A STUDY OF INTER-DEVELOPMENTAL RELATIONSHIPS
AMONG STANDING HEIGHT, SKELETAL AGE, AND
MENTAL AGE FOR SIXTY-SIX BOYS SELECTED

FROM THE HARVARD GROWTH DATA

by

Jean McKenney LePere

AN ABSTRACT

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

DOCTOR OF PHILOSOPHY
Department of Foundations of Education
1958

Approved [M infigfi
v—IT—‘v ' \

2
JEAN MCKENNEY LePERE ABSTRACT

The Problem

 

It was the purpose of this investigation to analyze
longitudinal data for sixty-six school age boys with respect
to growth in standing height, skeletal age, and mental age.
The cases were selected from the Third Harvard Growth Study
which was inaugurated in 1922 in the Psycho-Educational
Clinic of the Harvard Graduate School of Education. The
data consisted of annual measurements in standing height,
skeletal age, and mental age for the boys from approximately
seven through seventeen years of age, and were representative
of those taken from a normally distributed population.

Specifically, the study attempted to determine (1)
growth relationships among the three aspects of development
with respect to beginning and end points of adolescent
development; (2) other developmental relationships such as
those inherent in growth constants of rate, incipiency, and
maximum; and (3) correlative relationships of timing aspects

of physical and mental growth of school-age boys.

Methods and Procedure

 

The determination of points of cycle break for each
of the sixty-six cases in each developmental measurement
was made by the utilization of normal probability paper.
Using the points thus obtained, the Courtis technique for
analysis of growth was then applied to each case to deter-

mine cycle growth constants of rate, incipiency, and

 

‘flnm

 

 

 

 

 

 

3
JEAN McKENNEY LePERE ABSTRACT
maximum. The use of the formula made it possible to reduce
all variables to common maturation units known as isochrons,
which could then be used to determine correlation coeffici-
ents among the three aspects of development. Coefficients
of correlation were obtained by the use of the Pearson r

formula.

Summary and Conclusions

 

The Courtis technique, which utilizes the Gompertz
equation, was found to describe growth patterns of the
sixty-six boys in standing height, skeletal age, and mental
age with better than ninety-five per cent efficiency.

Correlation coefficients were computed among the
cycle growth constants of maxima, rates, and incipiencies
as well as times of occurrence of cycle break, time of
ninety-nine per cent of achieved adult maturity, and per
cents of development of first cycle maxima and adult maxima
at the time of cycle break. Mean annual increments were
also compared to determine the degree of relationship in
patterns of growth in physical and mental aspects of
development among the sixty-six boys.

The pattern of growth for each of the boys was that
of a two-cycle curve in standing height, skeletal age, and
mental age, with the cycle breaks occurring between mean

ages of ten and twelve years.

u
JEAN McKENNEY LePERE ABSTRACT

Correlation coefficients between equation constants
of rate, incipiency, and maximum were not statistically
significant.

Correlation coefficients between times at which cycle
breaks occurred were positive but too low to be stated as
reliably significant.

Growth is so variable from one individual to another,
and from cycle to cycle, that a comparison of equation con—
stants within a given cycle (because they are dependent
upon each other) does not provide a sufficient basis on
which to compare growth relationships.

Significant relationships between physical and mental
aspects of growth of the boys were revealed when all equa-
tion constants were analyzed as a composite whole. The
correlation between all aspects of growth was positively
significant when mean annual increments obtained from
equation constants were compared.

The use of a multi-cyclic regression equation for
describing growth of the boys in standing height, skeletal
age, and mental age predicted growth with good efficiency,
provided a means of smoothing the growth curves and tended
to reduce testing errors.

The degree to which ethnic and cultural influences
affected the growth patterns of the sixty—six boys was not

known. However, for these sixty-six boys who lived in the

5
JEAN MCKENNEY LePERE ABSTRACT

vicinity of Boston, patterns of growth in standing height,
skeletal age, and mental age were significantly related as
indicated above.

Correlation coefficients between and among the mean
annual increments of the sixty—six boys were much higher
than those obtained in previous studies where growth aspects

were analyzed on a cross-sectional basis.

A STUDY OF INTER-DEVELOPMENTAL RELATIONSHIPS
AMONG STANDING HEIGHT, SKELETAL AGE, AND
MENTAL AGE FOR SIXTY-SIX BOYS SELECTED

FROM THE HARVARD GROWTH DATA

by

Jean McKenney LePere

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Foundations of Education

1958

51/91.

‘1

ACKNOWLEDGMENTS

Grateful appreciation is extended to Dr. Cecil V.
Millard under whose helpful guidance and assistance this
study was undertaken. Further appreciation is expressed
to Dr. Clyde Campbell, Dr. C. R. Hoffer, Dr. Leonard Luker,
and Dr. Troy L. Stearns for their assistance in criticizing
and editing the material.

It is impossible to list the names of the many
Michigan State University students who assisted in setting
up the case books and who worked on the computation of the

data. Grateful thanks is extended to these students.

 

.. n.o I1“.

\‘Qfi

1

TABLE OF CONTENTS

CHAPTER PAGE
I. THE PROBLEM AND DEFINITION OF TERMS USED . . l
The problem. . . .
Statement of the problem
Statement of hypotheses.
Secondary problems . . . . .
Importance of the study.
Limitations of the study
Definition of terms
Growth
Development. . . . . . . .
Growth curve . . . . .
Growth cycle . . . . . . . . .‘
Organismic growth.
Rate . . . .
Incipiency .
Maximum .
Isochron. . . . . . . . .

Growth constant

\oxomkoooooooooooooxlxloxwwmmm

Courtis technique.

|._.I
O

II. REVIEW OF THE LITERATURE

H
H

Anthropometric studies

H
H

Longitudinal data.

iv

CHAPTER PAGE
Mental growth . . . . . . . . . . l6

Skeletal maturation . . . . . . . . 21

Growth analysis . . . . . . . . . 24

'III. PROCEDURE . . . . . . . . . . . . 38
The data. . . . . . . . . . . . 38
Methodology. . . . . . . . . . . 41
Determination of cycles. . . . . . A2

The Courtis method . . . . . . . A5

Correlative techniques . . . . . . 63

IV. ANALYSIS OF THE DATA. . . . . . . . . 65

V. SUMMARY, CONCLUSIONS, AND IMPLICATIONS. . . 95
Conclusions. . . . . . . . . . . 96
Implications . . . . . . . . . . 97
BIBLIOGRAPHY . . . . . . . . . . . . . . 100
APPENDIX A . . . . . . . . . . . . . . . 112

APPENDIX B . . . . . . . . . . . . . . . 147

TABLE

II.

IV.

VI.

VII.

VIII.

IX.

XI.

LIST OF TABLES

Computed and Critical X2 Values of Observed
Measurements in Standing Height, Mental
Age, and Skeletal Age of the Sixty-Six
Boys at Age 8 . . . .

Ethnic Origin and Socio-Economic Status of
the Sixty-Six Boys . . . . . . .

Observed Measurements and Computed Per Cents
of Development in Standing Height, Mental
Age and Skeletal Age for Case 343M . .

Per Cents of Childhood Cycle Maximum for
Measurements in Standing Height, Case 3A3M

Computation of First Cycle Rate and Incipiency

in Standing Height for Case 343M.

Observed and Predicted Measurements in
Standing Height, Case 343M, and Deviations
of the Two Measurements. . . .. . . .

Data for Isochronic Graph Sheet--Percentages
of Total Development.

Computation of Adolescent Cycle Rate and
Incipiency . . . . . . . .

Predicted Measurements for Childhood and
Adolescent Cycles of Growth in Standing
Height, Case 343M. . . . . . .

Observed Means, Composite Predicted Means,
Deviations, and Per Cent of Equation Error
at Annual Intervals for Mean Standing
Height Measurements of Sixty-Six Boys

Observed Means, Composite Predicted Means,
and Per Cent of Equation Error at Annual
Intervals for Mean Skeletal Age Measure-
ments of Sixty-Six Boys.

PAGE

40

Al

A3

54

56

59

61

62

69

69

vi
TABLE PAGE

XII. Observed Means, Composite Predicted Means,
and Per Cent of Equation Error at Annual
Intervals for Mean Mental Age Measurements
of Sixty-Six Boys. . . . . . . . . 7O

XIII. Average Composite Equation Errors from
Observed Mean Scores and Per Cents of
Efficiency of Equations for Standing
Height, Skeletal Age, and Mental Age of
Sixty-Six Boys. . . . . . . . . . 7O

XIV. Average Annual Increments in Growth in
Standing Height, Skeletal Age, and Mental
Age for Sixty-Six Boys, Computed from
Composite Equations of Growth Constants . 72

XV. Distribution of Errors of Equation Estimates
for Sixty- -Six Boys in Standing Height
Growth . . . . . . . 76

XVI. Distribution of Errors of Equation Estimates
for Sixty-Six Boys in Skeletal Age Growth. 77

XVII. Distribution of Errors of Equation Estimates
for Sixty-Six Boys in Mental Age Growth . 77

XVIII. Means, Standard Deviations, and Ranges of
Rates of Development in Isochrons for
Childhood Cycle and Adolescent Cycle of
Growth for Sixty-Six Boys in Standing
Height, Skeletal Age, and Mental Age . . 79

XIX. Means, Standard Deviations, and Ranges of
Maximum Development of Childhood Cycle and
Adolescent Cycle of Growth in Standing
Height, Skeletal Age, and Mental Age for
Sixty-Six Boys. . . . . . . . . 83

XX. Means, Standard Deviations, and Ranges of
Incipiency in Isochrons of Childhood Cycle
and Adolescent Cycle of Growth in Standing
Height, Skeletal Age, and Mental Age for
Sixty-Six Boys. . . . . . . 82

XXI. Means, Standard Deviations, and Ranges of
Times of Cycle Break and Adult Maturity in
Months of Sixty-Six Boys in Standing Height,
Skeletal Age, and Mental Age . . . 83

TABLE

XXII.

XXIII.

XXIV.

XXV.

XXVI.

XXVII.

XXVIII.

vii
PAGE

Per Cents of Development of Childhood Cycle
Maxima and Adult Maxima of Achieved
Growth at the Time of Cycle Break . . . 85

Correlation Coefficients Between Growth
Constants of Equations for Standing Height,
Skeletal Age, and Mental Age of Sixty-Six
Boys . . . . . . . . . 86

Multiple Correlation Coefficients, Computed
F Values and Critical F Values for
Times of Cycle Break and er Cents of
Adult Maturity at Time of Cycle Break . . 88

Rank—Difference Correlation Coefficients and
Pearson r Correlation Coefficients for
Mean Annual Increments in Standing Height,
Skeletal Age, and Mental Age of Sixty—Six
Boys . . . . . . 89

Multiple Correlations, Observed F Values and
Critical F Values for Annual
Growth Incremégts) in Standing Height,
Skeletal Age, and Mental Age of Sixty-Six
Boys . . . . . . . . . . 9O

Correlation Coefficients of Mean Annual
Observed Increments in Standing Height,
Skeletal Age, and Mental Age of Sixty-
Six Boys. . . . . . . . . . . . 92

Distribution of Declining Mental Age Scores
at Annual Intervals . . . . . . . . 92

r L .£ 505.! dip.

FIGURE

19.

LIST OF FIGURES

Variation in Rate of Individual Height
Growth . . . . . .

Composite Normal Probability Graph of Per
Cents of Total Development in Standing
Height, Skeletal Age, and Mental Age for
Case 3A3M, Indicating Measurements within
a Given Cycle of Growth. . . . .

Semi- -Logarithmic Curve Showing Childhood
Cycle Development in Standing Height,
Case 343M . . . . . .

Line of Best Fit for Per Cents of Development
of Childhood Cycle in Standing Height,
Case 343M . . . . . . .

Semi-Logarithmic Curve of Second Cycle
Residuals Obtained from First Cycle
Equation Constants in Standing Height,
Case 3A3M . . . . . . .

Line of Best Fit for Per Cents of Development
of Adolescent Cycle in Standing Height,
Case 343M . . . . . . . . . .

Graph of Per Cents of CompositeEquation Error
for Standing Height, Skeletal Age, and
Mental Age . . . . . .

Standing Height--Curve of Equation Constants
and Mean Measurements . . . . . .

Skeletal Age--Curve of Equation Constants and
Mean Measurements. . . . . . . .

Mental Age—~Curve of Equation Constants and
Mean Measurements. . .

33

AA

49

53

57

6O

71

73

7a

75

CHAPTER I
THE PROBLEM AND DEFINITION OF TERMS USED

Testimony to the fact that man has long been seeking
to discover the mysteries of growth among his own species
is borne out in the voluminous literature to be found.
Many of the early studies which dealt with aspects of
growth in the human organism were cross-sectional in nature,
and in their quest to find the "normal" person they actually
obscured traits of growth within the individual.1 It is to
Gueneau de Montbeillard‘e’3 that present day investigators
are indebted for his pioneering work (1759-1776) in the
individual method of analyzing growth data, which today has
come to be known as the "longitudinal" method of studying
human growth and development. Since Montbeillard's time,

data collecting methods have improved vastly, new techniques

of growth analysis have been continuously applied, and the

 

lFranz Boas, "Observations on the Growth of Children,"
Science, LXXI (July, 1930), pp. 44-48.

2R. E. Scammon, "The First Scriatim Study of Human
Growth," American Journal 9: Physical Anthropology, X, No.
3 (1927): P. 333.

 

3Count de Buffon, "Sur l'accroissement successif des
enfants, Gueneau de Montbeillard mesure de 1759 a 1776,"
Oefivres Completes, Paris: Furne and Pie, 1873, Vol. III,
17 ~176.

search for the answer to the nature of human growth has

come more and more into a science of its own.

I. THE PROBLEM

 

Statement of the Problem

It was the purpose of this investigation to analyze
longitudinal data for sixty-six boys of school age with
respect to growth in standing height, mental age, and
skeletal age. The sixty-six cases were selected from the
Third Harvard Growth Study which was inaugurated in 1922 in
the Psycho-Educational Clinic of the Harvard Graduate
School of Education.“ The major problem was to determine
growth relationships in the three aspects of development
with respect to beginning and end points of adolescent

development.

Statement of Hypotheses

 

The statement of the major purpose led to the formu-
lation of fknu' major hypotheses. The hypotheses were (I)
that growth is multi-cyclic in nature, and that two major
cycles of growth would be evident from the data which were
analyzed, inasmuch as no data were available for the early
childhood cycle; (2) that the use of suitable statistical

tests would reveal positive correlative relationships among

 

LHM. F. Dearborn, J. W. Rothney, and F. K. Shuttleworth,
’"Data on the Mental and Physical Growth of Childrenfl'
Monogra hs of the Societ for Research in Child Development,
III. 0. 1 T3387. pp I436?

'0‘.

4)...

 

the three aspects of development, i.e., standing height,
mental age, and skeletal age; (3) that physical aspects of
growth in the individual show relationships to the mental
growth data; and (4) that the correlation among the three
aspects of development at the time when the adolescent

cycle of growth begins would be positively significant.

Secondary Problems

 

In the analysis of longitudinal data for the purpose
of investigating related aspects of growth at beginning and
end points of adolescent development, a number of pertinent
secondary problems arose. Such problems, which may be
regarded as essential to the investigation of the major
problem, included (1) the selection of a suitable mathe-
matical formula which would reduce the observed measurements
to common units which could then be used for comparative
purposes; (2) the consideration of other growth variables
which may be compared in order to investigate growth rela-
tionships, such as extra- and intra-growth relationships
among the growth constants, represented by rates of growth
within cycles of development, and beginning and end points
of cycles; and (3) the consideration of ethnic and cultural

influences upon growth and development.
II. IMPORTANCE OF THE STUDY

The fundamental tenets which underly this study and

influence its approach, its method, and its recommendation

should be pointed out as having profound implications for
those who are concerned with the nature of human growth and
development and for education and learning. The need for
such research and the value of the longitudinal approach

to the study of human growth and development was recognized
by Boas. He stated that:

The general growth curve of man has long been known,
but we have little evidence in regard to the growth
of individuals who ultimately reach various statures.
For this purpose it is necessary to follow the individ-
ual growth from childhood to the adult stage. Some
material of this kind has been collected but not 5
enough to give adequate insight into the phenomena.

Adkins noted the importance of using results of longi-

tudinal research for increased understanding of child growth
and development when she stated that:

Although the "wholeness" of each child, in its
developmental aspects is best revealed by individual
case studies, the fact remains that if no generali—
zations can be extracted from such records they
cannot6have the greatest of practical scientific
value.

Probably the first investigator to provide conclusive

evidence to the effect that cross~sectional studies do not
produce the same results as longitudinal studies was

Stewart, whose pioneering efforts were reported in 1916.7

 

5Franz Boas "Studies in Growth," A Journal 9£_Human
Biology, IV (1932), p. 307. "‘”‘"" "“"‘

6Margaret M. Adkins, et al, "Physique, Personality
and Scholarship," Mono a he of the Society for Research in
Chiid-Development,“VTIIEII9H3TT'p. 5.

 

 

7S. F. Stewart, "Physical Growth and School Standing
of Boys," Journal 2£_Educational Psychology, VII (1916),
pp. 414-426.

 

 

 

 

of. fp’l kl.._.;.9t . .x‘

.335... v I, 3.13.

2...». p... . 3.... . ..._....
r. . . .

r ._ . .

Subsequent investigations by other researchers have lent

8,9,10,11 This investi-

substance to Stewart‘s findings.
gation was designed with the purpose of providing another
link in the chain of longitudinal investigations which have
been cited as providing a more adequate basis on which to
evaluate the growing organism as a dynamic whole. It is
neither the process nor the cold facts of growth relation-
ships which lend value to such a study, however, but rather
the implications of the findings for increased understanding
of the "whole" child. Courtis has made a significant
statement in this regard:
The most recent book on Educational Measurement
(American Council on Education, 1951) in its 819
pages gives ample proof that measurement gets one
nowhere in education; that the dry rot of meaningless
juggling of statistical symbols has taken the place
of critical thinking and productive experiment.
In a society in which more and more emphasis is being

placed upon the guidance of individuals for the utilization

 

8Ethel Abernethy, "Relationships Between Mental and
Physical Growth, " Monogra hs of the Society for Research in
Child Development, I, 1N0. (I936), pp. 66-70.

 

 

 

9H. Gray and T. G. Ayres, Growth-in Private School
Children (Chicago: University of Chicago Press, 1931).

 

 

loH. Gray and A. M. Walker, "Length and Weight "
American Journal of Physical Anthropology, IV (1921),
23I-238.

11Arthur R. DeLong,'"The Relative Usefulness of Longi-
tudinal and Cross-Sectional Data," Paper presented at a
meeting of the Michigan Academy of Science, Arts, and Letters,
March 26,1955.

128. A. Courtis, Toward a Science of Education (Ann
Arbor, Michigan: Edwaras Eros.

pp.

 

of potential abilities to the highest possible degree, it

seems essential that those who hold the responsibility for
such guidance be apprised of all possible knowledge of the
nature of growth of the individual in order to perform the
task efficiently. With this purpose in mind this investi-

gation was undertaken.
III. LIMITATIONS OF THE STUDY

The greatest single limitation of a longitudinal study
of this type lies in the fact that the collection of longi-
tudinal data is necessarily so time consuming that often
more precise methods of data collection are discovered
before any analysis can take place. This is a weakness in
the case of the skeletal age measurements. At the time
that the Harvard Growth data were collected, the best
available standards for the assessment of skeletal age were
those which had been presented by Todd13 and which he later
published in his Atlas_2£ Skeletal Maturation (Hand').ll‘L
Until 1950, his Atlas and the radio-graphic standards of

Flory15 were the only scales available for the assessment

 

13W. F. Dearborn, et a1, op. cit., p. 9.

