )-

110p

100

I

90

I

Pounds

80 .

70

U

 

Actual —-——-—-
Predicted——————”

 

40 L 1 J J
O 100 120 1140 160 180 190

Chronological Age (months)

Figure 4. Case 83M Weight

 

 

37

 

63 -
60 P
55 P
[O
o
.c
0
c
r H
50 .
Actual —- - -—
Predicted
115 J L I I l 1
80 100 120 140 160 180 190

Figure 5.

Chronological Age (months)

Case ll8F Height

38

110:-

100-:

80F

Pounds

 

Actual -- —- —-
Predicted

50'

 

)40 J_ .l L J l _l
80 100 120 140 160 180 190
Chronological Age (months)

Figure 6. Case 118 F Weight

 

39

 

 

 

63-
60 t
551'
[D
o
.c
U
a
H
50 '
Actual -" '-"‘ ""
Predicted
245 _I_ l J L I
80 100 120 140 160 180
Chronological Age (months)

Figure 7.

Case 176M Height

4O

     

 

 

 

9C-
80.
01 7O )-
'o
5
o
a.
60 r
/ Actual -——-———
50.. Predicted
[40 _L _l L I L J
80 100 120 140 160 180 190

Chronological Age (Months)

Figure 8. Case 176 M Weight

41

the season of the year121’1‘22’123

as does height. Even
though height is relatively steady in its growth pattern,
it is subject to variability due to compression of the
spinal disks.12" Then, too, both height and weight may
show unreal variance because of errors of measurement.125
Figures 9 and 10 show how height deviations cluster closely
around zero, while weight deviations are more widely
dispersed.

As the Courtis method has been shown to be accurate
for describing height and weight growth, attention may be
given to the use of this technique to derive correlations
between various aspects of growth.

Correlations found by using the rates of height and

weight equations, were generally low and inconclusive

 

121A. B. Fitt, "Seasonal Influence on Growth Function
and Inheritance," New Zeland Council for Educational
Research (New Zeland: Whitcombe and Tombs, Ltd., 1941),
pp. 1-182.

 

 

122C. E. Turner and Alfred Nordstrom, "Extent and
Seasonal Variations of Intermittency in Growth," American
Journal pg Public Health, 1938, Vol. 28, pp. 499-505.

 

 

123E. A. Reynolds and L. W. Sontag, "Seasonal
Variations in Weight, Height, and Appearance of Ossification
Centers," The Journal 23 Pediatrics, 1944, Vol. 24, pp.
524-535-

 

 

124Krogman,‘"A Handbook of the Measurement and
Interpretation of Height and Weight in the Growing Child,"

02. Cit., p. 19'

125H. M. Walker and J. Lev, Statistical Inference
(New York: Henry Holt and Company, 1953), pp. 293-295.

 

42

1 Mean Deviation i .191
75 Range -1.35 thru +1.87
Total Number of
Measures 678
150 r h

F

125

100

T

Number of Scores

75

 

 

 

J __I J

 

-2 -1 0 +1 +2
Deviations in Inches

Figure 9. Distribution of Height Predicted
Scores from Actual Measures

Number of Scores

43

Mean Deviation i .848
Range -8.95 thru +6.99
Total Number of Measures 379

150

r

125 '

lOO -

T

75

 

 

 

.L 1 J L l
-2 -1 0 +1 +2 +3
Deviation in Pounds

Figure 10. Distribution of Weight Predicted
Scores from Actual Measures

44
(Table I). When rl height was correlated with the corres-

ponding rl weight, the boys‘ +.53 was significant at the
five per cent level. The girls‘ +.06, however, was not.
Correlations obtained between the height r2 and weight r2
resulted in much the same values. The boys‘ correlation
of +.44 was again significant, while the girls‘ +.06 once
again was not.

Height rl when correlated with height r2 gave a corre-
lation of +.O7 for the boys, and +.29 for the girls. Neither
figure was significant at the five per cent level. Weight
r1 when correlated with weight r2 produced wide differences.
The boys‘ correlation was -.14, while the girls‘ correlation
of +.4l was positively significant at the five per cent
level.

Therefore, even though some of the correlations
were significant at the five per cent level of confidence,
the rate correlations were not large enough to be used for
prediction. However, as all but one correlation was posi-
tive, there is a tendency for all rates to maintain their
position as to magnitude. In other words, faster growers
in height tend to be faster in weight growth, and faster
growers in the pre-adolescent cycle tend to be the faster
growers in the adolescent cycle.

The correlations obtained from predicted maxima
show an interesting pattern of growth. Four negative

correlations stand out from the host of positive

45

TABLE I

RATE CORRELATIONS

 

 

Boys Girls
rl height with rl weight +.53 (sig) +.06
r2 height with r2 weight +.44 (sig) +.06
r1 height with r2 height +.07 +.29
r1 weight with r2 weight -.14 +.41(sig)
m m

 

 

correlations, (Table 11). These four--two for boys and
two for girls-~are obtained by comparing the maxima of a
growth of the pre-adolescent cycle, with the maxima of the
same growth of the adolescent cycle. These negative
correlations are not large enough for predictive use. But
they do show a tendency, on the part of those who are
growing to high pre-adolescent maxima, to grow to smaller
maxima in the adolescent cycle. Vice versa, those growing
toward lower pre-adolescent maxima tend to grow to larger
adolescent maxima.

Herein lies a possible explanation of the cause of
the lower-than-perfect positive correlations obtained when
pre-adolescent (kl) and adolescent (k2) maxima are compared
with final or total (k3) maturities. As the negative
correlations are not large enough for predictive use, this

may be an inclination toward moderation of the extremes.

TABLE II

MAXIMA CORRELATIONS

46

 

 

 

__-

_-

 

 

I

A-

 

Boys Girls
kl height with k1 weight +.35 (sig) +.30
k2 height with k2 weight +.59 (sig) +.23
k3 height with k3 weight +.10 +.02
k1 height with k2 height -.38 (sig) -.41 (sig)
k1 height with k3 height +.70 (sig) +.67 (sig)
k2 height with k3 height +.38 (sig) +.41 (sig)
k1 weight with k2 weight -.14 -.27
k1 weight with k3 weight +.47 (sig) +.73 (sig)
kg weight with k3 weight +.62 (sig) +.47 (sig)

 

 

The very low correlations obtained when comparing

total maturities (k3) of height and weight may be a re-

flection of differences in body build.

correlation was obtained for this,

If a perfect

it would mean that

people of equivalent heights would also be of equivalent

weight.

The correlations obtained in this study (+.1O

boys, +.O2 girls) would suggest that a certain height does

not presuppose a certain weight.

This lends support to

the belief that each person must be studied as an individual

126

rather than forcing them to fit a norm.

 

p.

l26Millard, Child Growth and Development, op. cit.,

31.

 

47
Correlations derived from ages attained at one per
cent of adolescent growth, 99 per cent of pre-adolescent
growth, and 99 per cent of adolescent growth (Table III)
showed much the same results as were obtained through
comparison of rates (Table I). Once again the correlations
are positive--except for boys‘ tl weight with t2 weight--
but too low for predictive purposes. Correlations between
height and weight at one per-cent of the adolescent cycle
(+.41 boys, +.59 girls) were significant at the five per

cent level for both boys and girls.

TABLE III

CORRELATIONS OF AGES AT SPECIFIC PER CENTS
OF DEVELOPMENT

 

Boys Girls
b1 height with bl weight +.41 (sig) +.59 (sig)
tl height with tl weight +.56 (sig) +.14
t2 height with t2 weight +.42 (sig) +.23
tl height with t2 height +.1l +.36
t1 weight with t2 weight -.13 +.28

 

Positively significant correlations resulted when
boys‘ height and weight ages at 99 per cent of the pre-

adolescent cycle were compared (+.56 and +.42 respectively).

 

 

 

 

48
The girls correlations obtained in a similar fashion were
positive, but not significant (+.14 and +.23 respectively).

Correlations of +.36 and +.28 which resulted from
comparing girls‘ height ages at 99 per cent of the pre-
adolescent and adolescent cycles and weight ages at the
same percentages were not significant. The boys‘ corre-
lations of +.11 and -.13 respectively were also not signi-
ficant.

A tendency for both boys‘ and girls' height ages to
increase in proportion to their weight ages is shown by
these correlations. Such results may be expected due to
positive correlations obtained when rates of height were
compared with rates of weight.

Correlations found between height or weight values
at one per cent of the adolescent cycle and various maxima
(Table IV) bear out the previous interpretations of this
study.

The correlations +.38 for boys and +.59 for girls
found by comparing height values (inches) at one per cent
of the adolescent cycle (cl) with weight values (pounds)
at a similar percentage were both significant at the five
per cent level. Both figures were too small for predictive
use. Thus, height and weight values at one per cent of the
adolescent cycle show an inclination to be of equal

rankings.

49

TABLE IV
CORRELATIONS OF VALUES ATTAINED

 

 

Boys Girls

 

c1 height with c1 weight +.38 (sig) +.59 (sig)

c1 height with k2 height .50 (sig) +.Ol

Cl weight with kg weight -.21 -.51 (sig)
cl height with k3 height -.12 +.06
c1 weight with k3 weight -.22 -.22

 

Correlations between the same growth factors, 1. e.
height with height, each using one per cent of the adoles-
cent cycle, produced negative results in all but two cases.
These negative correlations would further support the
implication that growth tends to reverse its magnitude
during_the adolescent cycle of growth. Even though some
of the correlations are significant at the five per cent
level of confidence, they are too low for predictive
purposes.

The negative correlations obtained here and in
Table II, when combined with the positive correlations
between rates of the pre-adolescent and adolescent cycles,
would suggest that those children with high maxima and
high rates for the pre-adolescent cycle, have high rates

and lower maxima for the adolescent cycle. This suggests

50

a pattern of growth that is short in time, but fast as
to growth gains, during the adolescent cycle. The converse
of the above pattern would be that those individuals with
low maxima and low rates in the pre-adolescent cycle would
tend to have relatively higher maxima and low rates in the
adolescent cycle. This adolescent cycle would be one of
small gains or increments, coupled with a long period of
growth.

Table V shows cases taken from this study which

illustrate the above patterns.

TABLE V

REVERSALS OF HEIGHT GROWTH PATTERNS

 

 

 

=================================================== :::k
Case Average 163M 129M
Preadolescent Maximum 62.6 . 68.0 59.0
Adolescent Maximum 7.8 . 7.0 . 10.0
Preadolescent Rate .23237 .27824 .16813
Adolescent Rate .72467 1.02429 .6382h
Length of Adol. Cycle 84.55 59.82 96.00

Percentages of development convert different values
to a single scale. Thus, it is possible to compare these
different values, within the same cycles and between cycles.
If growth relationships do exist, such relationships should

aDpear when values are converted and compared on the single

51
percentage scale. Table VI partially confirms the exist-

ence of such relationships.

TABLE VI

CORRELATIONS OF PERCENTAGES OF GROWTH AT BEGINNING
OF ADOLESCENT CYCLE

 

 

Boys Girls
d1 height with d1 weight +.39 (sig) +.07
d2 height with d2 weight +.47 (sig) -.o3
d1 height with d2 height +.51 (sig) +.59 (sig)
d1 weight with d2 weight +.61 (sig) +.46 (sig)

Percentage correlations were positive and signifi-
cant at the five per cent level, except for two figures.
These two were approximately zero (+.07 and -.03). The

remaining correlations (dl and d suggest the inclination

2)
for the percentages to maintain their relative positions
in height and weight, and between height and weight at the
time the adolescent cycle begins. However, the coeffici-
ents of correlation are not large enough to be used for
prediction.

The Courtis method, which made possible correlative
proceedures with speed of growth, timing of growth, and

Starting and ending points in cycles, did not produce

definite proof of relationships. However, it did indicate

52

some tendencies which may become more sharply defined upon
further study.

Correlative procedures were used to find the exist-
ence and strength of relationships at specific points of
the growth cycle. For a less precise, yet more encom-
passing consideration of growth, curves of constants were
graphed from scores derived from the average case (see
Appendices D--G). To show how these curves of this study
compared with other curves, the curves of constants were
plotted with height and weight age norms established by
C. V. Millard.127 The age norms, were calculated by cross-
sectional methods on data supplied by the United States
Department of Health, Education, and Welfare. Figures 11
and 12 portrayed much the same patterns. Boys height and
weight curves of constants started lower than the age norms,
slightly exceeded, dropped below at the beginning of the
adolescent cycle once again, exceeded once more, and finally
dropped below. The noticeably important difference in the
comparison of the girls curves was that the curves of
constants ended above that of the age norms.

The effect of cross-sectional averaging on the slope
of the curves was well illustrated by Figures 11 and 12.

Normatively cross-sectional curves were more gentle and

127C. v. Millard and J. w. M. Rothney, The Elementary
School Child: A Book of Cases (New York: The Dryden Press,

1957), pp.638-6A5.

 

53

Nmm mwm awm
a

COmemQEoo
c>s50 semecm .HH spawns

.eco pm: .mfisfie
sescm meeeamatec
.nco sz.nsom
aessm were .msom

 

omfl mma mmH noH

ELL

 

m:

m:

om

mm

mm

on

seuouI

5h

 

 

comfihmmsoo o>p50 pcwfioz .ma opswfim
mnucoz 2H mw< Hmofiwoaocopno
mmm mmm sow own” 03 «me boa em
_ _ q _ ~ _ 4‘ O:
..\ 18
\\\\
.u\.
x..\ cm
\
\u.\\
II--|.. .pmu sz.maefio \mv.
......... acsem nese.nasfic n
Ill .93 pm: .esom \ \.. nooH
35% were .nscm \ ....
a ..
.\H\ \
--u|--..\--\ \
\ .\ ioma
\ .
‘!\o\\\\\\
.:--..-.--- \
.u-.-..--t-. \
\
\ L
\ 03H
\

 

spunog

55
flat, while curves of constants were more prominent and
showed more definitely discernable cyclic starts.

A comparison of the curves of constants of the cases
in this study in like factors of growth (Figures 13 and 14)
revealed (1) that boys and girls growth is quite equivalent
until eleven years of age, at about which time the girls
start their adolescent growth, (2) that girls start and
finish their adolescent height and weight cycles before
the boys, (3) the girls cycles exceed those of the boys
from approximately twelve years to fourteen years of age,
and (4) the boys finally reach superiority in both factors
of growth between fourteen and fifteen years of age. Many
books mention this disparity in the growth of the sexes}?8

Still another way of examining the over-all design
of growth was utilized. Height and weight values were
converted into percentages of development, by dividing
each derived score by its total maturity value. The
resulting percentages of total maturity, when graphed,
described the curves shown in Figures 15 and 16. As was
readily seen, there was no crossing of curves in these two
figures. Girls‘ height and weight development were con-
tinually ahead of that of the boys. The girls' adolescent

height cycle began at 83.4 per cent of total development,

 

128Helen Thompson, Child Psychology, Leonard

Charmichael, ed., (New York: John Wiley and Sons, Inc.,
1946), p. 270.

 

56

pcwfiomuamucmumooo mo mo>mdo .MH omzwfim

mmm mmm :om omH mma mma moa um
_ u, a. . e1
mnpooz cfi mw< Hmoawoaocopno

    

x. macho mo wcficcfimmm
' II .II mHhHG
whom

 

 

seqouI

 

57

unwfimznnmucmumcoo mo mo>pdo .za mssmfim
mnpooz CH mw< HmOfionoooano

 

 

 

mew mmm mmm :om oma mma mma moH am
.41 41 . A» 4. a 4d . ,0:
om
om &
o
m.
x macho mo wchcfiwom s
III II 3.3.0 \
whom 4 OOH
nioma

 

 

 

 

ITO#H

58

mmwmpcmohmm pcwfimmunzuHmSpmz Hmuoe mo mm>p30

.mfi enemas

mcpcoz CH mw< Hmoawoaocopso

mmm sow owe mma
‘ ‘1

_ 41

x macho mo woficoawom
II I maps
whom

 

mma

 

4mma

J
0
ON

iOOH

 

squeo Jag

59

 

mmwwpcoopom uzwfimzuuzufipdomz Hence no mo>p50 .oa mpswfim
mcpooz CH mw< Hmofiwoaocosco
05m mmm mmm :om owa mma mma woa :w
+1 41 A 4 A a A a .
x
\.
\\\ i
.\
\
\
\
\ I
\\
.\
Mn
\ L
\
x macho mo wcficcfimom \
\ i
lllllu mafia \
i m%0m \\
\ a
\
\
\
\ I
\\

 

 

B 8
squeo Jed

0
CD

om

OOH

 

1 lllllll .. {it‘ll‘ .Il ( 1.1:!1 |.|.,I‘..|I|! ll! HI

60
and the boys' corresponding starting point was 82.2 per

cent of total development. Boys and girls adolescent weight
percentages at the beginning of the adolescent cycle were
even closer at 55.5 per cent for the boys and 55.9 per cent
for the girls. The above figures showed a close relation-
ship between the percentage of development at which both
sexes started their height and weight development.

When height and weight percentages of total maturity
at the beginning of the adolescent cycle, were graphed
according to sex (Figures 17 and 18), another relationship
was discernible. The starting times of the boysl height
and weight cycles were very nearly the same. Boys‘ adoles-
cent height began at 144 months, and their weight cycle
began at 145.5 months. A difference of only 1.5 months.

The difference between starting times for the girls
was greater as their adolescent height cycle began at 128
months, while their adolescent weight cycle began at 135
months.

Use of the Courtis method to view growth over a long
period of time revealed the advancement of girls' growth
timing over that of the boys and the similarity of adoles-
cent starting per cents and starting times within each sex.
Such close timing within both sexes leads one to conjecture
about the possibility of simultaneous starting times.

It is possible for two sets of scores, which are

very closely grouped about their means, to produce no, or

61

mowmpsoopom .mzomanhquSpwz Hmuoe mo mo>pSo

newcoz CH mw¢ Hmofiwoaocopco
owa
id

G J

OWN mmm mmm JON

Kmaozo no wcficcfiwom
l I. | magic
whom

 

oma

.ea themes

Nma

1

 

 

squeo Jag

OOH

62

mowmpooopom .mHechnszpSumz Hopoe mo mm>pzo .mH madem

ncpcoz CH ow< HmonoHooopno

 

me mmm mmm :ON omH omH NMH mOH
_ H d I! q 4 a J)
\\
\
\
\
gxx
\
_\
X mHon mo mchcmem

mHLHO
whom

 

 

O
[\-

8
squeo Jed

O
(I)

om

OOH

63

smal 1 correlations. This could be due to very small changes

in magnitude, yet moderate changes in ranking. The compil-

a‘cion of means, and deviations from those means necessary

for the last three figures, was a check upon the possibility

of Just such an occurrence.

The mean ages at which the adolescent cycles began

are shown in Figure 19. The boys' mean starting time was

142 .77 months for height and 143.85 months for weight.

These two ages were quite close. However, the standard

deviations of 8.83 months for height and 10.17 months for

Weight were large enough to show that prediction from the

means would be unreliable.

The same holds true for girls‘ height and weight

adolescent starting ages. The mean beginning time in

height for the girls was 127.16 months with a standard

deviation of 6.80 months. The mean beginning time in

Weight was 131.70 months with a standard deviation of 13.11
mOnths. Once again the mean starting times were quite
C’lcose, but both height and weight had large deviations.
Therefore, the use of the girls‘ mean starting time of the

ad olescent cycle in either height or weight for prediction

W<>Llld be of doubtful value.