14T. Wingate Todd, Atlas of Skeletal Maturation (Hand)
(St. Louis: C. V. Mosby Company, l937)f’ 'I—

15Charles D. Flory, "Osseous Development in the Hand
as an Index of Skeletal Development," Monographs of the
Society for Research in Child Development, I, MOI—3 (1936).

 

of the skeletal age of a child during the entire postnatal
osseous stage as based upon sequence of appearance of the
intermediate skeletal maturity indicators of bones.16 Since
1950, three additional standards have been published.17 A
more detailed report of the study by Pyle as to the effect
of the difference in standards in interpreting skeletal age
ofinfants will be included in Chapter II of this thesis.

It is sufficient to note here that current research has
raised serious questions in reference to earlier studies
dealing with the assessment of skeletal age.

Time is a factor not only in the collection of the
data, but also in the analysis of each case. Because of
this, often too few cases are selected to make it possible
to subject the data to parametric statistical analysis. It
is for this reason that the Harvard Growth data represents

probably the most complete set of longitudinal data on

school age children which is currently available.
IV. DEFINITION OF TERMS

Growth
The term growth, as used throughout this thesis,
shall refer to a phase of the total development of the

organism.

 

16s. Idell Pyle, "Effect of the Difference in Stan-
dards in Interpreting Skeletal Age of Infants," Merrill-
Palmer Quarterly, IV, No. 2 (Winter, 1958), p. 75.

 

17lbid.

Development

 

The term development will be used to describe the

 

general organization of the individual and organismic change

in the total organism.

Growth Curve

 

The growth curve for the individual represents the

 

total pattern of development in a given trait or in total

organismic structure.

Growth Cycle

 

A ggowth cycle is the representative growth curve

 

for a given trait within a given developmental period.

Organismic Growth

 

The concept of organismic growth, as used in this

 

paper, holds that the human individual is a biological
organism whose growth takes place as a complex organismic

whole and not as segmented parts.

Rate

 

Rate refers to the increment of growth in a particular
aspect of development. It is variable from individual to
individual and from one stage or cycle of development to

another.

Incipiency

 

Incipiency represents the beginning point of growth

 

in a given developmental aspect, within a given growth cycle.

Maximum

The term.maximum refers to the maturity point toward
which an individual is growing in a given trait in a given
cycle of growth. The term is also used to indicate the

maturity points of total development of a given trait.

Isochron

Isochron is the name given to the lolog value of a
per cent of total development in a given aspect of growth.
A more detailed discussion of the isochron as a maturation
unit will be presented in Chapter III, Section II, which

deals with methodology.

Growth Constant

 

A ggowth constant represents a variable which charac-

 

terizes the elements by which growth may be analyzed. The
three constants involved in the Courtis technique, using

the Gompertz equation, are: incipiency, rate, and maximum.

Courtis Technique

 

The Courtis technique is a method of growth analysis

 

which was devised by S. A. Courtis18 and utilizes the

Gompertz formula for describing a simplex growth curve.

 

18$. A. Courtis, "Maturation Units for the Measure-
ment of Growth," School and Society, XXX (1929), pp. 683-
690.

 

CHAPTER II
REVIEW OF THE LITERATURE

Extensive research into the related aspects of various
growth processes of the child has been reported in the
research literature pertaining to child growth and develop-
ment. Several authors have presented exhaustive reviews of

1,2,3,“

the literature at various times. Comprehensive

bibliographies have also been compiled.5’6 Scammon noted

 

1Richard E. Scammon, "The Literature of the Growth
and Physical Development of the Fetus, Infant, and Child:
AuQuagtitative Summary," Anatomical Records (1927), pp.
2 1-2 7.

 

2Howard V. Meredith, "Physical Growth of White Children:
A Review of American Research Prior to 1900," Monographs of
the Society for Research 22 Child Development, I, No.2 (1936).

 

 

3Review of Educational Research. Vol. III (April,l933);
Vol. VI (FebruEFy, 1936); V61. IX (February, 1939); Vol. X
(Dec. 1941); Vol. XIV (Dec. 1944); Vol. XX (Dec. 1950); Vol.
XXII (Dec. 1952); and Vol. XXVI (June, 1956).

 

“Wilton M. Krogman, "The Physical Growth of Children:
An Appraisal of Studies 1950-1955," Mono raphs of the
Society for Research io;Chilo_Developmen , XX, SErIEI No.
‘66?“N67‘I"(1 55 .

5Children's Bureau of the United States Department of
Labor, References on the Physical Growth and Development of
the Normal Child, 1927, No. 179.

6Bird T. Baldwin, "Physical Growth of Children from
Birth to Maturity," University'o£ Iowa Studies lo Child
Welfare, I, No. 1 (19217.

 

 

11
that "the research literature pertaining to human physical
growth is literally voluminous."7 The present review will,
therefore, confine itself to a sampling of the studies per-

tinent to the problem.

Anthropometric Studies

 

Much of the early anthropometric research was of a
cross-sectional nature and revealed little information as
to the individual nature of growth. Baldwin reports, how-
ever, that,

as early as 1700 Sir Joshua Reynolds called attention,
in an address delivered before the Royal Academy of
Fine Arts, to the differences in the measurements of
the human form from childhood to adult life. But it
was to M. Quetelet, who coined the word anthropometry,
that credit should be given for t8€ first scientific
study of physical growth in 1836.

Longitudinal Data

 

In 1873 Buffon9

reported the studies of Geneau de
Montbeillard which were actually the first records of a
longitudinal study as it is known today.

In America, Dicksonlo is credited with having been

the first person to collect anthropometric data on children.

.....

 

7R. E. Scammon, op. cit.

8Bird T. Baldwin, "Physical Growth and School Progress,"
Bulletin 10, United States Bureau of Education, Washington,
D. C., 1941, p. 142.

9Buffon, op; cit.

lOSamuel Henry Dickson, "Some Additional Statistics of
Height and Weight," Charleston Medical Journal and Review,
XIII, No. 4 (1858).

12
Although the data which he collected and reported in 1858
were analyzed cross-sectionally, it is of significance to
describe here since it represented a pioneering effort in
collection and analysis.
The first American study employing the longitudinal
method was that undertaken by the Harvard Medical School

h.11

and reported by Bowditc In his 1872 report, he ex-

hibited a diagram showing the rate of growth in height in
the two sexes. The curves of growth in height and the
abscisses gave the age in years and the ordinates in height
in feet and inches. These curves represented the average
measurements of thirteen girls and twelve boys. He reports
that:-

An examination of the curves shows the following facts:

1. Growth is most rapid during the early years of
life.

2. During the first twelve years boys are from one
to two inches taller than girls of the same age.

3. At about twelve and a half years of age girls
begin to grow faster than boys and during the
fourteenth year are about one inch taller than
boys of the same age.

4. At fourteen and a half years of age boys again
become taller, girls having at this period
nearly completed their growth, while boys con-
tinue to grow rapidly till nineteen years of age}2

This report represented the first of many later studies
reported by Bowditch. In 1877 he reported a study, the pur-

pose of which was "to determine the rate of growth of the

 

11H. P. Bowditch, "Comparative Rate of Growth in the
Two Sexes," Boston Medical and Surgical Journal, X (1872),
pp. 434-435.

l2Ibid.

 

_ l 3
human race under the conditions which Boston represents."l3
The subjects were 24,595 Boston school children of both
sexes, aged five to nineteen years. Stature was measured
without shoes, body weight in ordinary clothing was recorded,
and the nationality of the parents as well as the birth
place of the children was reported.lLL

In a paper read at the thirty-second annual meeting
of the American Medical Association in 1881,15 he indicated
further research in his pioneering efforts to analyze growth
longitudinally. At that time Bowditch presented a graph
Showing the rate of growth of a girl between two and three
years and the relationship between growth and disease.16
It was obvious that Bowditch recognized the value of longi-
tudinal records in determining growth relationships when
he said:

It must not be supposed that loss of weight in a

growing child is in every instance a percursor of

actual disease. The weight of a healthy child is
liable to oscillations within limits which have yet

 

13H. P. Bowditch, "The Growth of Children," Eighth
Annual Report, Massachusetts State Board of Health (I877),
276. 59‘

lulbid.

”

15H. P. Bowditch, "The Relation Between Growth and
Disease," Transactions of the American Medical Association,
XXXII (1881), 371-377.

 

161mm , p. 375.

14
to be determined. It is only by systematic obser-
vations on an extensive scale that the real impor-

tance of this branch of preventive medicine can be
ascertained.1

Following the example set by Bowditch, Peckham,l8

in
1881 reported a study of Milwaukee school children in which
he pointed out similarities in rate of growth to Bowditch's
findings, but pointed out differences which may have been
due to environment and ethnic origin. In 1882 he reported
body weight means for young children based on measurements
of one hundred boys and one hundred twenty girls.19

An attempt to compare the rate of growth of normal
and feeble-minded children was reported by Tarbell20 in
1883. In this report he concluded that growth of the two
sexes of feeble-minded children follows a similar course

to that of the two sexes of public school children except

that the adolescent acceleration is delayed about two

 

17Ibid., p. 376.

18George W. Peckham, "The Growth of Children," Sixth
Annual Report State Board of Health of Wisconsin (18811),
pp. lxxiv-146.

 

 

19George W. Peckham, "Various Observations on Growth,
Seventh Annual Report, State Board of Health of Wisconsin,
PuElIc Document No I4 (I882 m) WJI88.

 

20G. G. Tarbell, "On the Height, Weight and Relative
Rate of Growth of Normal and Feeble-Minded Children," Pro-
ceedings of the Association of Medical Officers of American
InSEitut tions of Idiotic and FeebleéMinded Persons, PhIlaael-
phia, Pa.: LippIHEEEE‘(I8837, 188-189.

 

 

 

15
years.21 Thus, Tarbell, at this early date implied the
relationship between patterns of physical and mental growth.
It is significant that this first American study of the
physical growth of feeble-minded children contributed its
findings with the caution that they "may be proved to be
erroneous by a larger number of observations."22

Several of the early studies noted the difference in
patterns of growth in the two sexes, as well as evidence
which pointed to the "adolescent spurt" which today's
researchers recognize as the adolescent cycle of growthg3’24’25
Stephenson noted that, "the well-marked retardation of growth
in the ninth and eleventh years is a fact to which attention
has not previously been drawn, but will doubtless be found

to have important clinical bearings."26 Bowditch noted

that the growth curves showed marked differences between

 

2llbid., p. 188. 22Ibid.. p. 189.

23William Stephenson, "On the Rate of Growth in
Children," Translated from International Medical Congress
Ninth Session, Washington, III (1887). 446-452.

24H. P. Bowditch, "The Growth of Children, Studies by
Galton's Method of Percentile Grades," Twenty-Second Annual
Report, State Board of Health of Massachusetts,IPubliC

Document No. 34 (189I7, 479-5227

 

 

25L. M. Greenwood, "Heights and Weights of Children,"
Twentieth Annual Re ort of the Board of Education of the
XEnsas‘City PuEIio gcfiooI§,EKEnsaS'CiE§,7Missouri, 1890-
189I, Kansas CIty, Missouri:’Electric PrintIng Co., 1891.

26

 

 

 

Stephenson, op. cit., p. 452.

l6

sexes at the adolescent period, but were found to be similar

27

for each measurement on a given sex. Greenwood found that

for all groups studied, girls exceeded boys in both stature
and weight at thirteen and fourteen years, further evidence
of the "adolescent spurt."28
Another of the pioneers in studying growth longitud-
inally was Franz Boas. In 1892, commenting on the value of
longitudinal data for the study of physical and mental
growth, he observed that:
In order to carry out such a plan, it would be nec-
essary to organize a bureau with sufficient clerical
help to carry on the work. The questions underlying
physical and mental growth are of fundamental impor-
tance for hygiene and education, and we hope the time

may not be far disgant when a work of this character
can be undertaken.

Mental Growth

 

Thus the search for understanding growth of the human
individual was launched, by pioneers who were primarily
interested in anthropometric measurements. The turn of the
century found psychologists and educators becoming more and
more interested in the mental growth of the child, and in

particular, the relationships of physical and mental traits.

 

27Bowditch, "The Growth of Children Studied by Galton's
Method of Percentile Grades," op. cit.

28

Greenwood, op.'cit.

29Franz Boas, "Growth of Children," Science, XX:516
(1892), 351-352. _.__.__.__

17
Conventional correlation techniques applied to mental and
physical traits revealed positive but low relationships.
Whipple, in 1914, reported that:

The apparent correlation between height and mental
ability raises an important question which reappears
whenever we discuss the correlation between any
physical trait, e.g., weight, strength, vital capacity,
etc., and mental ability. The trend of evidence is
to the effect that all such correlations, where found,
are largely explicable as phenomena of growth, i.e.,
as correlations with relative maturity. . . . This
makes intelligible the fact that, in general, the
positiveness of all such correlations lessens with
age, and that many of them, indeed, become difficult
or impossible of demonstration in adults.30

Credited as the pioneer investigator of the relation-

ships between intelligence of School children and indices
of physical growth, however, was Porter,31 who in 1893,
reported the first investigation of this sort.

Baldwin,32 in 1914, described his work as the "first

attempt to follow consecutively some groups of Children
through the elementary and high School, either in physical

growth and school standing or the relation of the two."

 

3OGuy Montrose Whiplle, Manual of Mental and Physical
Tests, Part I (Baltimore: Warwick aha—York, 1914), p. 71.

31William Townsend Porter, "The Physical Basis of
Precocity and Dullness," Transaotions of the Academy of
Sci. of St. Louis, VI, NoiI7‘le93), IEIJIBI.

 

 

 

32Baldwin, "Physical Growth and School Progress,"
op; cit}, p. 7.

18

The first height-weight norms to receive general
attention in this country were those published by Wood
in 1910.33

As more research was undertaken, others began to
realize the value of the longitudinal approach and pointed
out limitations of cross-sectional studies. One of the
first to recognize that the pattern Shown by averaging
the growth of a group of children had little relationship
to the pattern of individual growth was Stewart, who
recorded some interesting conclusions in 1916.34 He pointed
out that:

1. when we consider averages of groups of the same
age, the group one year ahead of the normal grade
averages both heavier and taller than the group
of the normal grade. In some cases the group one
year below the normal average both heavier and
taller than the group of the normal grade.

2. When individual curves and correlations are con-
sidered without reference to the size of the boy
or to his stage of development, it is difficult
to see any relation between physical growth and
school standing.

3. When individual curves and correlations are con-
sidered, together with the size of the body at
fourteen years of age and his stage of development,
the following are suggested:

a. Heavy or tall boys of early development rank
better than light boys of early or medium
development.

 

33T. D. Wood, "Health Examination," Ninth Yearbook,
National Society for'the’Study'of Education, IX, Part I
(19107, 34-25.

3&8. F. Stewart, "Physical Growth and School Standing
of Boys," Journal'of Educational Psychology, VII (1916), 426.

 

 

 

 

19

b. Light boys of late development rank better
than light boys of early or medium develop-
ment. Short boys of late development do
not rank high.

c. Boys of medium size or of medium period of
development are hard to classify, though a
majority of them appogr to be doing school
work of medium rank.

Attempts to correlate measurements of mental capacity
with those of physical growth have been numerous. Abernethyes
summarizes the studies by observing that the general con—
clusion indicates that mental and physical measurements of
children are to some extent positively related.36

In 1920, Professor Frank N. Freeman protested the~r~
customary identification of mental maturity with superiority
in intellectual capacity and stated that the only means of
distinguishing between the leval of capacity which the
individual will ultimately reach and the rate of maturing
of that capacity is through repeated measurements up to
maturity.37

AS the search for relationships between mental and

physical aspects of growth progressed, several investigators

employed techniques which Showed the growth curves of

 

35Ibid.

*

36Ethel Abernethy, "RelationshipsBetween Mental and
Physical Growth," Monographs of the Sociepy for Research 2E
Child Development, I, No. 7 (I9367, p. 1.

37Ibid., p. 2.

*—

 

 

 

20
individuals in the two aspects of development and the rela-
tionship of mental and physical growth as a function of the
total organism.38’39’uo’ul Stolz and Stolz in presenting a
detailed case history of one boy showed the relationship
between physical and social development.“2

In 1955, Greenshields43 presented some interesting
data which raised another serious question as to the reli-
ability of I Q. test scores when other aspects of growth
are not considered, and pointed out that "it is of necessity

to know something of the individual's total develop-

ment before adequate appraisal can be made in a specific

area of growth."1m

 

38Bird T. Baldwin, "Relation Between Mental and
Physical Growth," Journal of Educational Psychology, XIII

(April, 1932), 193-293. '—_

39Donald G. Paterson, Physique and Intellect (New
York: The Century Co., 193OT.

uoCharles D. Flory, "The Physical Growth of Mentally
Deficient Boys," Monographs of the Society for Research $2
Child Development, I, No. 6‘TI936).

41W. F. Dearborn, J. W. M. Rothney, Predictipg the
Child's Development (Cambridge, Massachusetts: Sci-Art
Publishers, Harvard Square, 1941).

 

 

 

 

 

 

 

42H. R. Stolz and L. M. Stolz, Somatic Development 93
Adolescent Boys (New York: Macmillan Co., 19517.

 

43C. M Greenshields, "The Relationship Between Con-
sistent I.Q.Scores, Decreasing I.Q.Scores, and Reading Scores
Compared on a Developmental Basis" (unpublished M.A. thesis,
Michigan State University, East Lansing, Michigan, 1955).

qubid., p. 30.

21

Skeletal Maturation

 

Numerous studies have also been presented in the
analysis of skeletal maturation. Probably the most complete
set of skeletal growth standards up until 1950, was that
presented by Todd.LL5 He selected the hand and knee as
points which are most stable as indices. An exact repro-
duction of the original roentgenograms permits a direct
comparison between the standards and the roentgenograms to
be assessed. Many other studies have revealed the nature

“5,47,48,49,50,5l,52

of skeletal growth. The very close

 

"5T. Wingate Todd, Atlas op Skeletal Maturation (Hand)
op. cit.

 

"6H. D. Stuart, P. Hill, and C. Shaw, "Growth of Bone,
Muscle, and Overlying Tissues as Revealed by Studies of

Roentgenograms of the Leg Area," Mono ra hs of the Society
for Research 12 Child Development, V, No.3 (I940),Serial 26.

 

 

"7S. Idell Pyle and Camille Menino, "Observations on
Estimating S eletal Age from the Todd and the Flory Bone
Atlases," Child Development, X, No. 1 (March, 1939), 27-34.

48
W. M. Krogman, W. W. Greulick, D. Wechsler, and S.

M. Wishik, "The Concept of Maturity from the Anatomical,
Physiological, and Psychological Point of View," Child
Development, XXI (1950), 25-60.

 

 

"9Vernette S. Vickers Harding, "Time Schedule for the
Appearance of Fusion of a Secondary Accessory Center of
Ossification of the Calcaneous," Child Development, XXIII,
No. 3 (1952), 181-184.

 

50Charles D. Flory, "Osseous Development of the Hand
as an Index of Skeletal Development," op. cit.

51Psyche Cattell, "Preliminary Report on the Measure-
ment of Ossification of the Hand and Wrist," Human Biology,
VI (1934), 454-471.

 

22
relationship between skeletal and sexual maturity has been
amply demonstrated.53’5"’55 Seils56 found, also, a slight
relationship between skeletal maturity and motor performance.

Bailey, using the Todd standards for skeletal age
norms, concluded that:

It appears that growth in size is closely related to
the maturing of the skeleton. As a given skeletal
age we may say that a child has achieved a given
proportion of his eventual adult body dimensions.
Consequently, mature size can be predicted with fair
accuracy 15 a child's present size and skeletal age
are known. 7

 

522Bird T. Baldwin, "Physical Growth of Children from
Birth to Maturity," op. cit.

53W. W. Greulich, "The Rationale of Assessing the
Developmental Status of Children from Roent enograms of
the Hand and Wrist," Child Development, XX 1950), 33-34.

 

5"Katherine Simmons, "The Brush Foundation Study of
Child Growth and Development II--Physica1 Growth and-Devel-
opment," Mono raphs of the Society for Research $2 Child
Development, X, SerIElIND. 37 (1944), l-87T

 

 

 

55Frank K. Shuttleworth, "Sexual Maturation and the
Skeletal Growth of Girls Age Six to Nineteen," Monographs
op the Society for Research pp Child Development, III, No.
5, Serial No. 18*(1938).

 

 

 

56Leroy Seils, "The Relationship Between Measures of
Physical Growth and Gross Motor Performance of Primary
Grade School Children," Research Quarterl of the American
Association o3 Health, XXII (Ma , 1941), 244:260.

 

 

57Nancy Bayley, "Skeletal Maturing in Adolescense as
as Basis for Determining Percentage of Completed Growth,"
Child Development, XIV, No. l (19 3), pp. 44-45.

 

23
These conclusions were further corroborated in a

later study.58

In spite of the many scientific efforts to adequately
assess the nature of skeletal maturity in the growing
organism, much more research is still needed. In evaluating
Skeletal X-rays as indicators of skeletal maturity, Bailey,

in 1940, noted that:

Little is known as yet concerning individual differ-
ences in the pattern of Skeletal maturation. The
prediction of individual maturing . . . must ait
upon the further study of longitudinal data.5

She concluded that:

All clinical norms now available for skeletal develop-
ment have the same defect as mental age scales, in
that they are dependent on chronological age. This
forces the average curve of growth into a straight
line, failing to g63tinguish the period of rapid and
slow development.

Since 1950, however, three additional standards for

the assessment of Skeletal age have been published. They

 

58Nancy Bayley, "Size and Body Build of Adolescents
in Relation to Rate of Skehatal Maturing," Child Development,
XIV, No. 2 (1943), 47-89.

59Nancy Bayley, "Skeletal X-Rays as Indicators of
Maturity," Journal o3 Consulting Psychology, IV (1940),
72.

 

 

6OIbid., pp. 70-71.

24

62 63

61 Speijer, and Mackay.

are those of Greulich and Pyle,
The different components of the scales of Todd, Flory,

Greulich and Pyle, Speijer, and Mackay is pointed out by

Pyle as being that of temporal spacing.6" On this point

she writes:

In 1939, differences in the temporal spacing of
the osseous features in the Flory and Todd standard
were analyzed according to assessments of the films
of the Fels Research Institute Children who were less
than Six years old. From that study and the present
one it would seem necessary to include an analysis of
the temporal spacing of the standards of reference
used for population studies with the skeletal age
assessments before conclusions about differences in
calcification rates or skeletal ages of groups of
children are made.

Growth Analysis

 

Many analytical and mathematical methods have been
employed to determine the nature of growth. The multi-

cyclic nature of the human growth curve is a phenomenon of

 

61W. W. Greulich and S. I. Pyle, Radiographic Atlas
op Skeletal Development op the Hand and WrISt (Stanford,
CalIPCrnia: StanPBrd’UniversityIPress, 1950).

 

 

 

 

. 62B. Speijer, Betekenis En. Be aling Van 22 Skeletee-
ftyd (Leiden, Holland: A. W} SIthogf's Uitgevers Moats-

chappiJ, 1950).

63D H. Mackay, "Skeletal Development in the Hand:
A Study of Development in East African Children," Trans-
actions, Ro a1 Society op Tropical Medicine and Hygiene,
36:I35 (199%).

648. Idell Pyle, "Effect of the Difference in Stan-
dard's in Interpreting Skeletal Age of Infants," Merrill-
Palmer Quarterly, IV, No. 2 (Winter, 1958), p. 8 .

 

65Ibid., p.87.

 

 

... 3. . t. 2.,

.6. .o. r. w...

to

 

25
growth which has challenged investigators during this cen-
tury. Davenport pointed out that there is at least more

66

than one cycle. One of the earliest presentations of

the Cyclic pattern of growth was that of Scammon67 in 1927.
Using Montbeillard's data, he indicated that the growth
curve showed four phases. The theory that growth Shows a
pattern of four phases was supported by Shuttleworth68 and
he demonstrated very striking differences in growth patterns
of early and late maturing girls in aspects of physical
growth.69 the concept of a single cycle of growth was also

0
challenged by Wallis,7 Meredith,71 Gray,72 and Count.73

 

66C. B. Davenport, "Human Growth Curve,‘ loc. cit.

67R. E. Scammon, "The First Scriatim Study of Human
Growth," op. cit.

68Frank K. Shuttleworth, "The Physical and Mental
Growth of Girls and Boys Age Six to Nineteen in Relation to
Age at Maximum Growth," Monogpaphs 23.222 Societ ‘pop
Research pp Child Development, IV) No. 3 (1939).

 

 

 

69Frank K. Shuttleworth, "Sexual Maturation and the
Physical Growth of Girls Age Six to Nineteen," Monographs
of the Society for Research pp_Child Development, II, No.
'5—(1937W

7ORuth Wallis, "How Children Grow," University_op
Iowa Studies pp Child Welfare, V, No. l (1930).

 

 

 

 

 

 

71H. V. Meredith, "The Rhythm of Physical Growth,"
Univorsity op Iowa Studies pp_Child Welfare, XI (l935),l-l28.

 

 

 

72Horace Gray, "Individual Growth Rates from Birth to
Maturity for Fifteen Physical Traits," Human Biology, XIII

(1941). 306-333.

73Earl W. Count, "Growth Patterns of the Human Physi-

que--An Approach to Kinetic Anthropometry," Human Biology,
XV (1943), 1-32.

 

 

26
The nature of growth curves was described by Freeman and
Flory in 1937:
These curves severally and jointly show, first,
a slight acceleration in pre-adolescence, second a
moderate decline in rate of growth beginning in
early adolescence, and third, a continuance with

very little further decline in rate to the end of
the adolescent period, or nineteen or twenty years.

74
A critical evaluation of current literature dealing

with growth curves may be found by referring to Shock,75

Tanner?6 and Jensen.77 Several equations have been

utilized with the purpose of determining the cycles of

growth. These include those of Pearl and Reed,78 Huxley

 

Frank N. Freeman and Charles D. Flory, "Growth in
Intellectual Ability as Measured by Repeated Tests,"
Mono ra he of the Society for Research in Child Development,
I , o. , SErial No. 9 (1937), 88. '7—

 

 

75Nathan S. Shock, "Growth Curves," in Handbook op
Experimental Psychology, edited by S. S. Stevens ew
York: Wiley and Sons, 1951), p. 336.

 

76J. M. Tanner, "Some Notes on the Reporting of Growth
Data," Human Biology. XXIII (1951), 93-159.

 

77Kai Jensen, "Physical Growth," in Review op Edu-
cational Research, XXII (December, 1952), 39I-420.

8 .
7 R. Pearl and L. J. Reed, "Skew Growth Curves,‘
proceedings of the National Academy of Science, XI (1925),
16-22. W

 

 

 

27

and Thissler,79 Jenss and Bayley,80’81 Davenport,82 Gray,83
84

and Courtis. Other methods have also been presented.

Burgess presented a height chart using percentile curves
in 1937.85 Norms of growth variability were utilized by
86,87,88,89

others.

 

79R. Huxley and S. Thissler, "Standardixation of
Growth Formula," Nature, Vol. 137 (May 9, 1936), 780-781.

80R. M Jenss and N. Bayley, "A Mathematical Method
for Studying Growth of a Child," Human Biology, IX (1937),

556- 563

81Nancy Bayley, "Predicting Height of Children,"
Paper presented at the annual meeting of the Society for
Research in Child Development, 1955.

 

82C. B. Davenport,"Interpretation of Certain Infantile
Growth Curves," Growth, I (December 1937), 279-283.

83Horace Gray "Individual Growth Rates," Human
Biology, XIII (1941), 306- 333

Bus. A. Courtis, "Maturation Units for the Measure-
ment of Growth," School and Society, XXX (1929), 683-690.

 

85M. A. Burgess, "The Construction of Two Height
Charts," Journal of the American Statistical Association

XXXII (193777-29of314.

86Meinhard Robinow, "The Variability of Weight and
Height Increments from Birth to Six Years," Child Develop-
ment, XIII, No. 2 (1942), 159-164.

 

 

87Read D. Tuddenham and Margaret M. Snyder, "Physical
Growth of California Boys and Girls from Birth to Eighteen
Years, " University of California Publications in Child
Developmefit, I, ‘No. 2 (1954), I83- 364.

 

 

 

88K. Simmons and T. W. Todd, "Growth of Well Children:
Analysis of Stature and Weight, Three Months to Thirteen
Years," Growth, II (1938), 93-134.

28
One of the most widely known and used methods for
plotting relationships of height and weight was that pre-
sented by Wetzel.90 The method utilizes a "channelwise
grid" sheet for plotting height and weight relationships
in such a manner that normal growth should follow a straight
line. This method has since been challenged as one which

91

truly describes normal growth by Garn who showed that

channelwise progression is not common in girls, and that

the grid construction does not fully correct for changes in

92

body form during growth and development. Krogman also

concluded that:

Height and weight alone (and hence the Grid) cannot
substitute for basic skeletal age in assessing the
maturation 8% the child in terms of "advanced" or
"retarded."

 

89L. W. Sontag and E. L. Reynolds, "The Fels Composite
Sheet: A Practical Method for Analyzing Growth Progress,"
Journal 23 Pediatrics, XXVI (1945), 327-335.

 

90Norman C. Wetzel, The Treatment of Growth Failure
in Children (Cleveland: N. E. A. “Services, Inc. 1948), and
The Motion of Growth--Theoretical Foundations," Growth,
I (April 1937) “‘—

 

 

91 Stanley Marion Garn, "Individual and Group Deviations
from 'Channelwise‘ Grid Progression in Girls," Child Develop-
ment, XXIII, No. 3(September, 1952).

92W. M. Krogman, "A Handbook of the Measurement and
Interpretation of Height and Weight in the Growing Child,"
Mono ra hs of the Society for Research in Child Develop-
men fl, XIII, _No. 3, Serial No.

93

 

Ibid., p. 63.

29
A method of graphically plotting growth of children
from one to nineteen years of age was devised by Bayer and

9" The chart showed the relation of the individual to

Gray.
the average of the group. Meredith95 devised a method of
predicting stature through the use of T-scores.

Another widely used method of growth analysis known
as the "Organismic Age" was devised by Olson and Hughes.96
They developed growth ages in months for physical growth
such as dental, carpal, height, weight, and grip. The
average of such growth measurements was then plotted as
the total "organismic age" of the growing child. Olson
and Hughes pointed out the inefficiency of cross-sectional
analyses of growth data as is indicated in Figure 1.97 If
line A represents growth in height of one boy and line B
represents growth in height of another individual, then

the dotted line would represent the average for the two,

 

4
9 L. M Bayer and H. Gray, "Plotting of a Graphic
Record of Growth for Children Aged One to Nineteen Years,"
American Journal of Diseases of Children, L (1935), 1408-17.

 

95H. v. Meredith, "The Prediction of Stature," Human
Biology, VIII (1936), 279-283. ‘""""'

96W. C. Olson and Byron 0. Hughes, "Growth of the
Child as,a Whole," in Barker, Kounin and Wright, Child
Behavior and Development (New York: McGraw-Hill Book
50mpany,'T§43).

 

97W. C. Olson and Byron O. H hes, Manual for the
Description of Growth in Age UnitS‘ Ann Arbor, Michigan:
Uhiversity of7MichIgan Elementary School, 1950), p. 22.

 

 

I. I {.01 .0 n (II- I It I. .\..\ .. i .4 4
II I will; 1)?)3‘3.‘ Z.
AI v ‘
a(J «7 pr» n/ 1,.
A‘d .(d

~
axe

num< 81m « fiv-

 

 

JIIIII) j

Height Age

32

 

2O

 

17-.

Figure l.

30

Average

Height
Growth

B

-

l ‘J _L '4
j r T r

28 30 34 36 38
Age in Months

Variation in Rate of Individual Height Growth

31
and does not truly represent growth in height of either boy.
The "organismic age" method, they feel, holds real value
for the field of education in that it represents a means of
studying growth relationships longitudinally.98 Bloomers99
applied the "organismic age" concept to selected data and
noted "some relatedness in rate of growth among various
physical measures." He obtained a correlation coefficient
of .57 between height age and weight age.

The most serious criticism aimed at the organismic
age theory was that of Tyler.100 He utilized Cattell's
P-TechniquelOl to study the interrelatedness of growth among
physical characteristics during adolescence, and concluded
that there was no common factor of relatedness of growth in
twelve areas. In a later article, however, he admits that:
No doubt there are important relationships among
growth of testesand certain aspects of growth or

development of learning. These related character-
istics are more likely to be in the realm of physical

 

98W. C. Olson, Child Development (Boston: D. C. Heath
and Company, 1949), pp. 19-29.

 

99F. Bloomers, et al, "The OrganismicA e Concefi,"
Journal of Educational Psychology, XLVI (1955, 142 l 8.

 

lOOFred T. Tyler, "Concepts of Organismic Growth--A
Critigue," Journal of Educational Psychology, XLIV (1953),
321 3 2

 

101R. B. Cattell, "P- -Technique, A New Method for
Analyzing the Structure of Personal Motivation," Trans-
actions of the New York Academy of Science, XIV (11951),
EgT§ET‘* ““““

32

growth, and possibly in social and emotional learning
than in academic learning . 02

The work of S. A. Courtis103 in presenting a formula
for the analysis of maturation and the prediction of growth
has represented one of the most valuable contributions to
the field. In presenting his formula, he notes the efforts
of Verhulst (1838), Mitscherlich (1909), Robertson (1913),
Thurston (1919), Pearl and Reed (1920), Spillman (1924),
and Brody (1926), each of whom had derived a mathematical
formula for analysis of growth.104

The Courtis method is based on the Gompertz equation
which was reported by Benjamin Gompertz in 1825.105 A
detailed description of the Courtis method will be made in
Chapter III of this thesis under Methodology.

Courtis describes the Gompertz formula as being simple,
subject to direct experimental verification of the meaning

of the various constants; having rational, objective explan-

ation; and one which represents a universal relationship

 

lOQFred T. Tyler, "Organismic Growth: Sexual Maturity
and Progress in Reading," Journal of Educational Psychology,

XLVI (1955), 85-93.

 

1038. A. Courtis, "Maturation Units for the Measure-
ment of Growth," op cit., p. 686.

1048. A. Courtis, Maturation Units and How to Use Them
(Ann Arbor, Michigan: Edwards Bros., 1950), pp. 179-180.

 

lO5Benjamin Gompertz, "0n the Nature of the Function
Expressive of the Law of Human Mortality," Philosophical
Transactions of the Royal Society of London for theIYear
1825, Part I'CStTfiJames_PalI MalI:_W. Nicol, Prifiters to
the Royal Society, CXV (1825), Ch. XXIV), pp. 513-585.

 

 

 

 

33

between the factors involved in all biologic maturations.106

His research substantiates this statement and points out

107,108,
the multi-cyclic nature of growth by use of the formula. 109

Millard's use of the Courtis method has shown three

10

cycles of growth.1 In 1940 he presented a study which

showed the extent to which the Gompertz function adequately

describes growth.111 At that time he noted that:

The conclusion must be made that the concept of
norms needs revision. Evidence such as that shown
in this study illustrates the injustice done many
children by comparing their performances with so-
called norms which so inadequately describe the
true nature of growth.

 

106s. A. Courtis, loc. cit.

107s. A. Courtis, The Measurement of Growth (Ann Arbor:
Michigan: Brumfield and Brumfield, 195277

1088. A. Courtis, "The Prediction of Growth," Journal
.2: Educational Research, XXVI (1933), 481-492.

1098. A. Courtis, "Maturation as a Factor in Diagnosis,"
Thirty-Fourth Yearbook of the National Society for the Study
§ZfEducation (1935), 1691187:

llOCecil V. Millard, Child Growth and Development in

the Elementary School Years (Boston: D. C. Heath and com:—
pany;_I951), p.65.

111Cecil v. Millard, "The Nature and Character of Pre-
Adolescent Growth in Reading Achievement," Child Development,
XI, No. 2 (1940), 71-114.

 

112Ibid., p. 105.

*—

‘0’!

.5

1.1 .

"o

 

34
An early evaluation by Winsor of the Gompertz curve
as a growth curve has provided a valuable critique on the
function. He reported that:

The Compertz curve and the logistic possess similar
qualities which make them useful for the empirical
representation of growth phenomena. It does not
appear that either curve has any substantial advantage
over the other in range of phenomena which it will
fit. Each curve has three arbitrary constants, which
correspond essentially to the upper asymptote, the
time origin, and the time unit or "rate constant;"

. It has been found in practice that the logistic
gives good fit on material showing an inflection
midway between the asymptotes. No such extended ex-
perience with the Gompertz curve is yet available,
but it seems reasonable to expect that it will give
good fits on material showing an inflection when
about thirty-seven per cent of the total growth has
been completed. Generalizations of both curves are
possible, but here again there appears to be no reason
to expect any marked differencein the additional
freedom provided.11

The sort of extended experience with the use of the
Gompertz curve to which Winsor referred has been reported
by several researchers. Millardll" has shown the extent
to which the Gompertz function adequately describes growth.
Other studies which have contributed to the verification
of the method are those by Nally,115 Kowitz,116

 

113C. P. Winsor, "The Gompertz Curve as a Growth
Curve," Proceedings of the National Academygf Science,

XVIII (1932): 7.

 

 

1140. V. Millard, o2.-cit.

115Thomas P. F. Nally, "The Relationship Between
Achieved Growth in Height and the Beginning of Growth in
Reading" (unpublished Ph.D. thesis, Michigan State College,
East Lansing, Michigan, 1953).

35
Rusch,ll7’118 Udoh,119 Greenshields,120 Holmgren,121 and

Wolrerd.122

Meredith attempted to apply the Courtis method to
test its usefulness on six cases ages seven to nine years,
nine months, using three measures each.123 He made a
critical evaluation of the Courtis "universal law" method
of prediction of individual growth and reported that it is
"considered unsuited to the prediction of individual growth

in stature for white males between six and eleven

 

116Gerald T. Kowitz, "An Exploration into the Rela-

tionship of Physical Growth Pattern and Classroom Behavior
in Elementary School Children" (unpublished Ph.D. thesis,
Michigan State College, East Lansing, Michigan, 1954).

117Reuben R. Rusch, "The Relationship Between Growth
in Height and Growth in Weight" (unpublished Master's thesis,
Michigan State College, East Lansing, Michigan, 1954).

118Reuben R. Rusch, "The Cyclic Pattern of Height
Growth from Birth to Maturity" (unpublished Ph.D. thesis,
Michigan State University, East Lansing, Michigan, 1956).

119Ekanem (Benson) Akpan Udoh, "Relationship of
Menarche to Achieved Growth in Height" (unpublished Ph.D.
thesis, Michigan State University, East Lansing, Michigan,
1955).

120C. M. Greenshields, OP- C??-

121Gordon E. Holmgren, "A Study of Relationship of
Certain Developmental Measures to Maturity of Boys as In-
dicated by Measures of Height" (unpublished Ph.D. thesis,
Michigan State University, East Lansing, Michigan, 1957).

122Gerald H. Wolferd, "An Evaluation of the Courtis
Method in the Study of Growth Relationships" (unpublished
Ph.D. thesis, Michigan State Universit, East Lansing, Mich-
igan, 1957)-

123B. V. Meredith, "The Rhythm of Physical Growth,"
op. cit.

36

'12" Nally and DeLong, however, reworked the Meredith

years.‘
material, and found errors in the computations. From their
analysis, it was their conclusion that "Courtis' law of
growth is applicable for the prediction of growth in stature
with an accuracy that is within rigorous scientific limits.
."125 In general, this conclusion was confirmed by
Dearborn and Rothney.126
Thus, as the literature was reviewed, an atmosphere
of critical analysis seemed to pervade. Krogman stated
that "as one views the literature in this field in the past
five years one is struck by an atmosphere of ferment and
discontent."127 This atmosphere he noted,
has engendered a positive rather than a negative
attitude. . . . The work now going on, the con-
structive criticism being levelled, all permit one
to hope, and to expect, that 1955-1960, and there-

after will see remarkablg reorientation and
considerable progress.12

 

l2"Ibid., p. 120.