Due to large standard deviations, the chronological

age at which the adolescent cycle began, has been shown to
be of little predictive value. When starting ages for each

(Ba-Se were converted into percentages of pre-adolescent

 

150

140 t

130

120

Months

100

90

 

Height

\C\

 

4?

 

"C\

 

 

Weight
/

x¢:\

I<3Lll
II) \

 

 

 

 

Height

 

 

X“

\
Weight

/‘¢\

 

 

 

\
Sé

 

64

\“c\

 

 

 

J\/ J/ ‘
so- \ /\/
7

Males Females
Figure 19. Age at which Adolescent Cycle Began

65

development, the standard deviations of height means for
both boys and girls dropped to less than three per cent.
The boys‘ mean of 91.43 per cent had a standard deviation
of 2.97 per cent, while the girls‘ mean of 92.22 per cent
had a standard deviation of 2.50 per cent. This is such
a small deviation that it can be said that boys and girls
adolescent height cycles start at 91.43 and 92.22 per cent
of their respective pre-adolescent height development.

Weight per cent of pre-adolescent development at
the beginning of the adolescent cycle, probably due to its
fluctuations of values and subsequent difficulty of
Smoothing, still showed a large standard deviation for
both boys and girls.

The girls' per cent of pre-adolescent development
0f 77.35 with a standard deviation of 9.71 was slightly
better than the boys‘ 75.60 per cent with a standard
deviation of 10.43 per cent. Though the mean starting
per- cents of development were close, the size of the
Standard deviations restricts their use for prediction.

Conversion of height and weight values to percent-
ages of total maturity improved weight standard deviations,
W1Bile leaving the height deviations approximately the same.
The boys' height mean percentage of 81.10 with a standard
dev:Lation of 2.83 per cent, compared favorably with the
girls‘ height mean of 82.96 per cent with a standard

deviation of 3.08 per cent. Boys‘ weight mean per cent of

Per Cents

90

80

7O

6O

50

4O

3O

20

 

VC\

43 43 6
.C.‘ .C I
b0 U)
H H
m m
U: 3

\

[/53

/

 

 

 

 

 

 

T“\

 

 

Height

\

//'Q

\

 

 

 

 

66

>‘c\

 

 

/
/
a
x “1
A
\
do
3,6
r \
$0
6"
/ N
/ \

 

 

 

Males

Figure 20.

Females

Per Cent of Pre-Adolescent Cycle
Attained when Adolescent Cycle Began

Per Cent

80

77(2)

60

50

:20

 

 

7 ll fell 4.]
le

 

 

 

 

 

 

 

1/‘1

 

 

 

 

 

 

67

 

 

 

at Beginning of Adolescent Cycle

m 'r-
77
6
V / ""
‘ r1 (\J W
p p
f 8 e 8
H .C H 4—3
s flgg/ eN gar,
. l/B‘N/
fl 5
r/ \ V) 5 5
JR) LUHW \,/ \/
' 4‘ K4 Tr 15
\4/ 4° 4‘
\./* ,
l A \/ \/
Males Females
Figure 21. Per Cent of Total Development Attained

 

. - 2.5..

 

 

 

 

 

 

68
53.48 with 6.84 as a standard deviation, and the girls'

weight mean per cent of 53.76 with 8.65 per cent as a

standard deviation were still a bit too large for pre-

dicti ve use .

The close agreement of height starting per cents
of both boys and girls, and also weight starting per cents,
8118888 bed the possibility of equal starting percentages

for eac h factor of growth regardless of sex.

The use of the Courtis method to derive starting
POUNDS of the adolescent cycle has proved of little value

as far

as chronological age is concerned. It did prove

or val—1233 when derived scores were changed to percentages

0f deve lopment. The comparison of mean starting percent-

ages Of both pre-adolescent and total growth produced
likene sses of height starting percentages and weight

Starting percentages without considering sex. Height

start; 111g percentages of development were grouped closely
about;

their mean, thus lending themselves to predictive
use .

Weight percentages of development were more dispersed

frown their means. Future studies may well show these

Star“hing percentages to be more similar.

 

CHAPTER V

SUMMARY, CONCLUSIONS, AND IMPLICATIONS

Summazéayr

'this study was conducted to test the accuracy with

whhfil 'tsfirje Courtis method describes height and weight growth,

to test; the use of correlative procedures on derivations of

this be chnique, and to use extrapolation to arrive at new

“13181113 8 into growth.
4911 cases used in this study were selected from the
Dearborn Data to meet the following criteria:
1. Measures must be included in a span of from
96 months through 180 months.
2. Each pre-adolescent and adolescent cycle must

contain at least three measures of both height

and weight.

The Inmeasures of twenty-six boys and eighteen girls met the

above criteria .

Height and weight growth equations were written for
eackl

were

case by use of the Courtis method. Predicted measures

fitted as closely as possible to actual measures.
Cyclic starting and ending times were obtained by

Subsitituting the isocronic values for one per cent and

99 loam-cent respectively, for 'y' in the above equations

 

 

70

and solving for ‘t' . Values attained at one per cent of

the adolescent cycle were obtained by substituting age at

one per cent for 't' in the pre-adolescent equation and

solving for 'y‘ . Percentages of development were obtained

by div iding derived scores by proper maxima.

Conclu S :ions

The Courtis method describes growth in height and

weight well within a two per cent average deviation}? Height

SPOth’l was described more accurately than weight growth.

The Courtis method describes height and weight growth so

accurately that it may be used to test for growth relation-

ships through various statistical techniques.

The correlative findings were as follows:

1. Correlations between rates were generally

positiVe. Some were significant at the five per cent level

or con fidence, but none were large enough to be used for
prediL<Etion.

2. Correlations between maxima were generally

positive--of which many were significant at the five per

cent; level. Four correlations were noticeably negative.

They were those of pre-adolescent height maxima correlated
With adolescent height maxima, and pre-adolescent weight
maxima correlated with adolescent weight maxima. This

w
ould seem to indicate that large pre-adolescent maxima are

f
c)llowed by small adolescent maxima and vice versa. No

c
Q.r‘l‘elations were large enough for predictive purposes.

*See pp. 42 and 43 for mean errors.

71
3 . Correlations of ages at one per cent of adoles-

cent growth, 99 per cent of pre—adolescent, and 99 per cent
of adole scent growth are generally positive, but too low
for pre dictive purposes.

LL. Correlations between the values of height and
weight attained at one per cent of the adolescent cycle,
and corresponding maxima tended to verify the suggestion
that larger pre-adolescent growth is followed by smaller

addescent growth, and smaller pre-adolescent growth is

followed by larger adolescent growth.

55. Correlations of percentages of development at
the beg :inning of the adolescent cycle were generally posi-

tive and significant but not large enough for predictive
use.

The use of the Courtis method to find growth rela-

tionsh Zips through correlative techniques did not produce

ou'C'S‘taj’iding results. Correlations obtained between final

maxima were no better than those noted in the Review of
Literature.

Comparison of the curves of constants revealed the
earl ier maturing of girls, which caused them to be heavier
and taller than the boys between the years of twelve to
four“been. Conversion of the curves of constants into
percentages of total development curves disclosed simil-

a
I‘th‘oies of adolescent starting ages, and percentages of

t
01353.1 development at the beginning of adolescent development.

72
Trhe mean ages at which the boys started their

adolescent height cycles was within 1.08 months of the

mean time of the starting of their weight cycles. The

girls mean height cycle starting time was only 4.54 months

before their mean weight cycle starting time. This close

agreement of mean starting times would suggest the possi-

bility of establishing a single starting age for factors

of adolescent growth. Wide standard deviations somewhat

diminshed such a possibility.

The means of boys and girls per cent of preadolescent

height. growth that was attained when the adolescent cycle

b68311 were within .79 per cent of each other. Mean weight

per Cents attained by boys and girls by the time the

adoles Qent cycle began were within 1.75 per cent.
quite

These

similar percentages would imply single percentage

POint'e at which height and weight adolescent growth would
begin - Weight standard deviations were still large, but

height standard deviations were small.

The mean percentages of total growth attained by
boys and girls at the beginning of adolescent growth in

height were within 1.86 per cent of each other. Mean

weight percentages attained at a like time were only .28

Per

cent from one another. Weight deviations were reduced,

and height deviations remained small. These figures added

1.3
o the implication that single starting percentages of

d
evelopment may be found through further study.

73
EBA—1 c ations

In order to best describe growth by use of the

Courti 8 method, accurate measuring of growth is essential.

Courti S states that three measures are all that is neces-

sary to define one cycle of growth. The writer would like

to rec ornmend that adequate describing of a cycle of growth

demand S at least four values within that cycle. Of course,

the more values within a cycle, the more adequately that

CYCle c an be described. This is especially true of weight,

as weight values are prone to fluctuation. As many of the

GQuati one of this study are based upon three measures in a
CYCIS , further research using data having more measures per

CYCle may prove the Courtis method of greater value.

This study has suggested the existence of several

POSSible height--weight relationships, which are worthy of

furthe I‘ study. The negative or reverse relationship between

height and weight values attained at the time of the
beginning of the adolescent cycle, and respective height

and Weight adolescent maxima, is one such area. The

e“stence of a uniform age at which boys start their

adolescent cycles in both height and weight, and girls,

likewise, is another area. A third area for further study

is tZl'le possibility of determining a uniform percentage of
adolescent or total height and weight deve10pment, which
m

ugh be attained before the adolescent cycle may begin.

T
he Courtis method offers a precise procedure for the

74
determination of the necessary age and percentage values.
it is hoped that more research will employ this technique

to good advantage.

BIBLIOGRAPHY

BIBLIOGRAPHY

Abernethy, Ethel M. "Relationships Between Mental and
Physical Growth, " Monographs of the Society for
Research in Child Development, _Vol. 1, No. 7,
viii80.

 

 

American Seating Company. Better Seating for America
Through Research, Testing, Inspection. Grand Rapids,
Michigan: American Seating Company, 1953.

Baldwin, B. T. "The Physical Growth of Children from Birth
to Maturity," University of 1Iowa Studies of Child
Welfare, 1921, Vol. 1,7No. .

 

 

 

. '"Physical Growth and Progress," Bulletin 19;
U+. 8. Bureau of Education. Washington, D. C.
Government Printing Office, 1914.

 

 

 

Baldwin, B. T., et a1. Hei ht-Weight Age Tables. New
York: American Chilg Health Association, 1923.

"Basic Body Measurements of School Age Children." U. S.
Department of Health, Education and Welfare.
Washington, D.C.: Government Printing Office, June,
1953.

Baum, M. P. and V. S. Vickers. "Anthropometric and
Orthopedic Examinations: A Technique for Use with
Children," Child Development Monographs, Vol.12,
No. 4, pp 339- 345

Bayer, L. M. and Nancy Bayley. "Directions for Measures
and Radiographs Used in Predicting Height," Child
Development Monographs, 1947, Vol. 18, No. 3, pp.
85487.

 

Bayley, Nancy. Studies in the Development of Young Children.
Berkeley, California: university of California
Press, 1940.

 

 

 

. "Tables for Predicting Adult Height from
Skeletal Age and Present Height, " Journal of
Pediatrics, Vol. 28, 1946, pp. 49-

Bloomers, P. , et al. "The Organismic Age Concept, " Journal
of Educational Psychology, 1955, Vol. 46, pp. 132- 48.

77

Boaz, Franz. "Observations on the Growth of Children,"
Science, Vol. 27, No. 1854, July, 1930, pp. 44-48.

Bruch, Hilde. "Obesity in Childhood: I. Physical Growth
and Development of Obese Children," American Journal
pf Diseases 9f Children, Vol. 58, No.3, pp. 457-484.

 

 

 

Chilxlren's Bureau of the United States Department of Labor.
References on the Physical Growth and Development 2:
the Normal Cfiild, No. 179. ‘Washington, D.C.:
Government Printing Office, 1927.

 

 

Cknnit de Buffon. "Sur l'accroissement successif des enfants,
Gueneau de Montbeillard mesure of 1759 a 1776,".
Oeuvres Completes. Paris: Furne and Pie, 1873,

Vol. III, pp. 174-176.

 

Courtis, S. A. Maturation Units and How 29 Use Them. Ann
Arbor, Michigan: Litho-printed. Edwards Bros.,1950.

. '"Maturation As A Factor in Diagnosis," The
34th Yearbook pf the Society for the Study pf
Education, 1935. V

 

 

 

 

. '"Maturation Units for the Measurement of
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APPENDICES

 

4 .l. . . ad. fitfllflilqa

 

 

 

 

kw me . mm HmH - Hm m mH 2mmH
HmH - mm mNH - mm m mH szH
mNH . mm mmH . mm OH NH zHNH
mNH - ON mNH . ON O NH ZNOH
HNH . mN moH - mN HH NH EHOH
:NH - Hm NNH - NN HH NH EmOH
NOH - mm moH . Hm m mH smoH
mNH - mm wNH - mm OH :H zme
OOH . Nm mNH - mm N :H 2mmH
NOH . mm ONH . HO O :H SmHH
mNH - mHH HmH.- OOH w mH zOHH
mNH - mm HmH - Om HH NH sz
HmH . NN mNH . NN mH NH 2mm
ONH . mOH mNH . :OH m mH sow
me - mm mmH - mm OH mH ZNN
mNH . mm mOH - NO O NH :HN
NwH . Nm mmH - mm HH NH 2mm
mNH . HOH HOH . mm O NH 2H0
OOH . no moH . HO HH NH 2mm
mNH.- HN mmH - HN OH Hm sz
me . 3N mmH . :N OH OH zOm
HNH . we mmH - we .OH mm 2m:
ONH . we OOH - mm OH NH 2::
NOH - mm :OH . mm OH NH 2m:
HNH . om HNH - om O NH sz
mNH . mN OOH - mN OH NH 2Nm

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panmz Ho mwcmm panmm Ho mwcmm uanoz Ho .02 pngmm Ho .02 .

 

 

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ONH mNH ON O NH OON
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ONH OOH mO OH NH OOO
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H.mozv mOOSmmmz A.mozv mwOSOOOE mmpzmmmz mmOSOOmz .oz mmwo
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87

APPENDIX C

INDIVIDUAL INTELLIGENCE QUOTIENTS

 

 

 

/
Males Females
A
( Case No I Q Case No. I. Q.
fl

2714 111.2 52F 106.8
3 1M 106.3 55F 125.6
4+ 2M 111.4 58F 94.5
444M 117.2 59F 104.7
445M 110.2 62F 106.8
5014 97.3 64F 108.2
5 114 120.5 65F 107.2
5 5M 104.8 69F 103.5
61M 103.1 71F 110.7
65M 86.8 78F 109.9
'7 1M 112.3 80F 101.3
77M 103.0 84F 112.7
80M 104.2 97F 109.0
8 3M 86.1 105F 108.5
87m 121.5 1181* 100.3
1 10131 99.0 189E 93.6
1 1 511 110.0 19011 103.2
1 2911 117.0 2271? 121.6

1 3 614 122.2

l 6211 109.0

1 631/! 121.5

1 6414 104.0

1 6711 104.6

173.11 109.5

17614 101.2

19514 79.2
Average I.Q. 106.7 107°1

Tetal Average I.Q.. 106.8

A
,_——

 

 

88

 

 

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OOH O0.00 - OOHOO. OH O0.0 + OOOOO. OO OHN
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HOH OH.OO - ONNHO. HH HN.NH+ OOOOH. OHH OHO
OOH OO.OO - ONOOO. ON OH.NH+ OOOOH. OHH OOO
OHH OO.OHH- NHONO. OH HO.OH+ HHOHO. OOH OHO
OHH O0.00H- OOOOO. OH ON.OO+ HHOHH. OOH OOO
OOH O0.00 - ONONO. OO OO.NH+ OOHOH. OHH OOH
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mHH mO.HO u ONmOO. mO O0.00+ NOOOH. OO OOO
EOEHsz Hmuoe OocmHOHOcH mumm ESEHsz OocmHOHocH mumm ESEHMOZ .oz OOOO
mH0OO pcmommHOOH mHoOO pcmommHOO<umam
r ,:.L rHHnunuunuuu

 

APPENDIX H--l

PREDIC TED HEIGHT SCORES

DEVIATION OF MEASURED HEIGHT SCORES FROM

 

92

 

/—-
555.9 Measured Predi cted Average
No. Age Inches Inches Deviations Deviation
fi
271’1 97 52.0 52.0 0 L.,...
109 54.5 54.72 +.22 .
114 55.5 55.68 +.18
121 57.0 56.83 -.17 w.
126 57.1 56.96 -.l-’4 7
130 58.0 58.14 +.14 ,‘
133 58.6 58.51 -.09
138 59.1 59.16 +.06
142 60.1 59.74 -.36
145 60.3 60.26 -.04
150 61.2 61.38 +.18
154 62.5 62.5 0
157 63.4 63.43 +.03
162 65.1 65.06 -.04
166 66.1 66.33 +.23
169 67.0 67.21 +.21
174 68.5 68.5 0
176 69.0 69.0 0 .116
31“ 90 44. 5 44.09 - . 41
2102 46.5 46.5 0
:114 49.2 48.68 -.52
119 - 49.5 49.5 0
123 50.0 50.16 +.16
126 50.6 50.62 +.02
131 51.0 51.41 +.41
:135 52.0 52.01 +.01
:138 52.2 52.40 +.20
143 53.0 53.13 +.13
147 53.4 53.66 +.26
150 53.6 54.02 +.42
155 54.4 54.65 +.25
159 55.0 55.11 +.11
l 62 55.5 55.44 -.06
167 56.0 56.02 +.02
171 56.5 56.6 +.10
174 57.2 57.2 0
179 58.6 58.61 +.01
183 60.1 60.1 0 .115

 

 

 

 

 

93

 

APPENDIX H--l (Continued)

OO"IIII:;;;;;—_ Measured Predicted Average

 

 

 

 

% m0 - Age Inches Inches Deviations Deviation
/
41 71 46.6 46.23 -.37
83 49.0 49.0 0
95 51.4 51.45 +.05
:107 54.0 53.60 -.40 ”elk”
1112 54.3 54.4 +510 {
:119 55.2 55.51 +.31 1
1124 55.5 56.21 +.71 i
2131 57.1 57.15 +.05 ;
1136 58.0 57.75 -.25
.143 58.6 58.61 +.01 a
148 59.4 59.24 -.16 2
152 60.5 59.98 -.52 a
155 60.7 60.7 0 L
160 62.2 62.28 +.08
164 63.0 63.64 +.64
167 65.0 64.65 -.35
‘172 66.1 66.1 0
:176 66.5 67.0 +.50 .250
""N‘ 92 48.2 48.2 0
104 51.0 50.81 -.19
116 52.7 52.78 +.08
121 53.3 53.43 + 13
128 54.3 54.3 0
133 54.7 54.91 +.21
137 55.5 55.44 ~06
.140 55.3 55.88 +.58
145 57.0 56.73 -.27
$149 57.5 57.5 0
:L52 58.0 58.16 +.16
3-57 59.0 59.33 +.33
1.61 60.4 60.33 -.07
164 60.4 61.07 +.67
3.69 62.5 62.28 -.22
3L76 63.5 63.97 +.47
3.81 65.6 64.94 —.66
1.85 65.7 65.7 0 .227
45M. 2102 52.1 51.94 - 16
‘114- 54.4 54.4 0
119 55.4 55.31 -.09
123 55.4 55.94 +.54
126 56.4 56.39 -.01
131 56.4 57.09 +.69
135 57.1 57.59 +.49