125Thomas P. F. Nally and A. R. DeLong, "An Appraisal
of a Method of Predicting Growth," Child Development Labora-
tor Publications, Series 11, No. 1, East Lansing, Michigan
1 52).

 

 

126w. F. Dearborn and J. w. M. Rothney, Predicting
the Child's Development, op. cit., PP. 218-220.

 

 

127Wilton M. Krogman, "The Physical Growth of Children:
An Appraisal of Studies 1950-1955," op. cit., p. iii.

128Ibid., p. 76.

37

He observed that "a major issue centers around the
cross-sectional versus longitudinal, or serial, philoso-
phies . . . [and] only from the second can we derive any
idea of growth progress."129

It was with such a philosophical frame of reference,
and with an earnest desire that a contribution could be
made to the scientific approach to longitudinal growth

studies, that the present study was undertaken.

aaaaaaaaa

 

CHAPTER III
PROCEDURE

The Data

The cases selected for analysis in this study were
sixty-six boys whose measurements were reported in the
Harvard Growth Study which was inaugurated in the fall of
1922.1 Some thirty-five hundred children were included in
the original study which was conducted by the Psycho-
Educational Clinic of the Harvard Graduate School of Edu-
cation. They represented a population of first grade
school children who were entering school in three cities
in the vicinity of Boston. Twelve annually repeated
measurements were recorded for each subject. The measure-
ments included standing height, body weight, sitting height,
sternal height, iliac diameter, head length, head width,
dental age, skeletal age, mental age, chest depth, and
chest breadth.

The completed measurements represent longitudinal
data for 747 boys and 806 girls, from first grade through

senior high school.

 

1W. F. Dearborn, J. W. Rothney, and F. K. Shuttleworth,
"Data on the Mental and Physical Growth of Public School
Children," Mono raphs of the Society for Research 13 Child
Development, II%, No. l (1938).

 

 

 

 

39

In appraising the Harvard Study, Shuttleworth points
out the classic nature of the data.2 He states that:
It is the considered judgment of the writer that
the materials of the Harvard Growth Study represent
easily the finest collection of longitudinal records
available for the study of physical growth during the
adolescent period. Better data, in the sense of more
data and longer records, will probably never be
available. Better data, in the sense of half as many
cases followed over as long a period together with
either more measurements or more accurate measure-
ments or more supplementary data, will not be
available for gnalysis within a period of at least
fifteen years.
The sixty-six cases selected for this study represent
a random sampling from the 1553 completed cases on whom
measurements in standing height, skeletal age, and mental
age measurements were available. A Chi-Square test of
"Goodness of Fit" was used to test the sampling distribution
of the measurements at age eight for the sixty-six cases.
Table I gives the Computed values of Chi-Square for the
sampling distribution as well as the critical value of Chi-
Square at the ninety-five per cent level of confidence.
Examination of the figures in Table I indicates that for
all three measurements, the sampling distribution can be
assumed to be that of one taken from a normally distributed

population, at the ninety-five per cent level of confidence.

 

2Frank K. Shuttleworth, "The Physical and Mental
Growth of Girls and Boys Age Six to Nineteen in Relation to
Age at Maximum Growth, " Monographs of the Societ for
Research in Child Development, IV, NB'.—37(11939)

 

3Ibid., p. 6.

40

TABLE I

COMPUTED AND CRITICAL x2 VALUES OF OBSERVED
MEASUREMENTS IN STANDING HEIGHT,MENTAL AGE,
AND SKELETAL AGE OF THE SIXTY-SIX BOYS AT

 

 

 

 

 

 

 

 

 

AGE 8
Measurement Computed X2 Critical X2 95
Standing Height 3.68 11.07
Mental Age 10.89 15.51
Skeletal Age 2.67 7.81

 

In the case of the distribution of observed measure-
ments in standing height at age eight, for instance, it can
be noted that an observered x2 = 11.07 would need to be
obtained before the hyopthesis that the observed measure-
ments were those taken from a normally distributed popul-
ation could be rejected. The observed value of X2 = 3.68
led to the assumption of normal distribution at the ninety-
five per cent confidence level, and represents a value well
within the acceptable area. Further observation of Table I
leads to the same assumption for all three aspects of
development.

The observed measurements for each case in standing
height, mental age, and skeletal age, as well as the com-
puted percentages of total development in each aspect of
growth, ethnic origin and socio-economic status may be

found in Appendix A of this thesis. Examination of this

Al
data revealed that the ethnic origin and the socio-economic
status in regard to the occupation of the boys' fathers

were distributed as indicated in Table II.

TABLE II

ETHNIC ORIGIN AND SOCIO-ECONOMIC
STATUS OF THE SIXTY-SIX BOYS

 

Ethnic Origin Frequencies Socio-Economic Frequencies

 

Status*
Jewish 2 I A
North European 44 II 7
Mixed Stock 2 III 25
Italian 17 IV 18
Negro 1 V A

Unknown 8

*I--Professional .
II--Semi-professional, large business, important

managerial
III--Skilled labor, small business, small managerial

IV--Semi-skilled labor
V--Unskilled labor

Methodology

In order to analyze longitudinal growth data for the
INIPpose of determining coorelative relationships among
beginning points and end points of the adolescent cycle of
IMIturation, it was necessary first of all to employ a
Eillitable mathematical method for determining the multi—
Cbflzlic nature of growth in the three developmental aspects
Of‘ standing height, skeletal age, and mental age. This
Saction will present the mathematical method which was

111Silized as well as the test used to determine the

A2
efficiency of the method for prediction of growth in the
three aspects, and correlative techniques which were

employed.

Determination of cycles. The determination of the

 

number of cycles of growth which were present in the meas-
urements for each of the sixty-six cases in each of the
three developmental aspects (height, skeletal age, and
mental age) was made by the utilization of normal probab—
ility paper. To do this, each measurement was first
reduced to a per cent of maximum development. The measure-
ment taken as that representing maximum development in each
case was the largest observed measurement in a particular
aspect of growth. By way of example, the data for Case
343M is presented in Table III. The observed measurements
and computed per cents of development in each developmental
aspect for all of the sixty-six cases may be found in
Appendix A of this thesis.

Figure 2 shows the per cents of development in
standing height, mental age, and skeletal age after they
have been plotted on normal probability paper and deter-
mined by the resulting 1ines of best fit through the plotted
points. It can be noted that the lines of best fit in each
of the three aspects of growth indicate a two cycle pattern

of growth.

OBSERVED MEASUREMENTS AND COMPUTED PER CENTS
OF DEVELOPMENT IN STANDING HEIGHT, MENTAL
AGE, AND SKELETAL AGE FOR CASE 343M

TABLE III

43

 

 

Age Height % of % of % of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.
7.11 85.32 1160 68.96 81.90 36.25 78 34.36
8.07 96.84 1207 71.75 117.17 51.87 90 39.64
9.09 109.08 1273 75.68 121.14 53.63 102 44.93
10.08 120.96 1317 78.29 119.14 52.74 113 49.77
11.10 133.20 1363 81.03 146.52 64.86 126 55.50
12.08 144.96 1403 83.41 160.18 70.91 140 61.67
13.08 156.96 1441 85.67 160.80 71.18 151. 66.51
14.08 168.96 1491 88.64 174.02 77.04 167 73.56
15.07 180.84 1571 93.40 184.45 81.65 178 78.41
16.09 193.08 1641 97.56 207.56 91.88 198 87.22
17.09 205.08 1664 98.92 213.28 94.42 214 94.27
18.10 217.20 1682* 100.00 225.88* 100.00 227* 100.00

W

*Represents the measurement taken as maximum for
computation of per cents of development.

b... 1.: B. \IQ 1.3.}..31...

3. . .
. .. .q; .2... .._ r; .2” ..

.l 5‘ k."

Height

44

l J
j
\0 \O
(I) \O

l
u)?”
U1

‘
+
\O
O

‘ x

Q
\
\ \.
4 i
\1 CD
0 O

0
§
O
588
Per Cent of Development

1
T
L0
0

 

 

Figure 2.

8 10 l2 l4 l6 18
Age in Years

Composite normal probability graph of per
cents of total development in standing
height, mental age, and skeletal age, for
Case 343M, indicating measurements within
a given cycle of growth.

45
The usage of normal probability paper for the deter-
mination of points which lie within a given cycle is not a
new idea. Cornell and Armstrongl‘L utilized the method with
good success in determining end of childhood and beginning
of adolescent cycles of growth. Their conclusions, after
plotting the percentage of development in mental age for
each individual at yearly intervals, was that the resulting
lines consisted of a straight line between the ages of six
or seven, usually up to a point varying for different in-
dividuals from about age eleven to age fourteen or fifteen,
followed by another straight line at a steeper slope toward
maturity.5
Similar conclusions to those of Cornell and Armstrong
were drawn from the observations of the probability lines

in the present study. A more detailed report of the

findings will be included in Chapter IV of this paper.

The Courtis Method. After the measurements to be

 

included in each of the two cycles of growth were deter-
mined by use of the normal probability paper, the Courtis
technique for analysis of growth was applied to determine_

(1) the maximum amount of development in each cycle of

 

“E. L. Cornell and C. M. Armstrong, "Forms of Mental
Growth Patterns Revealed by Reanalysis of the Harvard Growth
Dgta,"4Child Development, XXVI, No. 3 (September 1955),

1 9-20 .7

51bid., pp. 173-175.

46
growth for a given developmental aspect; (2) the rate of
growth in a given cycle; (3) the incipiency, or amount of
growth at the beginning of a cycle; (4) the predicted growth
at a given age within a cycle; and (5) the deviation of the
observed score or measurement at a given age from the
predicted score.

A brief historical review of the development of the
Courtis technique seems necessary at this point before a
detailed explanation of the method is presented. The method
was first presented by Courtis in 1929.6 He defined the
method as a simplex growth equation and noted that the laws
of growth, and the effect of any one factor upon growth,
are most easily determined in simple situations, character-
ized by (l) progress toward a defined maturity which takes
place in (2) the immature organism of constant nature when
it reacts to (3) constant nuture under (4) constant condi-

7

tions. He noted further that all simplex curves may be

described by the formula y = kgcx which was deduced by

Gompertz9 in 1825, from mortality statistics. Other

6S. A. Courtis, "Maturation Units for the Measurement
of Growth, " School and Society, XXX (1929), 683-690.

 

7Ibid., p.685. 8Ibid., p. 686.

9Benjamin Gompertz, "0n the Nature of the Function
Expressive of the Law of Human Mortality," Transactions of
the Royal Society of London, for the Year 1825, Part I,
Vol. 115, CHapter'24, pp. 513:585.

 

 

47
references to the Gompertz formula may be found in

th as well as Croxton and Cowder.11

Prescot

In the equation, g, c, and k represent three con-
stants, x the time variable and y the measurement of growth
at time x.

The use of isochrons, or maturation units, reduces

the exponential equation to a simple linear equation:

Y1 = r1 t + sl

where Y1, 81’ and r1 are the isochrons of y, g, and c; and
t represent units of time.12 An isochron is defined as the
time required for the ordinate at the point of inflection
to increase to one-tenth of its own power of itself. It is
one per cent of the total time required for the growth
curve to change from development of 0.000,000,l89 per cent
to a development of 99.90917 per cent, or (practically)
from zero to complete maturity. Courtis has published a

table which gives the percentages of the period of maturation

corresponding to each tenth percentage of development.13

 

10R. D. Prescott, "Law of Growth in Forecasting
Demand," Journal of the American Statistical Assn., XVII,

No. 140 (TDEETT‘47I-H7g.

 

11

F. E. Croxton and D. J. Cowder, A lied General
Statistics (New York: Prentice Hall,Inc., , pp.447-452.

 

128. A. Courtis, "Maturation Units for the Measurement
of Growth," op. cit., p.686.

13S. A. Courtis, Natural Isochrons, Linear Maturation
Units for Use in Computations Involving Measurements-2:
Growth (Ann Arbor, Michigan: private publication).

 

 

 

48
He states that, "The use of isochrons, or time scores,
reduces the complex phenomena of biologic growth to the
simplicity of physical phenomena and makes possible the
setting up of standards and comparable units of measurement
in all biological fields."1“

In later writings, Courtis presented detailed explan-
ations of the method which explain the technique for the
analysis of growth.15’l6’l7’18 It was from these sources
that the method was taken for use in the current study.

The explanation of the use of the method in this study
follows.

After the points which were to be included in the
childhood cycle of growth were determined by use of the
normal probability paper, these measurements wens then
plotted on semi-logarithmic paper in order to determine
first-cycle maximum in each of the three aspects of growth
for every one of the sixty-six cases. Figure 3 illustrates

the resulting curve for the childhood cycle for Case 343M

 

148. A. Courtis, "Maturation Units for the Measure-
ment of Growth," op. cit., p. 690.

158. A. Courtis, The Measurement of Growth (Ann
Arbor: Brumfield and Brm PieIa, 1932).“

16S. A. Courtis, "The Prediction of Growth, " Journal
23 Educational Research, XXVI (1933), 481- 492. ""“”“

17S. A. Courtis, Toward a Science of Education (Ann
Arbor, Michigan: Edwards Bros.,l 1951).

18S. A. Courtis, Maturation Units and How to Use Them
(Ann Arbor, Michigan: Edwards Bros. , 1950).

 

 

Height in Millimeters

49
“1600

l

J

l

 

i1150

 

1100,‘ . . . . . . . I , I .

72 84 96 108 120 132 144 156 168 180 192 204
' Age in Months

Figure 3. Semi-logarithmic curve showing childhood cycle
development in standing height, Case 343M.

50
in standing height. Courtis original method then selected
three equally spaced points from the resulting curve, indi-
cated by A, B, and C in Figure 3. The cycle maximum was
then computed by the following formula, which is the

Freedman Method For Computing Maximum of a growth cycle.19

 

A é B = a per cent = isochronic value = A1
B f C = a per cent = isochronic value = Bl
C 5 B = a per cent
(A/B) (C/B) = a per cent = isochronic value = Cl
Maximum K = B 1
% B1 + Al — C1 ]

where the notation % ] directs one to change the value
obtained to a per cent before multiplying by B.

In the present study, however, it was found that the
maximum could be read graphically from the semi-logarithmic
curve and the resultant maximum did not differ significantly
from that which was computed by the formula.

The next step in the process was the computation of
the £232 of growth Ulisochrons within the cycle. Once the
cycle maximum had been obtained, per cents of cycle maximum
were computed for each measurement within the cycle. These

per cents, which are presented in Table IV for childhood

 

19Devised by Seymour Freedman, a student of S. A.
Courtis; reported in C. V. Millard, Problems of Pupil
Growth and Development (Ann Arbor, Michigan: Edwards
Brothers, Inc., 1948), p. 63.

 

TABLE IV

51

PER CENTS 0F CHILDHOOD CYCLE MAXIMUM FOR
MEASUREMENTS IN STANDING HEIGHT,

 

 

CASE 343M
Chronological Per Cent
YearggeMos. Mg::::Z:gnt Maxgmum Mgiiifigoiélg68lfi.m.
7.11 85.32 1160 73.97
8.07 96.84 1207 76.97
9.09 109.08 1273 81.19
10.08 120.96 1317 83.99
11.10 133.20 1363 86.92
12.08 144.96 1403 89.47
13.08 156.96 1441 91.90
14.08 168.96 1491 95.08
1571 ---

15.07 180.84

 

52

cycle for Case 343M, were then plotted on an Isochronic
Graph Sheet. The line of best fit for the points was then
determined, and two arbitrary points were selected as indi-
cated by X and Y on the line in Figure 4, which illustrates
the line for the childhood cycle in standing height for
Case 343M. The computation of cycle rate was then made by
the following process:

Age Y - Age X = age difference

per cent of development at Y converted to isochronic value
minus per cent of development at X converted to isochronic value

= Isochronic difference

Isochronic difference f age difference = rate of

growth in isochrons for one month in a given cycle.

After the two growth constants of maximum and rate
had been obtained, the third constant, that of incipiency,
or acquired growth at the beginning of the cycle, was com-
puted. This was done by multiplying the computed rate
times age Y, and subtracting the observed isochronic value
at Age Y from the product to obtain the accrued growth at
the beginning of the cycle which must be added into the
equation. Table V presents the data for determination of
rate and incipiency for Case 343M in standing height.

When the three growth constants for the childhood
cycle had been thus obtained they were substituted in the
equation: Y = K g rt i i], where y = estimated growth,K =

cycle maximum, r = rate; t = a given time; and i = incipiency.

53

Isochrons

ma
om

mm

m0
m8

 

mcucoz CH mEHB mo mpHED

oqa oma one oaa 00H
4. _. .

_, _,

.zmem sumo .ocwaom wcaocsom
a“ macho ooonoaano mo pcmerHm>oo
mo mpcmo pom pom paw pmmn mo mafia

om

.: mgdwfim

do:

' l

.8

 

Arum

 

AqIanem JO seBequeoJeg

 

.‘.u.."a.

t».-. . co .0

54

TABLEII

COMPUTATION OF FIRST CYCLE RATE AND INCIPIENCY
IN STANDING HEIGHT FOR CASE 343M

 

 

 

Max. 1568
Rate
Ages Per Cents Isoc. Is.Diff 5 Age Diff.
170 93 56.23
104 80 45.00 .1701
Diff. 66 Diff.ll.23

(A) (Rate) x Age (2) 17.69; (B) Isoc.Value at Age (2) 45.00
Diff. Between A and B 27.31; Sign +

Equation: y = ._12§§__ °lZQl_ t.__i__ 27'311
max rate diff. (B-A)

 

55

The expression % ] directs one to change the isoch-
ronic value thus obtained to a per cent of development
before multiplying by the maximum. Substituting the com-
puted values of childhood cycle constants in standing height

for Case 343M, the resultant equation reads:
y = 1 68 g .1701 t + 27.31]

Table VI shows the ages at which measurements were
taken, the observed measurements, predicted measurements,
and deviation of the estimated measurements from the
observed measurements in standing height for Case 343M.
Examination of the table indicates that the negative values
of the deviations increase in magnitude from age 156.96
months to age 217.20 months, the last observed measurement.
These negative values were then plotted on semi-logarithmic

paper in order to compute the maximum residual growth in

 

the adolescent cycle.

The same processes for obtaining the three cycle
constants of maximum rate and incipiency as those described
for the childhood cycle, were employed to obtain the
residual elements of growth in the adolescent cycle. Figure
5 shows the adolescent cycle curve which resulted from the
plotting of the residual negative deviations from the first
cycle equation for standing height for Case 343M. From
this, an adolescent cycle residual maximum of 166 milli-

meters was obtained, and per cents of maximum development

m

TABLE VI

OBSERVED AND PREDICTED MEASUREMENTS IN STANDING
HEIGHT, CASE 343M, AND DEVIATIONS OF THE
TWO MEASUREMENTS

56

 

Age in Observed Predicted
Months Measurement Measurement Difference
85.32 1160 1154.04 - 5.96
96.84 1207 1218.33 + 11.33
109.08 1273 1277.92 + 4.92
120.96 1317 1326.52 + 9.52
133.20 1363 1368.86 + 5.86
144.96 1403 1403.36 + 0.36
156.96 1441 1431.58 - 9.42
168.96 1491 1456.67 - 34.33
180.84 1571 1475.48 - 95.52
193.08 1641 1492.73 -l48.27
205.08 1664 1506.84 -157.16
217.20 1682 1517.82 -164.18

Deviations in millimeters

57

Figure 5. Semi-logarithmic curve of second cycle
residuals obtained from first cycle
equation constants in Standing Height,
Case 343M.