 

\\

 

 

 

 

APPENDIX H--l (Continued)

 

 

 

94

 

 

Case Measured Predicted Average
No. Age Inches Inches Deviations Deviation
45m: 138 58.0 58.0 0
con't;. 143 58.6 58.56 -.04

147 58.6 59.0 .40

150 59.5 59.5 0

155 60.4 60.42 +.02 r

159 61.7 61.47 -.23 1

162 62.4 62.4 0

167 63.6 63.85 +.25

171 64.7 64.91 +.21

174- 65.2 65.61 +.4l

179 66.7 66.54 -.16

183 67.1 67.12 +.02 .196
50M 98 45.4 45.43 +.03

110 47.6 48.06 +.46

122 50.2 50.2 . 0

127 51.0 50.98 -.02

134 51.7 51.98 +.28

139 52.3 52.6 +.30

143 53.0 53.04 +.04

146 53.4 53.41 +.01

151 54.2 54.04 -.16

155 54.7 54.68 -.02

158 55.3 55.3 0

163 56.4 56.62 +.22

167 58.0 57.78 -.22

170 58.6 58.6 0

175 60.1 59.82 -.28

179 60.6 60.61 +.01

182 61.2 61.08 -.12 .128
51M 107 51.1 51.1 .0

119 53.7 53.7 0

124 54.4 54.46 +.06

131 55.4 55.44 +.04

136 56.6 56.14 -.46

140 57.0 56.85 -.15

143 57.5 57.5 0

148 59.0 58.86 -.14

152 60.1 60.08 —.02

155 61.0 60.96 -.04

160 62.4 62.47 +.07

164 64.0 63.51 -.49

167 64.2 64.2 0

172 65.2 65.2 0

‘-.~ my. .tvw ......-.. ,.
l
1

 

 

95

. APPENDIX H--l (Continued)
W

 

Case Measured Predicted Average
No . Age Inches Inches Deviations Deviation
51M 176 65.7 65.78 +.08
conWtz. 179 66.0 66.17 +.l7
.184 67.0 66.69 -.31
188 _ 67.0 66.97 -.03 . .114
55M 88 49.7 49.7 0
100 52.6 52.8 +.20
112 55.3 55.34 +.04
117 56.2 56.27 +.07
124 57.5 57.45 -.05
129 58.2 58.31 +.11
133 59.3 59.01 —.29
136 59.6 59.6 0
141 60.5 60.71 +.2l
145 61.7 61.73 +.03
148 62.6 62.5 -.10
153 62.8 63.92 +1.12
157 65.0 65.0 0
160 65.4 65.77 +.37
165 67.4 67.07 -.33
169 68.0 68.0 0 .183
61M' 89 47.4 47.06 -.36
101 50.0 50.0 0
113 52.3 52.45 +.l5
117 53.1 53.17 +.07
125 54.4 54.44 +.04
129 55.0 55.0 0
137 56.2 '56.05 -.15
141 56.4 56.49 +.09
146 58.1 57.05 -1.05
149 58.1 57.38 -.72
153 58.1 57.91 —.19
158 59.1 58.71 -.39
161 _ 59.3 59.27 -.03 .217
65M 90 43.4 43.19 -.21
97 44.6 44.6 0
102 45.6 45.51 -.09
109 46.4 46.76 +.36
121 48.6 48.68 +.08
133 50.4 50.4 0
138 51.1 51.09 -.01
145 52.1 52.1 0
150 53.1 53.02 —.08

APPENDIX H--1 (Continued)

96

 

 

 

 

Case Measured Predicted Average
No. Age Inches Inches Deviations Deviation
65M 157 54.3 54.54 +.24
con‘t:. 162 55.0 55.74 +.74
166 56.4 56.69 +.29
169 57.7 57.36 -.34 mm
174 58.6 58.42 -.18 € ;
181 59.7 59.7 0 ' {
185 60.0 60.33 +.33 .184
71M 79 45.2 45.32 +.l2 1
84 46.5 46.5 0 Y
91 47.6 48.05 +.45 1 y
103 50.0 50.41 +.41 a J
115 52.4 52.42 +.02 "4
120 52.7 53.13 +.43
127 54.1 54.11 +.01
132 54.7 54.75 +.05
139 55.6 55.65 +.05
144 56.7 56.43 -.27
148 57.6 57.08 -.52
151 57.6 57.6 0
156 58.5 58.6 +.10
160 59.5 59.46 —.04
163 59.5 60.16 +.66 .189
77M 116 56.2 56.2 0
128 58.1 58.56 +.46
140 60.2 60.22 +.02
145 60.6 60.82 +.22
152 61.7 61.78 +.08
157 62.6 62.6 0
161 63.5 63.34 -.16
164 63.6 63.93 +.33
169 64.4 64.9 +.50
173 65.7 65.61 -.09
176 65.8 66.13 +.33
180 66.5 66.77 +.27
185 67.4 67.4 0 .189
80M 104 53.0 52.77 -.23
116 55.7 55.7 0
128 57.5 57.92 +.42
133 58.5 58.66 +.16
140 59.7 59.62 -.08
145 60.1 60.35 +.25
149 61.0 61.01 +.01

97
APPENDIX H--l (Continued)

 

rJ

 

 

 

Case Measured Predicted Average
No. Age Inches Inches Deviations Deviation
80M 152 61.6 61.6 0
con‘t. 157 62.5 62.68 +.18
161 63.5 63.58 +.08
164 63.7 64.26 +.56 (1.11
2168 65.1 65.18 +.08 g "
173 66.2 66.2 0 .158 3
83M 89 46.6 46.6 0 =
93 48.0 47.58 -.42
101 49.0 49.35 +.35
113 51.6 51.64 +.04
125 53.4 53.50 +.10 g ,
129 54.4 54.06 -.34 ::..g
137 55.0 55.06 +.06
141 56.1 55.58 -.52
149 57.0 56.74 -.26
153 57.4 57.4 0
158 58.6 58.33 -.27
161 58.6 58.96 +.38
165 59.4 59.84 +.44
170 61.0 60.98 -.02
173 61.7 61.66 -.04
177 61.7 62.51 +.81
182 63.0 63.59 +.59
185 64.2 64.20 0
189 65.2 64.95 -.25
194 66.0 65.78 -.22 .256
87M 112 52.2 52.2 0
124 54.6 54.91 +.31
136 57.0 57.02 +.02
140 57.7 57.66 +.16
148 58.7 58.75 +.05
150 60.0 59.04 —.96
157 60.5 60.17 -.33
160 60.7 60.7 0
164 62.0 61.47 -.53
169 62.5 62.57 +.07
172 63.2 63.2 0
176 64.0 63.97 -.03
181 65.6 64.77 -.83 .253
110M 100 51.2 51.15 -.05
112 53.7 53.7 0
124 55.2 55.56 +.36

APPENDIX H--l (Continued)

 

 

 

_—_
n;—

98

 

 

 

i—_ _*
______ w

 

Case Measured Predicted Average
No. Age Inches Inches Deviations Deviation
110M 136 57.6 56.88 . -.12
can't. 148 57.8 58.00 +.20
152 58.2 58.53 +.33
160 60.0 60.06 +.O6 F“
:164 61.1 61.1 0 z
169 62.4 62.56 +.16 ‘5
172 62.8 63.43 +.63 .
176 64.6 64.6 0 i
181 66.4 65.97 -.43 .195 ;
115M 101 50.7 50.62 H.08 ?
105 51.6 51.6 0 g
113 53 53.38 +.38
125 55.6 55.68 +.08
137 57.5 57.62 +.12
141 58.5 58.23 -.27
149 59.7 59.7 0
153 61.0 60.54 -.46
158 61.2 61.62 +.42
161 61.6 62.29 +.69
165 63.2 63.2 0
170 64.7 64.32 -.38 .240
129M 97 46.0 46.0 0
109 48.0 48.14 +.14
113 48.8 48.79 -.01
121 49.7 49.97 +.27
133 51.7 51.51 -.19
145 52.8 52.83 +.03
149 53.4 53.29 -.11
157 54.8 54.51 -.29
161 55.4 55.4 0
166 56.6 56.7 +.10
169 57.2 57.59 +.39
173 58.7 58.76 +.06
178 60.2 60.2 0 .122
136M 109 51.7 51.7 0
121 54.0 54.37 +.37
133 56.5 56.5 0
138 57.3 57.32 +.02
145 58.7 58.67 -.03
150 60.1 60.1 0
154 61.5 61.43 .07
157 62.7 62.47 .23

APPENDIX H--l (Continued)

99

 

 

‘
‘——‘

 

Case Measured Predicted Average
No. Age Inches Inches Deviations Deviation
136M 2162 64.0 64.04 +.04
con'tw 2166 65.1 65.11 +.01

169 66.0 65.83 -.17

173 66.6 66.6 0

178 67.1 67.38 +.28 .094
162M 113 56.2 56.2 0

125 58.7 59.23 +.53

137 61.5 61.43 -.07

141 62.0 62.0 0

149 63.0 63.02 +.02

153 64.7 63.72 -.98

161 65.7 65.7 0

165 67.0 67.0 0 .200
163M 120 56.7 56.71 +.01

132 59.7 59.7 0

137 60.5 60.72 +.22

144 62.0 61.95 -.05

149 62.7 62.74 +.04

153 63.5 63.49 -.01

156 64.2 64.2 0

161 65.5 65.75 +.25

165 67.2 67.15 -.05

166 67.5 67.55 +.05

172 68.6 69.47 +.87

177 70.8 70.8 0 .129
164M 96 48.1 48.1 0

108 50.6 50.75 +.l5

113 51.5 51.73 +.23

120 52.5 52.95 +.45

125 53.1 53.68 +.58

129 54.3 54.26 -.04

132 54.5 54.66 +.16

137 55.2 55.28 +.08

144 56.0 56.14 +.14

149 56.6 56.80 +.20

153 57.7 57.25 -.45

156 57.7 57.7 0

161 58.5 58.44 -.06

165 58.6 59.09 +.49

168 59.6 59.62 +.02

173 60.5 60.5 0

177 61.2 61.16 -.04 .182

APPENDIX H--l (Continued)

lOO

 

 

 

Case Measured Predicted Average

No. Age Inches Inches Deviations Deviation

167M 2100 49.7 49.7 0
112 52.4 52.32 -.08
117 52.7 53.13 +.43
124 54.3 54.14 -.16
129 54.7 54.84 +.14
133 55.0 55.49 +.49
136 56.2 56.08 -.12
141 57.2 57.2 0
148 59.0 59.08 +.08
153 60.1 60.46 +.36
157 61.7 61.49 -.21
160 62.1 62.21 +.11
165 63.5 63.24 -.26
169 63.8 63.94 +.14
172 64.5 64.35 -.15
177 65.1 64.98 -.12
181 65.1 65 37 +.27 .184

171M 101 49.0 49.0 0
113 51.5 51.9 +.40
125 53.5 53.46 -.04
137 55.6 55.68 +.08
142 56.2 56.2 0
147 57.1 56.68 -.42
154 57.6 57.6 0
158 58.7 57.89 -.81
161 59.0 59.01 +.01
166 60.1 60.32 +.22
170 61.5 61.38 -.12
173 62.2 62.2 0
177 62.7 63.16 +.46
182 64.5 64.23 -.27 .202

176M 97 50.0 50.0 0
109 53.4 52.08 -1.32
133 55.1 55.30 +.20
138 55.3 55.80 +.50
145 56.5 56.51 +.01
150 57.0 57.0 0
154 57.0 57.4 +.40
157 57.7 57.7 0
162 58.0 58.25 +.25
166 58.8 58.8 0
169 59.2 59.2 0
174 60.0 59.91 -.09

101

APPENDIX H-l--(Continued)

 

 

 

 

Case Measured Predicted Average
No. Age Inches Inches Deviations Deviation
176M‘ :178 60.0 60.5 +.50
con't. 179 60.8 60.65 -.15 .244
195m: 91 49.7 49.14 -.54

103 52.6 52.6 0

110 54.0 54.28 +.28

' 122 56.7 56.7 0

134 58.7 58.73 +.03

146 61.6 61.6 0

158 65.5 65.33 -.17

163 66.6 66.55 -.05

167 67.4 67.33 -.07

170 67.7 67.8 +.10

175 68.7 68.46 -.24

179 69.0 68.84 -.16

182 69.1 69.1 0

187 69.4 69.45 +.05

191 69.6 69.67 +.07 .117

Boys' Total Average Deviation .182

Boys' Range of Deviations .094 -- .256

1
—-_————

 

 

_DEVIATION OF MEASURED HEIGHT SCORES FROM

APPENDIX H--2

PREDICTED HEIGHT SCORES

102

 

 

 

Case» Measured Predicted Average
INO. Age Deviations Deviation
52F 102 52.0 51.0 -1.00
107 52.4 52.4 0
114 54.0 54.05 +.05
119 55.0 55.02 +.02
123 56.0 55.74 +.26
126 56.2 56.27 +.07
131 57.2 57.2 0
135 59.0 58.11 -.89
138 59.3 58.87 -.43
143 60.2 60.15 -.05
147 62.0 61.11 -.89
150 62.2 61.74 -.46
155 62.7 62.65 -.05
159 63.2 63.2 0
162 63.6 63.59 -.01
167 64.0 64.03 +.03
171 64.0 64.33 +.33 .267
55F 105 51.4 50.13 -1.27
112 52.6 52.6 0
117 54.0 54.0 0
121 55.0 54.94 -.06
124 55.6 55.6 0
129 56.4 56.64 +.24
133 57.6 57.6 0
136 58.3 58.45 +.15
141 60.2 59.96 +.24
145 61.7 61.2 -.50
148 62.0 62.11 +.1l
153 63.8 63.40 -.40
157 63.8 64.27 +.47
160 64.5 64.79 +.29
165 65.5 65.5 0
169 66.0 65.93 -.07 .238
58F 91 47.6 47.6 0
103 50.2 50.37 +.17
115 52.4 52.57 +.l7
120 53.5 53.29 -.21
127 54.2 54.25 +.05
139 56.0 55.83 -.17
144 56.6 56.6 0

APPENDIX H--2 (Continued)

103

 

IV

 

Case Measured Predic ted Average
2N0. Age Inches Inches Deviations Deviation
58F‘ 151 57.4 57.78 +.38
con't. 156 58.7 58.73 +.03

160 59.5 59.51 +.01

163 60.2 60.13 -.07

168 61.0 61.15 +.15

172 61.7 61.94 +.24

175 62.5 62.49 -.01

180 63.4 63.36 -.04

184 64.0 64.0 0 .106
59F 109 48.6 48.6 0

114 49.4 49.41 +.01

121 50.0 50.45 +.45

126 51.0 51.15 +.15

130 51.0 51.65 +.65

133 52.0 52.02 +.02

138 52.6 52.62 +.02

142 53.0 53.15 +.15

1’45 5306 53056 -.04

150 54.5 54.40 -.10

154 55.2 55.2 0

157 55.7 55.84 +.14

162 57.7 57.01 -.69

166 58.0 57.94 -.06

169 58.5 58.58 +.08

174 59.6 59.6 0

178 61.1 60.4 -.70 .192
62F 100 51.6 51.6 0

112 54.0 54.0 0

117 55.0 54.72 -.28

124 55.6 55.73 +.13

129 56.3 56.49 +.19

133 57.2 57.2 0

136 58.2 57.83 -.37

141 59.0 59.0 0

148 60.0 60.65 +.65

153 61.2 61.79 +.59

157 62.2 62.56 +.36

160 64.2 63.1 —1.07

165 64.2 63.9 -.26

169 64.4 64.4 0

172 64.4 64.75 +.35

177 65.2 65.19 -.01

181 65.2 65.48 +.28 .267

 

 

 

 

APPENDIX H--2 (Continued)

104

 

 

Case Measured Predicted Average
No. Age Inches Inches Deviations Deviation
64F 90 45.6 45.6 0
97 50.1 48.91 -1.19
109 53.0 52.88 -.12
121 55.2 55.2 0
126 56.0 55.90 -.10
133 57.2 56.76 -.44
138 58.0 57.96 -.04
142 59.6 59.32 -.28
145 60.4 60.4 .0
150 61.6 61.79 +.19
154 62.4 62.61 +.21
157 63.0 63.0 0
162 63.5 63.48 -.02
166 63.7 63.71 +.01
169 63.8 63.83 +.03
174 63.6 63.97 +.37
178 63.8 64.04 +.24
181 63.8 64.08 +.28 .196
55F 93 50.3 50.3 0
105 52.4 52.53 +.13
110 53.0 53.29 +.29
117 54.2 54.2 0
122 54.4 54.84 +.44
126 56.0 55.48 H.52
129 56.2 56.11 -.09
134 57.4 57.37 -.03
141 59.1 59.1 0
146 60.0 60.09 +.09
150 61.0 60.67 -.33
153 61.1 61.06 -.04
158 62.0 61.5 -.50
162 61.5 61.81 +.31
165 62.0 62.0 0
170 62.2 62.19 -.01
174 62.4 62.35 -.05 .166
69F 86 49.0 49.0 0
98 52.0 52.29 +.29
110 54.6 54.91 +.31
114 55.6 55.68 +.08
122 57.0 57.05 +.05
134‘ 59.4 59.33 -.O7
138 60.4 60.24 -.16
143 61.4 61.4 0

 

105

APPENDIX H--2 (Continued)

 

 

Case Measured Predicted Average
No. Age Inches Inches Deviations Deviation
69F 146 62.0 62.12 +.12
con'tw 150 63.2 62.95 -.25

155 63.6 63.93 +.33

158 64.2 64.43 +.23

162 65.2 65.04 -.16 .158
71F 91 50.2 50.2 0

103 52.6 52.94 +.34

115 55.1 55.04 ~.06

127 56.6 57.17 +.57

139 60. 0 60.01 +.01

144 60. 4 61.16 +.76

148 62. 0 62.0 0

151 63.0 62.56 -.44

156 63.4- 63.36 -.04

160 64.2 63.86 -.34

163 64.2 64.2 0

167' 64.7 64.56 -.14

172 65. 0 64.97 -.03

175 65. 0 65.15 +.15 .206
78F 76 45.6 45.9 +.30

81 47. 0 47.0 0

85 48. 4 47.82 -.58

100 50. 6 50.63 +.03

112 52.3 52.43 +.13

117 53.1 53.1 0

124 54.4 54.03 -.37

136 57.0 56.20 -.80

141 57.4 57.49 +.09

145 58.6 58.6 0

148 59. 4 59.38 -.02

153 ' 60. 6 60.54 -.06

157 61. 2 61.33 +.13

160 61.6 61.86 +.26

164 62.7 62.44 -.26

169 63.0 63.03 +.03

172 63.2 63.35 +.15

176 63. 7 63.70 0

181 63. 8 64.07 +.27 .183
80F 88 42.0 42.0 0

100 45.4 45.39 -.01

109 47. 1 47.1 0

117 48. O 48.20 +.20

 

 

 

 

 

 

 

 

 

 

 

 

 