200 *

180 r

160 T

H
O
O
44

(I)
O
J

O\
C)
1

40 4

20 m

 

0 ' l l I ”I l 'l l ‘l ‘l "'l ‘1
9 10 11 12 lg 14 '15 l6 l7 18 19 20
ge in Years

58
of adolescent cycle were computed as for the childhood
cycles. These percentages, as shown in Table VII, were
then plotted on an Isochronic graph sheet (see Figure 6)
and two arbitrary points were selected from the line of
best fit for the purpose of computing cycle rate and inci-
piency. The equation constants for the adolescent cycle
are shown in Table VIII. The resulting equation of resi—
duals for the adolescent cycle in standing height for Case
343M was as follows:

y = 166 % .9299 t - 131.66]

Using this formula, the estimated second cycle
residuals were then obtained and added to the estimates
which were obtained from the first cycle equation. These
results, as well as the deviations from the observed meas-
urements may be found in Table IX. Total estimated maximum
to which Case 343M was growing in Standing Height was
obtained by the formula:

K3 = Kl + K2,

K 1568 + 166 = 1734 millimeters

3

where K3 = total maximum development in a given growth
aspect; K1 = first cycle maximum, and K2 = second cycle
maximum, representing a residual of K1‘
A complete listing of all cycle constants, average
error of equations, time of cycle breaks and estimated time

of adult maturity in each of the three aspects of growth

(standing height, mental age, skeletal age), for each of

TABLE VII

DATA FOR ISOCHRONIC GRAPH SHEET--PERCENTAGES OF
TOTAL DEVELOPMENT IN STANDING HEIGHT FOR

 

CASE 343M

59

 

 

m =3:

 

Maximum-~l66 mm.

 

C.A. in Months

Observed Measurement

Per Cent
of Maximum

 

168.96
180.84
193.08
205.08

217.20

34.33 i
95.52
148.27
157.16
164.18

20.68
57.54
89.31
94.67
98.90

 

 

 

 

 

3 60
Figure 6. Line of best fit for per cents
of development of adolescent ‘
cycle in Standing Height, ~
Case 343M. 70 -
~98 .
~97 65 e
7 .
~96
J95 60 r
55 ..
h .
s~bo
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9
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+10 2
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l..,.[ ........... ,1. ,4; . 1 ,H1.. ..lllq ,15.3.
150 160 170 180 190 200 210 230 240

Units of Time in Months

61

 

 

 

 

 

TABLE VIII
COMPUTATION OF ADOLESCENT CYCLE RATE AND INCIPIENCY
¥t Max.166
Rate
Ages Per cents ISOC. IS.Diff ; Age Diff.
205.08 94.67 59.04
168.96 20.68 25.45 .9299
Diff. 36.12 Diff.33.59

(A)(Rate) x Age (2) 157.11; (B) Isoc.Valve at Age (2) 25.45
Diff. Between A and B 131.66; Sign -

Equation: y = .__199_ ._£%§Zi_ t - 131.66
max rate diff.(A-B)

 

TABLE IX

PREDICTED MEASUREMENTS FOR CHILDHOOD AND
ADOLESCENT CYCLES 0F GROWTH IN STANDING
HEIGHT, CASE 343M

 

 

Age in Observed Predicted

 

Months Measurement Measurements Kl + K2 Diff.
K1 K2
85.32 1160 1154.04 -- 1154.04 - 5.96
96.84 1207 1218.33 -- 1218.33 +11 33
109.08 1273 1277.92 -- 1277.92 + 4.92
120.96 1317 1326.52 -- 1326.52 + 9.52
133.20 1363 1368.86 -- 1368.86 + 5.86
144 96 1403 1403.36 -- 1403.36 + .36
156.96 1441 1431.58 13.44 1445.02 + 4.02
168.96 1491 1456.67 42.66 1499.33 + 8.33
180.84 1571 1475.48 98.43 1573.91 + 2.01
193.08 1641 1492.73 140.43 1633.16 - 7.84
205.08 1664 1506.84 157.03 1663.87 - .13
211.20 1682 1517.82 163.34 1681.16 - .84
Average error of
equation 5.09

 

63
the sixty-six boys included in this study may be found in
Appendix B of this thesis.

By substituting computed growth constant values in
the equations thus obtained, it was possible to determine
the age at which the childhood cycle had reached the point
of maturity. This age represented the computed age of
cycle break and is indicated at t2 in the tables in Appen-
dix B. Age of reaching adult maturity was computed in the

same manner and is reported as t for each aspect of growth

3
for all sixty-six individuals in Appendix B.

Correlative techniques. The statistical method which

 

was employed to obtain the various correlations which will

be reported in Chapter IV of this thesis is known as the

Pearson r.20 The partial correlations were obtained by

the formula:

r _ NZXY- (2x) (ZY) 21
xy \I[Nzx2 - (Z x)2] [NZY2 -: (2x)2]

and will be referred to as the zero-order coefficient of

 

 

correlation. First order partial correlations were

obtained by the formula:

 

20Helen M. Walker and Joseph Lev, Statistical Infer-
ence (New York: Henry Holt and Company, 1953), p. 233.

211bid., p. 234.

64

 

 

The multiple correlation coefficient of any three

factors was obtained by the formula:

2 _ 2
1 ‘13x.yz ‘ (l ' ny )

2

(l - rxy.z )

A discussion of the various partial and multiple
correlations which were computed from the data which was
analyzed by the use of the Courtis technique as well as
the findings which resulted from the computations will be

reported in the chapter which follows.

CHAPTER IV

ANALYSIS OF THE DATA

It is generally agreed that multiple relationships
among the various aspects of human growth and development
are best revealed through analysis of individual longi-
tudinal data. In order to examine relationships among
phenomena of growth in standing height, skeletal maturity,
and mental maturity during the school life of the child,
it was necessary to select what represented the best
available data for that purpose. The Harvard Growth Data
of the Third Study was selected as meeting this requirement.
Sixty-six boys were selected for whom annual measurements
in standing height, skeletal age, and mental age were
available from the approximate time of entrance into the
first grade of three public schools in the vicinity of
Boston until their graduation from senior high school.

The measurements covered the years from seven through
seventeen. Measurements were available for only three of
the boys before six years of age. Measurements at age six
were available for thirty-four of the cases. For twenty

of the sixty-six cases, measurements were available through
eighteen years of age. In four of the cases measurements

were recorded through nineteen years, and in one case the

66

recorded observations included the twentieth year. The
annual measurements in standing height, skeletal age, and
mental age for each of the sixty-six cases are to be found
in Appendix A of this thesis.

After the cases had been selected, it was then nec-
essary to determine whether the sampling represented one
which could be assumed to be that of a random sampling
from a normally distributed parameter. The test used to
determine the nature of the distribution of the observations
in the three developmental aspects was the Chi-Square test
of "goodness of fit." The results of this test indicated
that the distribution of the observations in each of the
three aspects of growth could be assumed to be that of one
representative of a normally distributed population.

Analysis of the data thus selected and tested with
regard to the nature of the distribution, revealed some
pertinent findings about the nature of physical and mental
growth of school-age boys when such analysis was undertaken
on an individual longitudinal basis. The utilization of
the Courtis technique for the analysis revealed the multi-
cycle nature of growth for each child in the three develop-
mental aspects. It also made possible the observation of
the individuality of growth in terms of times of cycle
breaks, rates of growth within a cycle, beginning and end
points of cyclic development, attained growth at the begin-
ning of a cycle, and maxima toward which individuals were

growing.

67

The cyclic nature of growth in the human organism is
a phenomenon which has been recognized by many researchers
whose studies were cited in Chapter II of this thesis.
Earlier studies have also emphasized the fact that the study
of grbwth relationships by the utilization of conventional
cross—sectional techniques has tended to obscure the nature
of individual growth patterns. The utilization of the
Courtis technique made it possible to compute an individual
growth curve from equation constants which revealed the
.magnitude of growth from one age interval to the next, the
points of cycle break, and provided a method for predicting
adult maturity which was consistent with the observed
measurements.

The adequacy of the method for describing growth is
revealed by the composite curvilinear regression line which
was obtained from the average equation constants for the
sixty-six cases for standing height, skeletal age, and
mental age. The resultant composite equations were as
follows:

1. Standing Height

y = 1576 4.1778t + 26.96] + 197 %.8719t - 110.72]

2. Skeletal Age

y = 158 %.2365t + 14.05] + 71 %.3433t - 26.85]
3. Mental Age
y = 148 %.3l63t + 11.62] + 60 %.5476t - 55.82]

68

It was possible to compute the magnitude of the error
of the equations by computing predicted scores at annual
intervals and then determining the deviation of the mean
predicted score from the mean observed score at each age
interval. These data are presented in Tables X, XI, and
XII. From the observed deviations, it was then possible
to compute a per cent of error of the predicted score from
the observed measurement. These per cents of error revealed
the efficiency of the curve of constants for describing
growth at yearly intervals, and also provided a means of
determining a composite efficiency percentage representative
of the compound equations for each of the sixty-six cases
in the three aspects of development.

The data in Table XIII indicates that the equation
described growth with better than ninety-five per cent
efficiency for all three aspects of development for the
sixty-six cases.

The mean per cent of error for the three equations
was 2.2 per cent. Thus it may be stated that the equation
obtained by the use of the Courtis technique for describing
growth in developmental aspects of standing height, skeletal
age, and mental age for the sixty-six boys was 97.8 per
cent efficient.

Figure 7 presents the percentages of error for each
of the three composite equations in graphic form. From the

graphic representation, it can be noted that the smallest

69
TABLE X
OBSERVED MEANS, COMPOSITE PREDICTED MEANS, DEVIATIONS AND

PER CENT 0F EQUATION ERROR AT ANNUAL INTERVALS FOR MEAN
STANDING HEIGHT MEASUREMENTS OF SIXTY-SIX BOYS

 

j: a

 

Observed Predicted Per Cent

Measurement Measurement Deviations of
Age in in in in Equation

Months Millimeters Millimeters Millimeters Error

 

]

89 1191.4 1183.5 - 7.9 .66
101 1247.5 1251.3 3.8 .30
113 1303.1 1308.0 7.9 .61
125 1352.8 1355.6 2.8 .20
137 1401.4 1394.8 - 6.6 .47
149 1454.7 1439.2 -15.5 1.06
161 1520.1 1526.1 6.1 .40
173 1590.8 1637.0 46.2 2.90
185 1649.2 1668.9 19.7 1.19
197 1687.2 1699.7 12.5 .74
209 1713.2 1717.8 4.5 .27

 

 

 

TABLE XI

OBSERVED MEANS, COMPOSITE PREDICTED MEANS, AND PER CENT OF
EQUATION ERROR AT ANNUAL INTERVALS FOR MEAN
SKELETAL AGE MEASUREMENTS OF SIXTY-SIX BOYS

 

vfi v fl

 

Per Cent
Observed Predicted of
Age in Measurement Measurement Deviations Equation
Months in Months in Months . in Months Error
89 84.03 86.58 2.55 3.03
101 96.39 100.49 4.10 4.25
113 108.77 112.49 3.72 3.42
125 120.89 123.56 3.27 2.70
137 132.81 135.09 2.28 1.71
149 145.51 148.81 3.30 2.26
161 158.15 163.57 5.42 3.43
173 171.06 178.27 7.21 4.21
185 184.43 190.97 6.54 3.54
197 197.16 201.28 4.12 2.09
209 208.75 209.12 0.37 0.18

fi‘v

TABLE XII

70

OBSERVED MEANS, COMPOSITE PREDICTED MEANS, AND PER CENT
OF EQUATION ERROR AT ANNUAL INTERVALS FOR MEAN MENTAL

 

AGE MEASUREMENTS OF SIXTY-SIX BOYS

 

 

 

Per Cent
Observed Predicted of

Age in Measurement Measurement Deviations Equation

Months in Months in Months in Months Error
89 97.75 101.52 3.77 3.85
101 109.21 114.40 3.79 3.47
113 118.21 124.02 5.81 4.91
125 128.72 131.32 2.60 2.02
137 143.43 140.52 -2.91 2.03
149 157.37 152.88 -4.49 2.85
161 165.68 169.55 3.87 2.33
173 175.80 183.99 8.19 4.65
185 186.41 193.81 7.40 3.97
197 193.15 199.98 6.83 3.52
209 200.23 203.45 3.22 1.61

TABLE XIII

AVERAGE COMPOSITE EQUATION ERRORS FROM OBSERVED MEAN
SCORES AND PER CENTS OF EFFICIENCY OF EQUATIONS FOR
STANDING HEIGHT, SKELETAL AGE, AND MENTAL AGE
OF SIXTY-SIX BOYS

 

Average Per
Cent of

Average Per

Average Error Cent of Error

 

of Composite of Efficiency
Measurement Equation Equation of Equation
Standing
Height 12.1 mm. 0.80 99.20
Skeletal Age 3.89 mos. 2.80 97.20
Mental Age 4.81 mos. 3.20 96.80

71

-——- Standing Height
-———— Skeletal Age

__.__Mental age
5 a] .
L1 0
o , .\\
E 4 4» . / \ ,
\\. . \q\\,
8 / \ \
p 3 .1 ' , I. . \
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£1 ’ \
1 ' ' \
u—(L ’0 I \\
o I, \\ I " ‘
\‘\.”.0\\ I’ll \: \\\
~L '
i 1’ t i i Tr %

 

 

7 9 ll l2 14 16 18
Age in Years

Figure 7. Graph of per cents of composite
equation error for standing height,
skeletal age, and mental age

deviation of predicted scores from the observed scores in
terms of percentages of deviation occurred at ages ten to
twelve, the termination of the childhood cycle, and again
at ages sixteen to seventeen years of age, the termination
of the adolescent cycle. The greatest deviations occurred
at ages eight to nine and again at ages fourteen and fif-

teen years. These ages represent the periods of most rapid

72
growth within the two cycles, as well as periods when growth
is most variable from individual to individual.

The average annual increments in growth for the
sixty-six boys which were computed from the equations are

presented in Table XIV.

TABLE XIV

AVERAGE ANNUAL INCREMENTS IN GROWTH IN STANDING

HEIGHT, SKELETAL AGE, AND MENTAL AGE FOR SIXTY-

SIX BOYS, COMPUTED FROM COMPOSITE EQUATIONS OF
GROWTH CONSTANTS

1 fig

Average Annual Increment

 

 

 

Age in Standing Height Skeletal Age Mental Age
Years in Millimeters in Months in Months
7-- 8 70.92 14.69 14.21
8-- 9 59.89 12.85 11.10
9--10 52.00 11.13 8.03

10--1l 44.13 11.24 7.14

ll--l2 36.83 12.63 10.92

12--13 67.58 14.54 16.10*

13--14 96.14* 14.84* 15.73
14--15 69.93 13.78 11.86

15--l6 40.83 11.40 7.57
16--17 19.65 8.78 4.40

*Year of greatest average increment in growth

a v w

Figures 8, 9, and 10 show the fit of the composite

curve of equation constants to mean observed measurements

at annual intervals, and demonstrate the curvilinear

regression line for the mean annual measurements in standing

height, skeletal age, and mental age.

73

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76

The distribution of individual equation errors is
presented in Tables XV, XVI, and XVII. From these data
it can be noted that 78.9 per cent of the cases‘fell within
or below the range which included the mean average error
for standing height. Sixty-five per cent of the cases fell
within or below the range which included the mean average
error for the skeletal age estimates, and fifty-nine per
cent of the cases were included in this range in the case
of the mental age estimate errors. Equation constants-for
each of the sixty-six cases in standing height, skeletal
age, and mental age are recorded in Appendix B of this

thesis.

TABLE XV

DISTRIBUTION OF ERRORS OF EQUATION ESTIMATES
FOR SIXTY-SIX BOYS IN STANDING HEIGHT GROWTH

 

Range of Cumulative
Deviations Number Per Cent Per Cent
Percentile in Millimeters of Cases of Cases of Cases

 

0- 10 4.11-- 5.55 12 18.2 18.2
10- 20 5.56-- 6.99 17 25.8 44.0
20- 30 7.00-- 8.43 9 13.7 57.7
30- 40 8.44-- 9.87 14 21.2 78.9
40- 50 9.88--11.30 6 9.1 88.0
50- 6O 11.31--12.74 3 4.5 92.5
60- 70 12.75--14.18 2 3.0 95.5
70- 80 14.19--15.61 1 1.5 97.0
80- 90 15.62--17.05 1 1.5 98.5
90-100 17.06--18.48 1 1.5 100.0

% fl
r

TABLE XVI

DISTRIBUTION OF ERRORS OF EQUATION ESTIMATES
FOR SIXTY-SIX BOYS IN SKELETAL AGE GROWTH

77

 

_.:—:__v
“l.

 

 

 

Range of Cumulative

Deviations Number Per Cent Per Cent

Percentile in Months of Cases of Cases of Cases
0- 10 .83--1.35 10 15.2 15.2
10- 20 1.36-—l.87 24 36.1 51.3
20- 3O 1.88--2.39 9 13.7 65.0
30- 4O 2.40--2.92 8 12.2 77.2
40- 50 2.93--3.45 10 15.2 92.4
50- 6O 3.46--3.97 O 0.0 92.4
60- 7O 3.98--4.50 l 1.5 93.9
70- 8O 4.5l--5.02 1 1.5 95.4
80- 90 5.03--5.54 2 3.0 98.4
90-100 5.55-~6.07 1 1.5 100.0

TABLE XVII
DISTRIBUTION OF ERRORS 0F EQUATION ESTIMATES

FOR SIXTY-SIX BOYS IN MENTAL AGE

m

 

GROWTH

m

 

Range of Cumulative

Deviations Number Per Cent Per Cent

Percentile in Months of Cases of Cases of Cases
0- 10 2.40-- 3.54 4 6.0 6.0
10- 20 3.55-- 4.68 9 13.7 19.7
20- 30 4.69-- 5.82 15 22.7 42.4
30- 40 5.83-- 6.96 11 16.6 59.0
40- 50 6.97-- 8.10 12 18.2 77.2
50- 60 8.11—- 9.24 l 1.5 78.7
60- 70 9.25--10.38 9 13.7 92.4
70- 80 lO.39--11.52 3 4.6 97.0
80- 90 11.53--l2.66 0 0.0 97.0
90-100 12.67--13.80 2 3.0 100.0

 

 

 

 

)4

 

78

Tables XVIII to XXII indicate the mean, standard
deviation and range for the various phenomena of cyclic
growth of the sixty-six boys in standing height, skeletal
age, and mental age. From these data, it was possible to
observe individual variability in growth aspects in terms
of the range represented within the various growth constants.
Examination of Table XVIII reveals, for instance, that the
range in rate of growth in isochrons during the childhood
cycle of development was from .1209 to .2280 isochrons in
standing height, with a standard deviation of .0265
isochrons.

During the adolescent cycle of development, individ-
ual variability in rate of growth appeared to be even more
disperse than in the childhood cycle as is revealed by
comparison of the standard deviations and ranges of
isochronic values in Table XVIII.

With respect to computed maximum development in each
cycle of growth for the three developmental aspects, the
variability of growth can again be noted. Inasmuch as
second cycle maxima represent a residual value of childhood
cycle maxima, it was not possible to determine the nature
of the difference of variability in second cycle maxima
from that of the childhood cycle. In Table XIX standing
height maxima values are given in millimeters, while
skeletal age and mental age are given in growth age equiva-

lents in months.

79

 

 

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80

 

 

 

 

 

 

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81

Examination of the data in Table XX for the incipi-
ency of each cycle led to similar conclusions about individ-
ual growth variability as were reached in the case of rates
of growth. Here again individual variability seemed to be
more disperse in the second cycle than in the first,
although the wide differences in individuals was immediately
clear upon examination of the ranges of the isochronic
values in the first cycle of growth.