106
APPENDIX H--2 (Continued)
Case» Measured Predicted Average
No. Age Inches Inches Deviations Deviation
80F‘ .124 49.4 48.93 -.47
can‘t. 136 51.1 50.66 -.44
141 ' 52.0 52.0 0
145 53.0 53.25 +.25
148 54.4 54.24 -.16
153 55.6 55.82 +.22
157 57.2 56.92 -.28
160 5707 57.62 -008
164 58.5 58.42 -.08
169 59.2 59.2 0
176 60.2 60.05 -.15
181 60.2 60.32 +.12 .154
84F 106 50.7 50.8 +.10
111 52.2 52.2 0
118 53.7 53.75 +.05
130 55.7 56.04 +.34
135 56.2 57.25 +1.05
139 58.0 58.35 +.35
142 59.2 59.2 0
147 60.7 60.49 -.21
151 61.2 61.37 +.l7
154 61.7 61.94 +.24
159 62.7 62.7 ' 0
163 . 63.5 63.15 -.35
166 63.5 63.4 -.10
171 63.5 63.75 +.25
175 63.7 63.97 +.27 .232
97F 111 51.1 51.1 0
123 54.0 54.0 0
135 56.0 56.0 0
139 56.5 56.51 +.01
147 58.7 57.79 -.91
151 58.7 58.7 0
156 59.7 59.79 +.O9
159 60.0 60.34 +.34
163 61.0 60.96 -.04
168 61.5 61.5 0 .140
105F 109 49.5 49.5 0
113 50.5 50.12 -.38
121 51.2 51.28 +.08
133 53.5 53.5 0
145 56.5 56.63 +.13

 

 

—
fl

APPENDIX H--2 (Continued)

 

 

 

 

 

 

107

 

 

 

 

 

 

 

Case Measured Predicted Average
N0. Age Inches Inches Deviations Deviation
lO5F 149 58.0 57.68 -.32
cont. 157 57.6 59.47 +1.87

161 60.2 60.163 -.04

166 61.0 60.93 -.07

169 61.2 61.30 +.10

173 61.7 61.7 0

178 61.7 62.14 +.44 .283
118F 94 47.7 45.65 -.05

106 49.2 49.2 0

118 51.0 51.65 +.65

130 53.5 53.58 +.08

142 55.7 55.7 0

147 57.0 55.26 +.26

151 59.2 58.56 -.64

154 59.2 59.53 +.33

159 60.5 60.86 +.36

163 61.7 61.7 0

166 62.2 62.2 0

171 62.5 62.9 +.40

175 63.2 63.28 +.08 .219
189F 108 49.7 49.7 O

120 52.5 52.68 +.l8

124 53.5 53.52 +.02

132 55.0 55.08 +.08

144 57.7 57.7 0

160 62.0 60.84 —1.16

168 63.2 63.49 +.29

172 64.2 64.2 0

177 65.2 64.99 +.21

180 65.2 65.37 +.l7

184 66.0 65.83 -.17

189 66.2 66.28 +.08 .197
19(DF 87 45.2 45.18 -.02

92 46.0 46.0 0

99 47.4 48.36 +.76

111 50.6 50.94 +.34

123 53.0 53.0 0

135 56.0 54.65 -1.35

147 58.2 58.2 0

152 59.2 59.79 +.59

156 60.7 60.7 0

159 61.0 61.24 +.24

a“

APPENDIX H--2 (Continued)

108

 

 

Case Measured Predicted Average
No. Age Inches Inches Deviations Deviation
l90F 164 62.0 61.90 -.10
cont. 168 62.2 62.35 +.15

171 62.5 62.5 0

175 63.0 62.73 -.27

180 63.0 63.0 0 .255
227R 80 47.0 46.81 -.19

88. 49.0 49.0 0

100 51.4 51.77 +.34

104 52.7 52.58 -.12

112 54.0 54.01 +.01

124 56.5 56.17 -.33

136 59.0 59.0 0

140 60.5 60.13 —.37

148 62.0 62.10 +.10

152 63.0 62.96 —.04

157 64.2 63.87 —.33

160 64.5 64.37 -.13

164 65.2 65.10 -.10

169 65.5 65.5 0 .147

Girls' Total Average Deviation .200

Girls' Range of Deviations .106 -- .283

 

 

 

109

APPENDIX H--3

DEVIATION OF PREDICTED WEIGHT SCORE FROM
ACTUAL WEIGHT SCORE

 

r—
t

 

Case Measured Predicted Average
No. Age Pounds Pounds Deviations Deviation
27M 86 55.3 55.3 0

97 65.0 61.61 -3.39

109 63.3 68.08 +4.78

121 74.2 74.2 0

133 82.2 79.85 -2.35

145 85.0 85.12 + .12

157 99.0 99.0 O

169 125.5 125.5 0

175 135.7 135.75 + .05 1.188
31M 126 56.2 56.2 0

138 61.0 61.75 + .75

150 67.0 67.0 0

162 73.0 73.0 0

168 78.5 78.39 - .11

174 84.5 84.5 0 .143
42M 71 47.2 47.2 0

83 53.0 54.02 +1.02

95 61.2 59.94 -l.26

108 65.2 65.33 + .13

119 69.1 69.1 0

131 77.1 72.79 -8.95

143 82.1 82.1 0

155 102.2 102.18 - .02

167 112.7 112.7 0 1.264
44M 80 45.2 45.2 0

92 52.2 52.73 + .53

104 60.0 59.08 - .92

116 64.2 64.23 + .03

128 68.3 68.45 + .15

140 74.3 74.3 0

152 87.1 87.11 + .01

164 100.0 105.31 +5.31

176 122.2 122.2 0 .772
45M 90 58.1 58.1 0

102 66. 66.47 + .37

114 74.2 74.2 0

126 81.1 81.06 - .04

138 94.3 88.77 -5.57

 

APPENDIX H--3 (Continued)

llO

 

 

 

Case Measured Predicted Average
No. Age Pounds Pounds Deviations Deviation
45M 150 105.3 105.3 0
con't. 162 118.7 124.73 -6.03

174 138.2 138.2 0 1.500
50M 86 42.0 41.69 - .36

98 47.0 47.0 0

110 52.2 52.2 0

122 58.3 57.12 -1.18

134 61.1 61.85 + .75

146 66.2 67.84 +1.64

158 75.2 75.2 0

170 92.5 92.51 + .01

182 108.0 108.0 0 .440
51M 95 53.0 53.0 O

107 66.3 62.4 +3.60

119 71.3 70.5 - .80

131 77.2 77.2 0

143 83.3 83.25 - .05

155 97.2 97.2 0

167 112.5 117.09 +4.59

179 130.2 130.2 0 1.130
55M 88 52.2 52.2 0

100 60.3 60.44 + .14

112 68.0 67.89 - .02

124 75.0 75.01 + .01

136 84.2 82.11 -2.09

148 95.0 95.0 0

154 106.5 104.90 -1.60

160 111.0 116.05 +5.05

166 127.2 127.2 0 .990
61M 101 55.0 55.0 0

113 62.1 62.04 - .06

125 68.1 68.53 + .43

137 74.3 74.3 0

149 80.3 80.3 0

161 89.3 89.4 + .10

167 95.5 95.5 0

173 101.5 102.21 + .71

179 110.0 108.89 -1 11 .268
65M 109 54.1 54.1 0

121 60.0 60.69 + .69

 

 

 

APPENDIX H--3 (Continued)

 

 

lll

 

Case Measured Predicted Average
No. Age Pounds Pounds Deviations Deviation
65M 133 66.2 67.0 + .80
cont. 145 73.0 73.01 + .01

157 79.1 80.91 +1.81

163 89.0 89.0 0

169 100.0 99.22 ‘ - .78

175 108.2 109.13 + .93

181 117.1 117.02 - .08

187 123.0 123.0 0 .510
71M 103 55.0 55.0 0

115 64.7 64.62 - .08

127 72.0 72.22 + .22

139 77.0 79.99 +2.99

151 91.0 91.0 0

163 104.1 104.03 - .07

175 115.7 115.7 0 .480
77M 117 69.7 69.7 0

128 77.2 76.82 - .18

140 80.2 82.82 +2.62

152 87.0 88.05 +1.05

158 91.7 91.11 - .59

164 94.7 94.7 0

170 97.5 98.76 +1.26

176 103.1 103.1 0

182 109.0 107.44 -1.56 .807
80M 105 68.2 68.2 0

117 76.5 76.43 - .07

128 80.5 81.89 +1.39

140 86.2 86.39 + .19

152 95.7 95.7 0

158 104.7 104.65 - .05

164 109.0 114.06 +5.06

170 122.0 122.0 0 .845
83M 101 52.3 52.3 0

114 60.0 59.95 - .05

125 63.2 65.65 +2.45

137 71.0 71.0 0

149 75.0 75.53 + .53

161 80.0 79.40 - .60

173 89.3 89.3 0

179 100.7 100.06 - .64

185 105.7 110.99 +5.29

191 119.5 119.5 0 .956

 

APPENDIX H--3 (Continued)

112

 

 

 

Case Measured Predicted Average
No. Age Pounds Pounds Deviations Deviation
87M 113 63.0 63.0 0