Table XXI shows the average computed times of one
per cent of development of the adolescent cycle of growth,
as well as the computed time of ninety-nine per cent of
adult maturity. Again the wider variability of the ranges
and standard deviations can be noted at the termination of
the adolescent cycle. From these data, the conclusion was
drawn that there is wide individual variance in growth in
standing height, skeletal age, and mental age. That is to
say, it may be concluded that each individual case revealed
a unique pattern of growth with respect to growth constants
which were represented by rate, incipiency, maximum, and
times of maturing. In the case of rate, incipiency, and
time, there appeared to be greater variance in growth of
the sixty—six boys during the adolescent cycle than during
the childhood cycle. It was not possible to make such a
conclusion with respect to maxima, because of the nature

of the data.

82

 

 

 

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83

 

 

 

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84

Table XXII indicates the average per cents of child-
hood development and of computed total development which
the sixty-six boys had reached in each developmental aspect
at the mean time of occurrence of cycle break. In standing
height, for instance, the boys had attained a mean of 89.77
per cent of childhood cycle maximum at a mean age of 144.07
months. The range was from 85.7 per cent to 96.3 per cent.
At the same time (144.07 months), they had reached a mean
of 80.01 per cent of their computed adult height maturity,
with a range from 74.11 to 88.49 per cent. The individual
variability of growth can be further noted by examination
of the data in Table XXII for skeletal age and mental age
per cents of development.

The major problem of this study was that of deter-
mining the degree of relationship which existed among the
timing aspects of growth for sixty—six boys in standing I
height, skeletal age, and mental age. After it had been
determined that the growth constants inherent in the
equation could be assumed to be efficient at the ninety-five
per cent level of confidence for describing growth of the
boys, it was then possible to compute partial and multiple
correlation coefficients in timing aspects among the three
growth variables as well as other correlations which will
be reported in the discussion which follows.

Table XXIII reveals the computed partial correlations

between the various growth constants. Examination of the

85

 

 

 

 

 

 

 

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amuse:

om.am-amm.om HH.O sm.om m.mm--m.oe ms.m om.me owe
Hmsoacxm

me.mm--aa.es em.m Ho.om m.om-ns.mw mm.H es.mw unmaom
wsaosmpm
emsmm cofipmfi>09 new: mwcmm cofiumfi>m9 new: 9208095mmoz

opmpcmOm Opmvcmpm

 

.sssaxnz 64:64 go some sod

¢2HX¢2 BQD9¢ 92¢ ¢2HN¢2 M9020 900299Hmo mo Bzmzmo9m>m9 mo mBzmo mmm

,.E:E«sz maozo
ooocoafico Oo ucmo pom

2¢mmm 99020 90 mSHB 929 B¢ 293093 9m>mHmo¢ mo

HHNX 99m¢B

86

TABLE XXIII

CORRELATION COEFFICIENTS BETWEEN GROWTH CONSTANTS
OF EQUATIONS FOR STANDING HEIGHT, SKELETAL AGE,
AND MENTAL AGE OF SIXTY-SIX BOYS

 

 

##1— m
mp.—

 

 

rfi‘: r* I’*
Height and Height and Skeletal Age
Skeletal Age Mental Age and Mental Age

 

Childhood
Cycle Rate -.100 p .132 .018

Childhood
CYCle
Inc ipiency .044 .148 .066

Childhood
CYCle
Maximum .135 -.142 -.l63

Adolescent
Cycle Rate -.006 -.086 -.025

AdOlescent
CYCle
Incipiency -.072 -.006 .035

Adolescent
CyCle
Ma-Ximum .185 .015 .136

Adult Maximum .000 .008 .000

Time of Cycle ,
I‘eak .153 .236 .357

Age of Adult
aturity .187 -.089 -.O91

P9P Cent of
Childhood
Maximum .153 .160 -.009

Per Cent of
Adult Maximum . .219 . g .126 .285 _

*r: Ngfixy-(ix) (sing
V [Nzx2 - (Z x)2 ] [N2372 - (£Y)2]

 

 

\film—H‘ffir

87

talile readily reveals that no correlation among the con-
stealts can be assumed except in the case of time at which
cycfile breaks occurred, and per cents of total development
at iihat time. The correlations at the time of cycle break
areejpositive but low. For N=66, the rejection region at
the ninety—five per cent level is r 5 .204, if/= 0, and
heruze the correlation between times of cycle break of height
auui Inental maturity where r = .236 may be assumed to have a
P081tive relationship. This was also true between skeletal
age and mental age times of cycle break where r = .357.
However, these values are so near the rejection region that
it \NOUld be difficult to state the degree of relationship
Witdlout some doubt as to its true efficiency. The same is
true in the case of the per cents of total development at
tkka ‘time of occurrence of cycle breaks, where the three

Correlation coefficients were:

rHeight, Skeletal .219

.126

rHeight, Mental

rSkeletal, Mental = .286
The multiple correlation coefficient among the three
‘tilWES of occurrence of cycle breaks was RMoHS = .302. For
991‘ cents of total developmentat the time of cycle breaks,
the multiple correlation coefficient was RM-HS = .138. An
F test, stating the hypothesis that RMoHS = 0, was accepted
at the ninety—five per cent level. Table XXIV gives the

multiple correlation coefficients, the computed F values,

88

and critical values for F 95, when nl = 3 and n2 = 62.
It was concluded that the hypothesis of no multiple rela-
tionships among the three variables must be assumed at the

ninety-five per cent level of confidence.

TABLE XXIV

MULTIPLE CORRELATION COEFFICIENTS, COMPUTED F

VALUES AND CRITICAL F VALUES FOR TIMES OF

CYCLE BREAK AND PER CENTS OF ADULT MATURITY
AT TIME OF CYCLE BREAK

w fl V a

I]

 

 

Computed Critical
R . F Value F '
M HS ‘95(3.62)
Time of Cycle Break .302 2.07 2.75
Per Cent of Adult
Maturity at Time of
Cycle Break .138 .40 2.75

 

.1..—

From the correlation coefficients obtained by com-
parison of the various constants inherent in the growth
equations, it Seems that no relationships existed among
the various growths for the sixty-six boys. The next step
Was then to compare the mean annual increments at yearly
intervals from age seven to seventeen as computed from the
cornIDosite growth equations for standing height, skeletal
age, and mental age, which were reported in Table IV.

Rwilt-Difference correlation coefficients and Pearson r

89
zero-order correlation coefficients between the mean annual
increments appear in Table XXV.1

Nor N=8, the critical rank—difference R.95 = .74.2
In this case, N=lO, and therefore it may be assumed that

values of .867, .843, and .946 are positively significant

values, and that they are significantly different from zero.

TABLE XXV

RANK-DIFFERENCE CORRELATION COEFFICIENTS AND
PEARSON r CORRELATION COEFFICIENTS FOR MEAN
ANNUAL INCREMENTS IN STANDING HEIGHT,
SKELETAL AGE, AND MENTAL AGE OF
SIXTY-SIX BOYS

fl v

 

rs* r
He ight-Skeletal . 867 . 884
He ight-Mental . 843 - 862
Sl(eletal-Mental .946 .972

*rS =71 -62.'d2
N(N2-1)

 

 

 

 

In the case of the correlations obtained by the

for‘mula:
NZXY - (2X) (éY)

 

I’ =
Xy

 

VI [NI x2 - (£1021 [N272 - E1572]

C 1By this method it is possible to compute a single
OPPelation between two series of means.

2He1en M. Walker and Joseph Lev, Statistical Infer-
$032 (New York: Henry Holt and Company, 1953), p. 478.

90
critical r.95 = .550 for N-2 degrees of freedom = 8. Hence,
the correlations of .884, .862, and .972 may be assumed to
be highly significant correlations.

The null hypothesis that / = 0 was rejected, and
the hypothesis that/074 0 was assumed to be true on the
basis of the F test which was applied to the multiple cor-
relation of annual increments in growth as reported in Table
XXVI.

TABLE XXVI

MULTIPLE CORRELATION, OBSERVED F VALUES AND CRITICAL
F.95(3,6) VALUES FOR ANNUAL GROWTH INCREMENTS

IN STANDING HEIGHT, SKELETAL AGE, AND
MENTAL AGE OF SIXTY-SIX BOYS

‘

 

Observed Critical
RM-HS F Value F.95(3’6)
.862 5.78 4.76

The general conclusion, then, from these findings
indicates that even though significant positive correlations
eMist among the growth aspects of standing height, skeletal
age, and mental age when mean annual increments are com—
pa-1"ed, such relationships are not revealed by comparison of
individual growth constants of rate, incipiency, maximum,
t1l’l'ling aspects, or per cents of development. It was only
when all constants were integrated as a composite whole

that true growth relationships were revealed. That is to

91
sayfi, the low correlation coefficients which were obtained
fox‘ each of the various equation constants were affected
by 1:he fact that all other equation constants were in
effkect immobilized. The multiple correlation of these
consitants was revealed only when the weighting of all con-
staxrts, that is their contribution to the whole, was
inrfiluded in the computation of the multiple correlations.
Stertistically speaking, the notion may be applied that the
Ccnnpmted coefficient of correlation between two variables
is Inisleading because there is little or no relation between
them beyond what is induced by their common dependence on a
tulixrd or upon several other variables. In this case, rate,
in-cipiency, and maximum are dependent on each other, and
the: wide individual variation between or among any of the
thI’ee constants which contribute to the equation as a whole
mag; be so disperse as to obscure true relationships.

The next question which was raised as a result of the
findings when annual increments from the composite growth
eQILations were computed, was that of the relationships
thueh may be revealed by simply averaging observed measure-
merrts for each of the sixty-six cases at annual intervals.
This was done, and the findings are reported in Table XXVII.

Examination of the individual observed scores revealed
that many of the mental age scores showed a decline from
Orua testing period to the next as is shown by examination

of ‘the data in Appendix A. Sixty—two of the sixty-six

92
cases showed a decline in mental age score from at least
one annual measurement to the next. The distribution of

declining scores at annual intervals appears in Table XXVIII.

TABLE XXVII

CORRELATION COEFFICIENTS 0F MEAN ANNUAL OBSERVED
INCREMENTS IN STANDING HEIGHT, SKELETAL AGE,
AND MENTAL AGE OF SIXTY-SIX BOYS

‘ 9V V —v

I’HS I’RM rSM

. 568 . 308 . 080

TABLE XXVIII

DISTRIBUTION OF DECLINING MENTAL AGE SCORES
AT ANNUAL INTERVALS*

‘

Yearly Age Interval Frequency of Declining Scores

 

 

7 -- 8 11
8 -- 9 16
9 --10 14
10 --11 6
11 --12 5
12 --13 16
13 --14 10
14 --15 15
15 --16 20
l6 --17 10
:‘Kk 1 - A 1 l

 

 

fl

B1 *The mental age scores represented here are Stanford-
t net percentile equivalents of average mental age scores
alien from two mental age tests administered at a given
m1 ual interval. It would be of future interest to deter-
he which tests were contributing to the declining mental
Pre equivalents. See Walter F. Dearborn and J. W. Rothney,
Apedictin the Child'ws Development (Cambridge, Mass.: Sci-
m t'7EUEIIghers, 1941), pp. 136-139 for table of equivalent
ental test percentiles.

93
From the table, it may be observed that the declining scores
were evident at all age intervals. This fact rules out the
hypothesis of faulty test scores at any one testing time.
The greatest number of declining scores occurred at age
fifteen to sixteen. Since the Stanford-Binet equivalents
assess adult mental maturity at sixteen years, it is
possible that this may have accounted in part for the larger
frequency of declining scores at that point.

These observations lend further support to former
eVidence that a multiplicity of factors influence mental
age scores. Further, inasmuch as mental age scores are
dependent on chronological age, the average curve of growth
tends to be directed toward a straight line, and fails to
distinguish periods of rapid and slow development. Obviously,
it would be expected that some growth in mental age would
Occur from one annual measurement to the next, and the de-
9lines in mental age measurements among the boys would need
to be explained by exterior factors such as health condi-
tions, rapport between the examiner and the subject, and
Val"iation in the tests used.

The norms which were used in the Harvard Study to
assGees skeletal age scores suffered from the same defect
as the mental age scores. That is, inasmuch as skeletal
age scores are dependent on chronological age, the growth
Curve was directed toward a straight line and hence the

eye1:10 nature of individual growth was obscured.

r .e . 3‘58?

94

The computation of a growth equation by use of the
Courtis method served the purpose of smoothing the growth
curves. It produced a curvilinear line of best fit for the
data and described the data with better than 97.5 per cent
efficiency. Therefore, the correlation coefficients
obtained from the comparison of mean annual increments from
equation computations represent the relationships of the
developmental aspectscn?standing height, skeletal age, and
mental age after the growth curves have been smoothed and
testing discrepancies have been reduced.

It is possible that a higher degree of correlation
among timing aspects may be found if integrated and non-
integrated growers are selected out of the total group for
analysis. That is, some children have what may be termed
a high integration index in terms of time when cycle break
occurs, while others show wide divergence in timing aspects
from one growth variable to another. While it was not the
purpose of this study to select out such individuals, but
rather to study the group of sixty—six boys as a whole, it
is recommended that such selection be made in future

studies of this nature.

CHAPTER V
SUMMARY, CONCLUSIONS, AND IMPLICATIONS

The purpose of this investigation was to analyze
longitudinal data for sixty-six boys in standing height,
skeletal age, and mental age for the purpose of determining
growth relationships between and among the physical and
mental growth aspects. The sixty-six cases were selected
from the Third Harvard Growth Study which was inaugurated
in 1922 in the Psycho-Educational Clinic of the Harvard
Graduate School of Education.

A Chi-Square test of "goodness of fit" was applied
to the distribution of scores in standing height, skeletal
age, and mental age. From this test, it was assumed that
the distribution of scores in all cases were representative
of those of a random sampling drawn from a normal distri-
bution.

The Courtis technique which utilizes the Gompertz
equation was employed to analyze the data, and was found
to describe growth patterns with better than ninety-five
per cent efficiency for all three developmental aspects.

Correlation coefficients were computed among the
growth constants of maxima, rates, and incipiencies as

well as time of occurrence of cycle break, time of ninety-

96
nine per cent of achieved adult maturity, and per cents of
development of first cycle maxima and adult maxima at the
time of cycle break. Mean annual increments were also
compared to determine the degree of relationships in
patterns of growth in physical and mental aspects of devel-

opment among the sixty-six boys.

Conclusions

 

The major conclusions which were drawn relative to
growth relationships among developmental aspects of standing
height, skeletal age, and mental age of the sixty-six boys
were as follows:

The pattern of growth for each of the boys was that
of a two cycle curve in standing height, skeletal age, and
mental age, with the cycle breaks occuring between mean
ages of ten and twelve years.

Correlations between equation constants were not
statistically significant.

Correlation coefficients between times at which cycle
breaks occurred in standing height, skeletal age, and mental
age were positive but too low to be stated as significant
with any degree of assurance.

Growth is so variable from one individual to the next,
and from one cycle to another, that a comparison of equation
constants, because they are dependent on each other, does
not provide a sufficient basis on which to compare growth

relationships.

97
The significant relationships between physical and

mental aspects of growth were revealed when all equation
constants were analyzed as a composite whole. The corre-
lation between all aspects of growth was positively signi-
ficant when mean annual increments obtained from equation
constants were compared.

The use of a multi-cyclic regression equation for
describing human growth in standing height, skeletal age,
and mental age predicts growth with good efficiency, pro-
vides a means for smoothing the growth curves, and tends
to reduce testing errors.

The degree to which ethnic and cultural influences
affected the growth patterns of the sixty—Six boys was not
known. However, for these children who lived in the area
of Boston, patterns of growth in standing height, skeletal
age, and mental age were significantly related.

Correlation coefficients between and among the mean
annual increments of the sixty-six boys were much higher
than those which have been obtained in previous studies
where growth aspects were analyzed on a cross-sectional

basis.

Implications

 

Several important implications for educators, psy-
chologists, pediatricians, social workers, and others who
deal with children emerged as a result of the major con-

clusions of this study.

98

The evidence to the effect that growth in physical
and mental aspects of development is multi-cyclic in nature
emphasizes the need for recognition that children grow at
different rates at various stages of development.

Growth is variable from individual to individual,
and hence no two individuals may be fitted into the same
pattern of educational treatment in terms of stresses for
learning at various ages. The wide divergence in times at
which cycle breaks occur provides evidence to support this
recommendation.

Total patterns of growth in terms of annual incre-
ment are significantly related, as was revealed by the
correlation coefficients obtained for the standing height,
skeletal age, and mental age annual composite equation
increments of the sixty—six boys. From this finding, it
is recommended that educators recognize that from a norm-
ative point of view, small incremental gains in physical
growth are generally accompanied by small incremental gains
in mental growth; and that conversely greater increments in
physical development are accompanied by increments of
greater magnitude in mental development.

On the basis of this study, total magnitude of mental
ability bears no relationship to total magnitude of physical
stature, as was revealed by the near zero or negative cor-
relations between physical and mental maxima. Therefore,
any precOnceived notions that tall people are dull and short

people are smart or vice versa must be abandoned.

 

99

Inadequacies of mental test scores and mental testing
situations shown in the study necessitate the analysis of
growth on an individual longitudinal basis by the utili-
zation of a suitable statistical technique which describes
growth efficiently, and will tend to reduce errors in
testing.

More adequate scales for the assessment of skeletal
age scores need to be employed which will more adequately
describe periods of slow and rapid development, rather than
direct the growth curve toward a straight line. More
adequate scales than those used in the Third Harvard Growth
Study, and which have been utilized since 1950, were cited
in this study.

It is recommended that future studies in the area of
growth relationships attempt to delineate integrated and
non-integrated growers in terms of timing aspects, in order
to analyze more fully the unique patterns of growth within

individuals.

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Stevvart. S. F. '"Physical Growth and School Standin
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414-4267"_'—" '—

1
‘Tables for Predicting Adult Height from Skeletal Age;
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. "Concepts of Organismic Growth: A Critique,"
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107

Wetzel, Norman C. "The Motion of Growth——Theoretical
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Alxernethy, Ethel. "Relationships Between Mental and Phys-
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Children' 8 Bureau of the United States Department of Labor.
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108

Dearborn, W. F., J. W. Rothney, and F. K. Shuttleworth.
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EgiflfliilishedVMaterials

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lll

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Ihlsczh, R. R. ‘"The Cyclic Pattern of Height Growth from

Udoh ,

Birth to Maturity." Unpublished Ph.D. thesis, Michi-
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'- . ‘"The Relationship Between Growth in Height
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Wolirred, Gerald. "An Evaluation of the Courtis Method in

the Study of Growth Relationships." Unpublished Ph.D.
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Michigan, 1957.

d.‘

APPENDIX A

113

Key to Ethnic Origin and Socio-Economic Status

fie.

It

(:12: '3.

II

III

IV

ETHNIC ORIGIN

-- Jewish

-- North European
-- Mixed Stock

—- Italian

-- Negro

-- Unknown

SOCIO-ECONOMIC STATUS

-- Professional

-- Semi-professional, large
business, important managerial

-- Skilled labor, small business,
small managerial

-- Semi-skilled labor

-- Unskilled labor

-— Unknown

.D 9": I111) .‘o~

~

0 2~o_v.nso..o« ... . .v. n.