124 70.0 72.56 +2.56

136 81.0 81.01 + .01

148 87.5 87.54 + .04

154 97.0 95.59 -1.41

160 95.2 99.86 +4.66

166 110.0 110.0 0

172 120.0 118.25 -1.75

178 123.5 123.5 0 1.159
110M 112 62.2 62.2 0

124 67.5 70.33 +2.83

136 78.0 78.0 0

148 82.0 84.89 +2.89

160 91.2 91.75 + .55

166 97.2 97.2 0

172 105.2 105.79 + .59

178 116.7 116.7 0 .856
115M 89 50.0 50.0 0

101 56.5 56.10 - .40

113 61.2 61.66 + .46

125 66.7 66.7 0

137 72.0 71.15 - .85

149 79.1 77.19 -1.91

155 82.5 82.5 0

161 89.2 89.54 + .34

167 97.5 97.5 0 .440
129M 97 53.0 53.0 0

109 58.0 58.19 + .19

122 63.5 63.61 + .11

133 69.0 69.0 0

146 77.2 77.2 0

157 83.1 84.28 +1.18

169 90.5 90.49 - .01 .213
136M 110 55.0 55.0 0

121 62.2 63.88 +1.68

133 72.0 72.0 0

145 78.5 79.27 + .77

151 89.1 85.44 -3.66

157 95.0 95.0 O

163 106.0 106.0 0

169 114.0 115.84 +1.84

175 125.0 .49 -1.51 1.051

 

APPENDIX H--3(Continued)

113

 

 

 

 

Case Measured Predicted Average
No. Age Pounds Pounds Deviations Deviation
162M 101 62.0 62.0 0

115 70.0 73.92 +3.92

125 80.0 80.0 0

137 89.5 88.1 -1.39

149 93.7 95.10 +1.40

155 102.5 102.5 0

161 108.7 110.88 +2.18

167 117.7 117.7 0 1.111
163M 96 62.2 62.2 0

109 71.2 74.41 +3.21

120 83.0 83.03 + .03

132 90.7 90.73 + .03

144 98.5 98.5 0

150 106.7 104.85 -1.85

156 112.0 113.75 +1.75

162 127.5 124.54 -2.96

168 132.1 132.53 + .43

174 146.2 146.2 0 1.026
164M 84 44.1 44.1 0

96 53.0 50.10 -2.90

108 56.2 56.2 0

120 59.2 62.21 +3.01

132 68.2 68.3 + .10

144 74.0 74.13 + .13

156 82.5 82.5 0

162 92.0 88.92 -3.08

168 95.0 95.03 + .03

174 100.0 100.0 0 .925
167M 88 52.0 52.0 0

100 60.1 60.14 + .04

113 66.0 67.64 +1.64

124 73.0 73.19 + .19

136 84.3 81.53 -2.77

148 99.0 99.0 0

160 123.5 123.52 + .02

172 146.2 146.2 0 .583
171M 101 53.0 53.0 0

114 61.2 61.1 - .10

125 67.0 67.2 + .20

137 75.7 73.0 -2.70

149 78.0 78.33 + .33

 

 

 

APPENDIX H--3 (Continued)

114

 

 

t

 

 

Case Measured Predicted Average
No. Age Pounds Pounds Deviations Deviation
171M 161 88.2 87.62 - .58
con't. 167 94.7 95.25 + .55

173 103.1 103.78 + .68

179 113.0 111.94 -1.06 .689
176M 85 45.1 45.1 0

97 49.0 49.5 + .50

109 60.0 53.60 -6.40

133 61.0 61.01 + .01

145 64.3 64.53 + .23

157 69.2 69.2 0

169 75.5 75.53 + .03

181 82.7 82.7 0 .896
195M 99 64 .0 63.36 - .64

110 70.7 70.7 0

123 75.7 78.32 +2.62

134 86.2 84.10 -2.10

146 95.2 95.2 0

158 112.1 112.95 + .85

170 128.0 127.45 - .55

182 136.0 136.0 0 .845

Boys‘ Total Average Deviation .811

Boys' Range

of Deviations

 

m

.143 -- 1.500

 

115

APPENDIX H--4

DEVIATION OF PREDICTED WEIGHT SCORE FROM
ACTUAL WEIGHT SCORE

 

 

L T—_

 

 

 

1— -—

 

 

Case Measured Predicted Average
No. Age Pounds Pounds Deviations Deviation
52F 91 56.2 56.2 0

102 60.1 60.11 + .01

114 65.0 65.69 + 269

126 75.0 75.0 0

138 90.3 90.32 + .02

150 106.2 106.2 0

162 118.2 118.18 - .02 .106
_55F 76 40.3 40.3 0

101 52.0 51.91 - .09

112 55.1 55.41 + .31

124 61.2 61.2 0

136 73.3 72.79 - .51

148 87.0 87.51 + .51

160 100.5 100.5 0 .203
58F 91 49.2 49.2 0

103 57.3 57.24 - .06

115 62.3 63.17 + .87

127 67.1 67.37 + .27

139 71.0 70.25 - .75

151 72.2 72.96 + 76

157 83.5 78.77 -4 73

163 89.2 89.2 0

169 98.7 98.99 + 27

175 106.2 105.45 - .75

181 109.2 109.2 0 .769
59F 110 56.2 56.2 0

115 59.2 59.2 0

121 58.3 62.2 +3 90

125 64.0 64.01 + 01

133 65.3 67.28 +1 98

139 69.1 69.93 -+ 83

145 71.0 73.60 +2 60

151 78.5 78.5 0

157 82.0 84.12 +2 12

163 90.2 89.99 - 21

169 93.2 95.38 +2.18

175 100.2 100.2 0 1.153

 

APPENDIX H--4 (Continued)

116

 

 

 

Case Measured Predicted Average
No. Age Pounds Pounds Deviations Deviation
62F 88 51.1 51.1 0

100 60.1 60.1 0

112 62.3 66.94 +4.64

124 72.0 72.37 + .37

136 83.2 83.2 0

148 100.0 102.06 +2.06

160 119.0 116.95 —2 05

172 125.0 125 0 0 1.140
64F 97 70.1 70.1 0

109 93.0 89.82 -3.18

121 100.0 105.84 +5.84

133 118.1 118.1 0

145 127.0 132.5 +5.50

15 169.1 169.1 0

169 193.0 192.68 - .32

181 201.5 201.50 0 1.855
65F 81 54.3 54.3 0

93 58.1 58.29 + .19

105 62.2 62.51 + .31

117 68.3 68.41 + .11

129 78.0 78.0 0

141 94.1 90.01 -4.09

153 99.7 101 69 +1.99

165 111.2 111 2 0 .836
69F 98 62.2 59.54 -2.66

110 73.0 73.0 0

122 81.0 84.67 +3.67

134 94.3 94.3 0

146 102.3 102 3 0

158 122.3 122.42 + .12

170 140.7 140.7 0 .921
71F 91 51.3 51.3 0

103 56.3 56.68 + .38

115 61.6 61.22 - .38

127 65.0 65.35 + .35

139 72.3 75.04 +6.99

145 88.3 88.3 0

151 94.3 94.7 + .40

157 99.0 98.67 - .33

163 101.0 101.12 + .12

169 104.7 102.64 -2.06

175 103.7 103.7 0 1.001

 

APPENDIX H--4 (Continued)

117

 

 

V

 

Case Measured Predicted Average
No. Age Pounds Pounds Deviations Deviation
78F 88 51.2 50.05 -1.15

101 58.3 58.3 0

112 64.0 64.79 + .79

124 71.2 71.28 + .08

136 77.0 77.88 + .88

148 89.3 89.3 0

160 105.0 105.84 + .84

172 119.70 119.70 0 .468
80F 76 32.2 31.75 - .45

88 36.0 36.0 0

100 37.4 40.10 +2.70

112 44.1 44.06 - .04

124 48.0 47.79 - .21

136 51.3 52.34 +1.04

142 57.3 57.21 - .09

148 64.2 65.0 + .80

154 74.2 74.2 0

160 78.0 83.08 +5.08

166 92.0 90.55 -1.45

178 100.7 100.7 0 .988
84F 70 43.5 41.79 -1.71

82 47.5 47.5 0

94 49.0 53.13 +4.13

106 58.2 58.49 + .29

118 63.5 63.5 0

130 70.5 70.5 0

142 87.7 88.32 + .62

154 104.0 104.0 0

166 112.2 112.13 - .07 .758
97F 99 49.0 49.0 0

112 53.5 59.97 +6.47

123 67.7 67.73 + .03

135 75.0 74.50 - .50

147 79.7 82.25 +2.55

153 91.0 91.0 0

159 102.5 98.12 -4.38

165 102.2 102.2 0 1.741
105F 89 50.5 50.5 0

109 51.7 54.20 +2.50

115 55.0 55.54 + .54

122 56.0 58.03 +2.03

APPENDIX H--4 (Continued)

118

 

 

 

 

Case Measured Predicted Average
No. Age Pounds Pounds Deviations Deviation
105F 133 65.5 65.5 0
con't. 145 79.3 78.76 - .54

157 93.0 93.67 + .67

169 106.7 106.7 0 .785
118F 107 48.5 48.5 0

118 56.7 56.7 0

130 63.5 64.4 + .90

143 72.0 71.27 - .73

154 81.7 81.7 0

100 91.7 91.69 - .01

166 103.0 100.4 -2.60

172 106.5 106.5 0 .530
189F 109 48.2 48.2 0

120 56.5 56.48 - .02

133 63.5 65.33 +1.83

144 71.7 71.72 + .02

159 81.5 81.5 0

168 88.2 91.0 +2.80

174 98.2 98.02 - .18

180 103.0 104.57 +1.57

186 110.2 110 2 0 .713
190F 99 53.5 53.5 0

112 60.7 62.13 +1.43

123 69.7 68.31 -1.39

135 74.0 74.32 + .32

147 83.7 83.7 0

159 98.5 98.48 - .02

171 111.1 111.1 0 .451
227F 100 55.0 55.0 0

113 61.0 66.59 +5.59

124 75.2 75.21 + .01

136 84.0 84.0 0

148 97.5 95.99 -l.51

154 101.0 102.9 +1.90

160 106.2 109.35 +3.15

166 115.0 115.0 0 1.520

Girl's Total Average Deviation .885

Girl's Range of Deviations .106 -- 1.855

 

 

 

119

 

 

 

 

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