114

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CASE 4M. Ethnic Origin--J; Socio-Economic Status--IV
Age Height % of % of % of
YBars.. Mos.. .1n.mm.. .Dev,,.,MJA.... Dev.” S.A.. Dev.
6.23 74.76 1119 67.6 84.48 44.93 77 36.2
7.19 86.28 1172 70.8 114.75 61.05 85 39.9
8.19 98.28 1229 74.2 122.85 65.37 96 45.1
9.19 110.28 1277 77.1 112.69 59.85 108 50.7
10.21 122.52 1322 80.0 139.67 74.33 120 56.3
11 .20 134.40 1369 82.7 160.61 85.46 131 61.5
12. 19 146.28 1396 84.3 174.80 93.01 144 67.6
133.18 158.16 1433 86.5 166.07 88.36 157 73.7
14 . 18 170.16 1524 92.0 167.61 89.18 170 79.8
15. 18 182.16 1605 96.9 184.89 98.38 183 85.9
16. 22 194.64 1637 98.9 187.83 99.94 199 93.4
17 . 21 206.52 1656 100.0 187.93 100.00 213 100.0

EASE 15M. Ethnic Origin--NE; Socio-Economic Status IV

w +— : ~.—.——.—.——

.Age Height % of % of % of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.
6.88 82.56 1242 70.4 71.82 37.37 84 37.0
7. 66 91.92 1282 72.7 91.00 47.35 96 42.3
8.73 104.76 1335 75.7 100.56 52.33 108 47.6
9. 69 116.28 —- -- 119.76 62.32 119 52.4
10. 72 128.64 -- -- 132.49 68.95 135 59.5
11 . 72 140.65 1500 85.1 132.20 69.16 150 66.1
1 ~ 69 152.28 1591 90.2 149.23 77.66 167 73.6
13 ~ 69 164.28 1685 95.6 172.49 89.76 185 81.5
1 - 66 175.92 1733 98.3 168.88 87.88 197 86.8
15 - 69 188.28 1749 99.2 180.74 94.06 208 91.6
15 - 68 200.16 1759 99.8 192.15 100.00 227 100.0
17 ~ 67 .09 227 100.0

212.

1763 100.0

186.

—v

_.__+
T—

CASE 37M. Ethnic Origin--NE; Socio-Economic Status--III

115

 

 

 

 

 

 

 

Age Height 5 of % of 5 of
Years Mos. in mm. Dev. M.A Dev. S.A. Dev.
6.59 79.08 1238 68.2 120 20 50.91 84 40.0
7.63 91.56 1303 71.8 128 18 54.29 96 45.7
8.58 120.96 1365 75.2 152 38 64.55 108 51.4
9. 61 115.32 1426 78.5 161.44 68.38 119 56.7
10 .58 126.96 1468 80.8 158.70 67.22 132 62.9
11 . 59 139.08 1533 84.4 190.53 80.71 144 68.6
12. 59 151.08 1578 86.9 216.04 91.51 150 71.4
13 . 56 162.72 1641 90.4 231.06 97.88 161 76.7
14 . 59 175.08 1728 95.2 236.35 100.00 174 82.9
15 . 57 186.84 1791 98.6 227.94 96.56 190 90.5
16. 57 198.84 1816 100.0 228.66 96.86 210 100.0
CASE, 56M. Ethnic origins-NE, Socio-Economic Status--III
M 1
.Age Height % of % of % of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.
8. 30 99.60 -- -- 121.51 60.24 89 39.2
9- 32 111.84 1263 74.4 117.43 58.22 101 44.5
10 - 3 6 124.32 1322 77.9 121.83 60.40 114 50.2
11 . 32 135.84 1372 80.8 123.61 61.28 125 55.1
12 - 34 148.08 1428 84.1 155.48 77.08 143 62.99
1}; ~ 31 159.72 1506 88.7 175.69 87.10 157 69.16
1 - 32 171.84 1611 94.9 178.71 88.60 180 79.3
15 . 28 183.36 1668 98.2 201.69 100.00 192 84.6
1 ~ 33 195.96 1693 99.7 194.00 96.18 212 93.4
17 - 35 208.20 1698 100.0 197.79 98.06 0

227

100.

116

CASE 60M. Ethnic Origin--NE; Socio-Economic Status--IV

 

fi—

7....—

Age Height 96 of 76 of 76 of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.

 

7.16 85.92 1135 67.23 105.68 59.68 68 32.
7.96 95.52 1174 69.54 99.34 56.10 80 38.
9 .02 108.24 1223 72.45 100.66 56.84 92 43.
9.97 119.64 1277 75.65 106.47 60.13 105 50.
11 .00 132.00 1321 78.25 117.48 66.35 -- --
11 .95 143.40 1361 80.62 139.09 78.55 130 61.
12.95 155.40 1413 83.70 139.86 78.99 144 68.
13.98 167.76 1457 86.31 132.53 74.85 156 74.
14 -94 179.28 1502 88.98 159.55 90.11 166 79.
15 . 97 191.64 1566 92.77 164.81 93.08 174 82.
16- 96 203.52 1659 98.28 177.06 100.00 187 89.
17 . 95 215.40 1688 100.00 174.47 98.53 210 100.

OO\OOwO\KO OCH-‘4?

 

CASE 68M. Ethnic Origin-~NE; Socio-Economic Status--111
M 11

 

 

 

- Age Height 96 of 0,! of 76 of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.
5- 81 81.72 1103 65.53 —- -- 78 36.3
7 .77 93.24 1150 68.33 97.90 45.35 89 41.4
8 . 68 105.36 1201 71.36 128.53 59.54 102 47.4
9 . '78 117.36 1241 73.73 143.17 66.32 115 53.5
10 . 79 129.48 1284 76.29 155.37 71.97 126 58.6
11 -78 141.36 1335 79.32 163.97 75.95 135 62.8
12077 153.24 1388 82.47 174.69 80.92 144 66.97
13-77 165.24 1440 85.56 188.37 87.26 157 73.0
1 .78 177.36 1528 90.79 202.19 93.66 172 80.0
12678 189.36 1624 96.49 215.87 100.00 185 86.0
1 ~77 201.24 1646 97.80 211.30 97.88 198 92.1
7 ~79 213.48 1683 100.00 194.26 89.06 215 100.0

 

117

CASE 69M. Ethnic Origin--NE; Socio-Economic Status--III

7

Age Height % of % of % of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.

 

7.51 90.12 1172 67.24 77.50 43.61 87 39.

 

 

 

 

9
8. 41 100.92 1230 70.56 86.79 48.84 97 45.4
9. 42 113.04 1293 74.18 97.21 54.71 111 50.9
10. 46 125.52 1346 77.22 110.45 62.16 122 55.9
11 .43 137.16 1388 79.63 133.04 74.87 134 61.5
12. 42 149.04 1441 82.67 141.58 79.68 147 67.4
13.43 161.16 1497 85.88 146.65 82.53 154 70.6
14. 39 172.68 1578 90.53 145.05 81.63 -- --
15. 42 185.04 1671 95.86 153.58 86.43 181 83.0
16. 44 197.28 1709 98.04 165.71 93.26 192 88.1
17 . 42 209.04 1731 99.31 177.68 100.00 213 97.7
18 . 48 221.76 1743 100.00 176.83 99.52 218 100.0
W m
9§§E2_j§yfl. .Ethnic Origin-~M; Socio-Economic Status--III
Age Height 96 of 96 of % of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.
g~09 85.08 -- -- 129.32 53.66 95 49.5
.08 96.96 1197 72.98 122.17 50.69 107 55.7
19- 12 109.44 1257 76.64 145.56 60.40 119 61.9
13- 10 121.20 1296 79.02 156.35 64.88 130 67.7
11- 09 133.08 1338 81.58 168.35 69.86 140 72.9
12-08 144.96 1377 83.96 179.75 74.59 148 77.1
12.07 156.84 1421 86.64 194.48 80.70 156 81.3
1 - 10 169.20 1466 89.39 208.96 86.71 162 84.4
12. 09 181.08 1541 93.96 220.01 91.30 172 89.6
17- 13 193.56 1613 98.35 230.34 95.58 182 94.8
- 09 205.08 1640 100.00 0

240.97 100.00 192 100.

 

118

 

 

 

 

 

 

 

1674 ’

..........

......

CASE 82M. Ethnic 0r1gin--1t.; Socio-Economic Status--IV
Age Height % of % of % of

Years M08. in mm. Dev. M.A. Dev. S.A. Dev.

6.77 81.24 1143 66.49 87.74 48.43 82 38.14

7.73 92.76 1183 68.81 102.04 56.32 94 43.72

8.75 105.00 1252 72.83 108.68 59.99 107 49.76

9.74 116.88 1298 75.50 107.53 59.35 120 55.81
10.76 129.12 1343 78.12 106.52 58.80 132 61.39
11 . 74 140.88 1382 80.39 133.13 73.49 143 66.51
12. 73 152.76 1431 83.24 147.41 81.37 156 72.55
13.74 164.88 1498 87.14 145.09 80.09 166 77.21
14. 73 176.76 1591 92.55 159.08 87.81 179 83.25
15.73 188.76 1662 96.68 168.00 92.74 191 88.83
16.74 200.88 1696 98.66 165.72 91.48 204 94.88
17.76 213.12 1719 100.00 181.15 100.00 215 100.00
CAEHE 83M. Ethnic Origin-~It.; Socio-Economic Status-~IV

Age Height % of % of % of
Years Mos. in mm. Dev. M.A. Dev. S A Dev.
\ _ ..... .
6- 14 73.68 1126 67.3 73.68 49.34 -- --

- 06 96.72 1223 73.1 108.68 72.68 91 45.04
l9~OES 108.72 1272 76.0 86.43 ' 57.80 105 51.98
10-07 120.84 1325 79.2 100.30 67.07 116 57.42
11-0 132.60 1365 81.5 98.79 66.06 127 62.87
19-04 144.48 1413 84.4 114.86 76.81 139 68.81
13-04 156.48 1452 86.7 106.41 71.16 153 75.74
15-05 168.60 1527 91.2 114.65 76.67 166 82.17
16. 05 180.60 1609 96.1 129.13 86.35 179 88.61
17-CDES 192.72 1650 98.6 146.47 97.95 191 94.55

- O7 .0 149 53 100.00

202 100.00

119

CASE 94M. Ethnic Origin--NE; Socio-Economic Status--III

 

,——~

Age Height % of % of % of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.

 

7.78 93.36 1164 70.84 85.89 48.38 77 43.50

8. 58 102.96 1208 73.52 119.43 67.28 88 49.71

9. 59 115.08 1261 76.74 111.63 62.88 101 57.06
10. 62 127.44 1300 79.12 102.59 57.79 113 63.84
11 . 59 139.08 1331 81.01 114.74 64.63 124 70.05
12. 63 151.56 1375 83.68 136.40 76.84 135 76.27
13. 61 163.32 1417 86.24 139.64 78.66 148 83.61
14. 58 174.96 1450 88.25 150.47 84.76 152 85.87
15 . 62 187.44 1499 91.23 159.32 89.75 159 89.83
16. 60 199.20 1571 95.61 173.30 97.62 168 94.91
17 . 61 211.32 1643 100.00 177.51 100.00 177 100.00

.....

 

 

T

£5§§L_212§Mn Ethnic Origin--NE; Socio-Economic Status--O

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

Age Height 76 of % of 96 of
YeaIWS Mos. in mm. Dev. M.A. Dev. S.A. Dev.
\

 

10-28 123.36 1305 76.79 92.52 45.61 —— --
11.10 133.20 1387 78.89 139.86 68.96 137 60.35
12-18 146.16 1442 82.02 125.70 61.97 149 65.63
13-15 157.80 1480 84.18 127.03 62.63 161 70.92
1 -12 169.44 1525 86.74 147.41 72.68 173 76.21
12.1 4 181.68 1576 89.64 169.87 83 .75 179 78.85
1 ~12 193.44 1662 94.53 176.03 86.79 185 81.49
1,909 205.08 1722 97.95 178.42 87.97 192 84.58
1 -12 217.44 1742 99.08 173.95 85.76 212 93.39
28-1 2 229.44 1752 99. 65 182.50 89.98 226 99 .55
'1 2 241.44 1758 100 . 00 202.81 100 . 00 227 100 .00

 

120

 

 

 

 

 

 

 

 

 

 

CASE 119M. Ethnic Origin-~NE; Socio-Economic Status—~I.
Age Height % of 3’6 of % of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.
7.06 84.72 1157 66.30 81.33 37.04 77 8.11
8 .03 96.36 1219 69.85 -- -- 90 4.55
9 .01 108.12 1274 73.00 132.45 60.32 101 50.00
10 .01 120.12 1314 75.30 134.53 61.26 113 55.94
11 . 01 132.12 1374 78.73 160.53 73.11 124 61.38
11 . 98 143.76 1423 81.54 171.79 78.23 136 67.32
13 . 00 156.00 1480 84.81 175.50 79.92 150 74.25
13 . 99 167.88 1550 88.82 177.95 81.04 161 79.70
15 - 00 180.00 1650 94.55 207.90 94.68 -— --
15 . 98 191.76 1714 98.22 219.57 100.00 188 93.06
1 6. 99 203.88 1745 100.00 203.88 92.85 202 100.00
LASE 12 3M. Ethnic Origin--NE; Socio-Economic Status-~O
Age Height % of 75 of % of
Yeflr‘s Mos. in mm. Dev. M.A. Dev. S.A. Dev.
\ 1v - 1 -
7. 28 87.36 1178 68.64 78.62 42.64 91 40.01
- 07 96.84 1229 71.62 93.93 50.94 106 46.69
9- 13 109.56 1304 75.99 107.36 58.23 119 52.42
10- 08 120.96 1356 79.02 130.64 70.86 126 55.50
11~ 1 133.32 1406 81.92 130.65 70.86 -- --
12- 0 144.96 1452 84.61 144.96 78.62 147 64.75
13~ 09 157.08 1511 88.05 157.08 85.20 156 68.72
1 -09 169.08 1587 92.48 165.70 89.87 164 72.24
15- 06 180.72 1660 96.73 178.91 97.04 177 77.97
1 ~C>SD 193 08 1691 98.54 173.77 94.25 195 85.90
g- 07 204.84 1707 99.47 184.36 100.00 216 95.15
~ 07 216.84 1716 100.00 182.15 98.80 227 100.00

CASE 150M.

Ethnic 0rigin--It.;

121

Socio-Economic Status--0

m

 

.Age Height % of % of % of
Years Mos. in mm. Dev. M.A. Dev. .A. Dev.
5.1H2 65.04 1025 62.12 59.83 28.26 58 25.55
6.363 76.56 1095 66.36 73.49 34.71 -— —-
7.40 88.80 1160 70.30 84.80 40.06 77 33.92
8.4K) 100.80 1218 73.81 101.30 47.85 90 39.65
9.1K1 112.92 1270 76.96 130.42 61.61 107 47.13
10.40 124.80 1342 81.33 144.14 68.09 124 54.62
11.39 136.68 1435 86.96 155.13 73.28 144 63.43
12.39 148.68 1527 92.54 179.15 84.63 166 73.12
13.4() 160.80 1598 96.84 190.54 90.01 180 79 29
14. 38 172.56 1627 98.60 199.30 94.15 202 88.98
15. 39 184.68 1637 99.21 197.60 93.34 216 95.15
16.41. 196.92 1650 100.00 211.68 100.00 226 99.55
17.463 209.76 1644 99.13 -- -- 100 00

W-

227

Ethnic 0rigin--NE; Socio-Economic Status--III

 

 

WV 1 1 1
Age Height 96 of % of % of
Years Mos. in mm. Dev. M.A. Dev. .A. Dev.
\1- _ . 3 - e 1 1 . , . . -
7~33 87.96 1146 70.09 106.43 47.36 77 34.84
-37 100.44 1202 73.51 120.53 53.63 89 40.27
18:38 112.56 1243 76.02 122.12 54.34 101 45.70
11-35 124.20 1283 78.47 137.86 61.34 113 51.13
12-39 136.68 1330 81.34 162.64 72.37 125 56.56
13°36 148.32 1380 84.40 171.30 76.27 138 62.44
1,-31 159.72 1452 88.80 184.47 82.08 156 70.58
15 - 31+ 172.08 1549 94 .74 197.03 87. 67 174 78.7
16'36 184.32 1603 98.04 210.12 93.50 190 85.9
17-311 196.08 1625 99.38 215.68 95.97 208 94.11
~ 31* 208.08 1635 100.00 224. 00

72 100.00

221 100.

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122

CASE 166M. Ethnic 0rigin--NE; Socio-Economic Status--IV

 

 

 

w v v v vv—v v v

 

Age Height 96 0f % 0f 76 of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.
6.59 79.08 1140 65.55 —- -- 58 29.29
7.55 90.60 1199 68.94 101.47 45.87 72 36.36
8.56 102.72 1255 72.16 102.20 46.20 84 42.42
9.56 114.72 1300 74.75 10 .82 46.93 -- ~-
10.59 127.08 1350 77.63 12 .98 58.31 107 54.04
11.58 138.96 1398 80.39 129.92 58.73 118 59.59
12.56 150.72 1446 83.15 143.93 65.07 129 65.15

13.56 162.72 1489 85.62 170.85 77.24 142 71.71
14.56 174.72 1537 88.38 179.08 80.96 155 78.28
15.57 186.84 1614 92.81 183.10 82.78 169 85.35
16. 57 198.84 1697 97.58 201.11 90.92 182 91.91
17 . 59 211 . 08 1739 100 . 00 221.18 100 . 00 198 100 . 00

v w a a w

CASE 203M. Ethnic 0rigin--It.; Socio-Economic Status-~III

:-- '..'::: ’ ':

Age Height % of % of 76 of
Y'e’ars Mos. in mm. Dev. M.A. Dev. S.A. Dev.

 

5-96 83.52 1137 68.41 81.85 37.99 92 40.52
£3092 95.04 1183 71.17 110.25 51.18 104 45.81
~ 94 107.28 1252 75 .33 119.08 55.28 118 51 .98
1834 119.28 1294 77.85 114.51 53.16 126 55.50
11 ~95 131.40 1342 80.74 137.97 64.05 134 59.03
12-94 143.28 1396 83.99 160.47 74.49 144 63.43
13-93 155.16 1446 87.00 172.23 79.95 161 70.92
~93 167.16 1539 92.59 168.83 78.37 172 75.77
15 179.16 1613 97.05 209.62 97.31 186 81.93
1694 191.28 1641 98.73 202.76 94.13 202 88.98
~94 203.28 1657 96.69 197.19 91.54 219 96.47
215.40 1662 100.00 215.40 100.00 227 100.00

fi V V V a

 

123

 

 

CASE 227M. Ethnic 0rigin--NE; Socio- Economic Status--II
Age Height % 0f % 0f % of
Years Mos. in mm. Dev. M.A. Dev. .A. Dev.
6.08 72.96 1122 63.21 88.28 33.03 76 35.64
6.87 82.44 1180 66.47 103.87 38.87 88 41.31
7.94 95.28 1240 69.85 131.49 49.20 102 47.88
8.85 106.20 1292 72.78 124.25 46.49 114 53.52
9.91 118.92 1356 76.39 147.46 55.18 124 58.21
10.88 130.56 1411 79.49 147.53 55.20 134 62.91
11.89 142.68 1472 82.92 169.79 63.53 148 69.48
12.89 154.68 1526 85.97 193.35 72.35 160 75.11
13.86 166.32 1607 90.53 207.90 77.80 170 79.81
14.89 178.68 1698 95.65 237.64 88.93 182 85.44
15.87 190.44 1750 98.59 257.09 96.20 196 92.01
16 . 87 202. 44 1775 267 . 00 213 00

 

100.00

 

 

EESE 232M. Ethnic 0rigin--NE; Socio-Economic Status--III
M 1
Height % 0f % 0f % of
Years Mos in mm. Dev. M.A Dev. .A. Dev.
_\ 1‘ . .
5-93 71.16 -- -- 163.18 59.21 85 41.66
7.00 84.00 1302 72.98 152.04 55.17 97 47.54
-01 96.12 1361 76.28 150.91 54.76 111 54.41
10-05 108.60 1418 79.48 177.02 64.24 121 59.31
1102 120.24 1462 81.95 167.13 60.65 132 64.70
12-01 132.12 1507 84.47 183.65 66.64 144 70.58
12-02 144.24 1566 87.78 219.24 79.56 152 74.50
14'98 155.76 1610 90.24 195.32 70.88 160 78.43
15-01 168.12 1710 95.85 221.92 80.53 1g5 85.78
1 ~03 180.36 1755 98.37 248.90 90.32 1 7 91.66
17-01 192.12 1776 99.55 226.70 82.27 204 100 00
~01 204.12 1784 100.00 275.56 100.00 -- -
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124

CASE 250M. Ethnic 0rigin--NE; Socio-Economic Status--IV

 

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Age Height % 0f % 0f % of

Years M08. in mm. Dev. M.A. Dev. S.A. Dev.

 

7 71.64 1103 65.92 64.47 32.51 80 42.78
8 82.56 1160 69.33 99.07 49.95 90 48.12
9 94.68 1212 72.44 88.05 44.40 102 54.54

8.93 107.16 1260 75.31 122.16 61.60 114 60.96
9.90 118.80 1306 78.06 134.24 67.69 122 65.24
10.89 130.68 1354 80.93 143.74 72.48 132 70.58
11.90 142.92 1406 84.04 165.64 83.53 141 75.40
12.86 154.32 1440 86.07 175.92 88.71 152 81.28
13.89 166.68 1505 89.95 190.01 95.81 164 87.70
14.91 178.92 1599 95.57 186.07 93.83 174 93.04
15 .89 190.68 1673 100.00 198.30 100.00 187 100.00

\1 mm
0300\0

CASE 255M. Ethnic 0rigin--NE; Socio-Economic Status--III

—_

Age Height 95 0f % 0f % of
Years M08. in mm. Dev. M.A. Dev. S.A. Dev.

 

 

7.01 84.12 -- -- 80.75 37.76 72 31.71
8.08 96.96 1305 74.82 95.02 44.43 88 38.76
9-17 110.04 1368 78.44 -- -- 103 45.37
3143.13 121,56 1427 81.82 122.77 57.41 125 55.06
11.10 133.20 1494 85.66 135.86 63.53 144 63.43
19-09 145.08 1592 91.28 163.94 76.67 161 70.92
1131'10 157.20 1697 97.30 183.13 85.64 185 81.49
1 ~06 168.72 1716 98.39 192.34 89.95 198 87.22
12-09 181.08 1738 99.65 178.16 83.32 216 95.15
17-11 193.32 1739 99.71 191.38 89.50 222 97.79
18 - 10 205 . 20 1740 99 .77 207.25 96. 92 227 100 .00

~ 09 217.08 1744 100 . 00 213.8 2 100 . 00 227 100 . 00

av V fi V V V

 

125

 

 

 

CASE 269M. Ethnic 0rigin--NE; Socio-Economic Status--III
Age Height % 0f % 0f % of

Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.
$3.163 97.92 1143 68.07 —- -- —- --
9.cy7 108.84 1230 73.25 96.86 53.09 103 47.68
10.1;1 121.32 1288 76.71 106.76 58.51 115 53.24
11.:L2 133.44 1340 79.80 125.43 68.75 126 58.33
12.cx; 145.08 1383 82.37 139.27 76.33 139 64.35
13.CK9 157.08 1424 84.81 150.79 82.65 150 69.44
14.11) 169.20 1505 89.63 172.58 94.59 162 75.00
15.113 181.20 1596 95.05 148.58 81.44 179 82.87
16.11) 193.20 1652 98.39 156.49 85.77 192 88.89
17.142 205.44 1670 99.46 164.35 90.08 204 94.44
18.11) 217.20 1679 100 182.44 100.00

_¥

——~

LASE 280M.

W

Height %
in mm.

 

206.28

1201
1246
1306
1367
1427
1475
1543
1637
1702
1752
1776
1783

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216

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Ethnic 0rig1n--N; Socio-Economic Status-~V

 

0f

Dev.

67.
69.
73.

76
80
82
86
91
95
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118
131
126
127
134
142
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102
125
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157
168
179
192
216
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(”HEB 288M. Ethnic Origin--NE; Socio-Economic Status--III
m 7 fi—t
Age Height % 0f % 0f % of
Years Mos. in mm. Dev. M.A. Dev. .A. Dev.
6.94 83.28 1163 65.89 100.76 39.70 89 41.58
7.75 93.00 1211 68.61 140.43 55.34 102 47.66
8.79 105.48 1277 72.33 140.28 55.28 113 52.80
9.75 117.00 1335 75.63 120.51 47.49 125 58.41
10.78 129.36 1385 78.47 153.93 60.66 136 63.55
11.74 140.88 1444 81.81 167.64 66.06 146 68.22
12. 75 153.00 1491 84.47 177.48 69.94 156 72.89
13.75 165.00 1543 87.42 207.90 81.93 162 75.70
14.75 177.00 1623 91.95 235.41 92.77 173 80.84
15 .78 189.36 1709 96.82 253.74 100.00 185 86.44
16.75 201.00 1754 99.37 239.19 94.26 196 91.58
17 .75 213.00 1765 100.00 253.34 99.84

¥

k

CASE 319M.

214

100.00

Ethnic 0rigin--NE; Socio-Economic Status--I

 

 

 

 

Height % 0f % 0f % 0f

Yeaxqg Mos in mm. Dev. M.A. Dev. .A. Dev.

\ , 3 - . . ..
7.10 85.20 -- -- 97.98 41.53 89 42.58
~12 97.44 1332 72.66 147.13 62.37 103 49.27
lg-l6 109.92 1396 76.15 167.07 70.83 118 56.45
ll~11 121.32 1450 79.10 172.27 73.03 130 62.19
12- 14 133.68 1507 82.21 204.53 86.71 143 68.41
13-11 145.32 1583 86.36 193.27 81.93 156 74.63
14'13 157.56 1722 93.94 206.40 87.50 169 80.85
15 ~ 12 169.44 1791 97.70 210.10 89 .07 18 87.55
6' l 2 181 . 44 1821 99 . 34 235 . 87 100 . 00 19 94 . 72
- 14 193 . 68 1833 100 .00 220 .79 93 . 60 209 100 . 00

127

CASE 343M. Ethnic 0rigin--NE; Socio-Economic Status-~I

mm

 

 

 

 

 

 

 

 

 

.....

1731

.82 234.

 

.00

227

Age Height % 0f % 0f % of
Years Mos. in mm. Dev. M.A. .Dev. .A. Dev.
7.11 85.32 1160 68.96 81.90 36.25 78 34.36
8.07 96.84 1207 71.75 117.17 51.87 90 39.64
9.09 109.08 1273 75.68 121.14 53.63 102 44.93
10.08 120.96 1317 78.29 119.14 52.74 113 49.77
11.10 133.20 1363 81.03 146.52 64.86 126 55.50
12.08 144.96 1403 83.41 160.18 70.91 140 61.67
13.08 156.96 1441 85.67 160.80 71.18 151 66.51
14.08 168.96 1491 88.64 174.02 77.04 167 73.56
15.07 180.84 1571 93.40 184.45 81.65 178 78.41
16.09 193.08 1641 97.56 207.56 91.88 198 87.22
17.09 205.08 1664 98.92 213.28 94.42 214 94.27
18.10 217.20 1682 100.00 225.88 100 00 227 100.00
:— ~ 71 7+ 7 44'“:
__CASE 350M. Ethnic 0rigin--NE; Socio-Economic Status--III
Age Height % 0f % 0f % of
Years Mos in mm. Dev. M.A. Dev. .A. Dev.
\ fi fi *1 ’ -
7-91 94.92 -- -- 116.75 49.75 92 40.53
-92 107.04 1281 73.87 142.36 60.66 104. 45.81
1992 119.04 1344 77.50 136.89 58.33 119 52.42
10-93 131.16 1390 80.16 136.40 58.12 131 57.70
11-99 143.28 1446 83.39 156.17 66.55 144 63.43
1297 155.64 1533 88.40 174.43 74.33 160 70.48
12'96 167.52 1627 93.82 185.94 79.23 172 75.77
15-91 178.92 1680 96.88 191.44 81.58 186 81.93
16.96 191.52 1711 98.67 197.26 84.06 198 87.22
”~94 203.28 1722 99.30 21 .44 90.95 212 93.39
8'94 215 28 1734 100.00 20 .82 88.98 217 95.59
:94 227 66 100 100.00

    

 

128

 

 

CAEHE 368M. Ethnic Origin--NE3 Socio-Economic Status-~III
Age Height 76 of % of % of
Years Mos. in mm. Dev. M.A Dev .A. Dev.
6. 64 79. 68 1142 69.54 71 .71 43. 64 70 40.46
7.€55 91.80 1198 72.95 88.12 53.63 -- --
8.652 103.44 1264 76.97 96.19 58.54 90 52.02
9.!51 115.32 1325 80.69 -- -- 112 64.73
10.f51 127.32 1380 84.04 106.94 65.08 126 72.83
11.56 138.72 1426 86.84 135.94 82.73 132 76.30
12.56 150.72 1479 90.07 149.21 90.81 138 79.76
13.59 163.08 1515 92.26 146.77 89.32 149 86.12
14.59 175.08 1546 94.15 155.82 94.83 160 92.48
15.556 186.72 1583 96.40 164.31 100.00 167 96.53
16.56 198.72 160.96 97.96

1642

100 .00

 

.T'..'.’.ZfT L

 

 

173

100

.00

 

 

SESE 371M. Ethnic Origin--It.; Socio-Economic Status-~V

7.14 85.68 1080 67.62 83.12 46.19 74 32.59
8.05 96.60 1128 70.63 95.63 53.14 84 37.00
9-14 109.68 1187 74.32 107.50 59.74 101 44.49
10.10 121.20 1232 77.14 106.65 59.26 113 49.77
11.07 132.84 1280 80.15 112.88 62.73 127 55.94
$306 144.72 1333 83.46 115.76 64.33 144 63.43
lENC)? 156.84 1444 90.41 -- -- 161 70.92
1 ~03 168.36 1526 95.55 134.72 74.86 178 78.41
12'06 180.72 1572 98.43 160.82 89.37 196 76.34
1 ~08 192.96 1573 98.49 167.91 93.31 209 92.07
1883 204.96 1586 99.31 170.15 94.55 221 97.35

2::=::£;:

216.

84

1597

100 .00

179.94

100.00

227

100 .

fl

129

CASE 372M. Ethnic 0rigin--It.; Socio-Economic Status-—O

 

Age Height 76 0f % 0f % of

Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.

8.54 102.5 1275 75.17 76.87 47.53 103 48.13
9.45 113.4 1320 77.83 137.21 84.84 118 55.14
10.54 126.5 1368 80.66 122.70 75.87 129 60.28
11.50 138.0 1409 83.07 138.00 85.33 142 66.35
12.47 149.6 1455 85.79 139.12 86.02 153 71.49
13.50 162.0 1497 88.26 150.66 93.16 164 76.63
14.49 137.9 1594 93.98 161.72 100.00 178 83.17
15.44 185.3 1655 97.58 155.65 96.24 190 88.78
l6.49 197.9 1684 99.29 154.36 95.44 203 94.85
17.51 210.1 1696 100.00 157.57 97.43 214 100.00

M —:=== m

 

 

W Ethnic 0rigin--It.; Socio-Economic Status-~O

 

 

 

\ iv
v v v V V +—

 

Age Height % 0f % of 96 of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.
\ V

9~O6 108.7 1134 73.54 92.39 52.62 88 38.76
9.97 119.6 1170 75.87 117.20 66.75 101 44.49
11-96 132.7 1217 78.92 116.77 66.51 114 50.22
12-02 144.2 1274 82.61 106.70 60.77 132 58.14
54:89 155.9 1341 86.96 120.04 68.37 148 65.19
1 ~02 168.2 1439 93.32 -- -- 162 71.36
15-00 180.0 1510 97.92 142.20 80.99 197 86.78
15-96 191.5 1517 98.37 143.62 81.80 210 92.78
lg-Ol 204.1 1537 99.67 155.11 88.35 221 92.51
1 -92 216.2 1540 99.87 170.79 97.28 227 97.35
9‘90 228.2 1542 100.00 175.56 100.00 227 100.00
m—

 

 

 

130

CASE 380M. Ethnic 0rigin--It.; Socio-Economic Status--IV

 

 

 

Age Height 7 of 7 0f 7 of

Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.
6.17 74.0 1107 66.01 85.84 43.02 60 26.54
7.13 85.6 -- -- 94.16 47.19 71 31.41
8.15 97.8 1232 73.46 117.36 58.82 82 36.28
9.15 109.8 1282 76.44 122.97 61.63 93 41.15
10.16 121.9 1336 79.66 125.55 62.92 108 47.78
11.15 133.8 1396 83.24 137.81 69.07 136 60.17
12.14 145.7 1491 88.90 163.18 81.79 154 68.14
13.14 157.7 1580 94.21 171.89 86.15 167 73.89
14.15 169.9 1631 97.25 176.69 88.56 180 79.64
133.13 181.6 1657 98.80 188.86 94.66 200 88.49
:16.14 193.7 1665 99.28 199.51 100.00 216 95.57
17 .17 206.0 1672 99.70 197.76 99.12 218 96.46
163.23 218.8 1677 100.00 -- -- 226 100.00

a '

 

QikSE 402M. Ethnic 0rigin--NE; Socio-Economic Status-~III

 

k

_1

Age Height 7 0f 7 0f 7 of

 

Ykeeus Mos. in mm. Dev. M.A. Dev. S.A. Dev.
7'.30 87.6 -- -- 77.96 43.14 90 39.64
53.32 99.8 1237 72.63 105.78 58.54 104 45.81
59.36 112.3 1326 77.86 99.94 55.31 114 50.22

1:3.31 123.7 1373 80.62 110.09 60.92 125 55.06

l]..34 136.1 1418 83.26 121.12 67.03 139 61.23

122.31 147.7 1465 86.02 134.40 74.38 154 67.84

133.33 160.0 1573 92.36 168.00 92.97 168 74.00

114.32 171.8 1641 96.35 163.21 90.32 179 78.85

15. 29 183.5 1672 98.17 159.64 88.35 200 88.10

16. 32 195.8 1678 98.53 156.64 86.68 211 92.95

137.131 207.7 1689 99.17 180.69 100.00 227 100.00

153.30 219.6 1703 100.00 175.68 97.22 227 100.00

 

 

 

 

 

 

‘ x

131

CASE 407M. Ethnic Origin--NE; Socio-Economic Status-~III

 

 

 

 

Age Height 7 0f 7 0f 7 of

‘Years M08. in mm. Dev. M.A. Dev. S.A. Dev.
6.92 83.2 1281 71.12 86.52 38.75 94 41.40
7.72 92.6 1329 73.79 96.30 43.13 107 47.13
8.78 105.4 1403 77.90 109.61 49.10 120 52.86
9.73 116.8 1456 80.84 131.98 59.12 131 57.70
10.76 129.1 1513 84.00 142.01 63.61 144 63.43
11.73 140.8 1556 86.39 143.61 64.33 155 68.27
12.74 152.3 1620 89 95 166.00 74.36 166 73.12
13.74 164.9 1692 93.94 187.98 84.20 178 78.41
111.71 176.5 1758 97.61 197.68 88.5 191 84.13
15.74. 188.9 1783 99.00 198.34 88.85 202 88.98
163.72 200.6 1790 99.38 210.63 94.35 215 .94.70
'17'.72 212.6 1801 100.00 223.23 100.00 227 100.00

 

 

 

 

— la: 1 fl
f

EJBEEZ412M. Ethnic 0rigin--NE; Socio-Economic Status--III

 

 

 

 

 

Age Height 7 of 7 0f 7 of

Years M08. in mm. Dev. M.A. Dev. S.A. Dev.
7'-73 92.8 1308 71.67 72.38 44.26 74 32.59
83.53 102.4 1346 73.75 69.63 42.57 87 38.32
59.60 115.2 1405 76.98 78.34 47.90 99 43.61
13.56 126.7 1454 79.67 90.59 55.39 .114 50.22
11..59 139.1 1507 82.57 102.93 62.94 129 56.82
123.59 151.1 1562 85.58 102.75 62.83 147 64.75
133.54 162.5 1614 88.43 122.69 75.02 160 70.48
14.52 174.2 1695 92.87 130.65 79.89 173 76.20
151-53 186.4, 1772 97.09 135.14 82.63 192 84.57
165.54 198.5 1806 98.95 136.97 83.75 205 90.30
if7-558 211.0 1817 99.56 163.53 100.00 219 96.47
€3-535 222.6 1825 100.00 153.59 93.92 227 100.00

 

 

 

_. m

 

 

132

CASE 417M. Ethnic 0rigin--NE; Socio-Economic Status--III

 

 

I
‘v__ V4

 

Age Height 7 0f 7 of 7 0f

Ybars Mos. in mm. Dev. M.A. Dev. S.A. Dev.
7.20 86.5 -- -- 102.94 53.57 80 44.20
8.22 98.6 1261 74.13 103.53 53.88 90 49.72
9.26 111.1 1311 77.07 120.44 63.68 101 55.80
10.22 122.6 1353 79.54 124.44 64.76 112 61.88
11.25 135.0 1398 82.18 145.80 75.88 125 69.06
12.21 146.5 1429 84.00 154.56 80.44 134 74.03
13.22 158.6 1472 86.53 166.53 86.67 145 80.11
111.22 170.6 1498 88.06 179.98 93.67 156 86.19
;15.22 182.6 1546 90.88 174.38 90.75 162 89.50
165.24 194.9 1619 95.17 179.31 93.32 172 95.03
137.22 206.6 1701 100.00 192.14 100.00 181 100.00

CIXSE 442M. Ethnic 0rigin-~It.; Socio-Economic Status-~O

 

 

 

 

 

 

: --5 4 ~ .._.L MW ——_Tr:========
Age Height 7 0f 7 0f 7 of
Ykears M08. in mm. Dev. M.A. Dev. S.A. Dev.

1215 67.91 79.49 46.02 84 43.97

65.90 82.8

'7.87 94.4 1275 71.26 80.24 46.45 96 50.25

53.88 106.6 1337 74.73 80.35 49.99 109 57.06

$9.88 118.6 1394 77.92 84.80 49.09 121 63.34
1:0.89 130.7 1444 80.71 111.75 64.70 132 69.10
1:1.88 142.6 1502 83.95 121.92 70.58 143 74.86
122.87 154.4 1564 87.42 128.15 74.19 156 81.66
123.87 166.4 1647 92.06 122.30 70.80 168 87.95
114.88 178.6 1729 96.64 169.67 98.23 -- --
-155.86 190.3 1789 100.00 158.90 91.99 191 100.00
1 .93 203.2 -- -- 172.72 100.00 -- --

 

133

CASE 444M. Ethnic 0rigin--It.; Socio-Economic StatuS--IV

 

 

 

Age Height 7 0f 7 0f 7 0f

Ybars Mos. in mm. Dev. M.A. Dev. S.A. Dev.
6.17 74.0 1180 66.36 59.20 28.81 77 35.81
7.00 84.0 1232 69.29 94.92 46.20 90 41.86
8.01 96.1 1300 73.11 87.93 42.80 102 47.44
9.04 108.5 1356 76.26 104.16 50.70 114 53.02
10.01 120.1 1402 78.85 109.89 5 .49 126 58.60
11.05 132.6 1463 82.28 116.69 56.80 137 63.72
12.02 144.2 1519 85.43 -- -- 152 70.59
:12.98 155.8 1581 88.92 142.50 69.36 164 76.27
111.00 168.0 1680 94.48 159.60 77.69 178 82.78
155.02 180.2 1743 98.03 205.43 100.00 192 89.29
165 01 192.1 1764 99.21 197.86 96.31 203 94.41
1T7.01 204.1 1778 100.00 189.81 92.39 215 100.00

CLASE 456M. Ethnic Origin-~It.; Socio-Economic Status--II

 

_¥

Age Height 7 0f 7 0f 7 0f

 

Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.
“7.31 87.7 1217 70.30 85.06 52.01 89 46.84
€3.11 97.3 1258 72.67 88.54 54.14 101 53.15
59.12 109.4 1320 76.25 110.49 67.56 113 59.47

110.15 121.8 1379 79.66 110.83 67.77 125 65.78

141.13 133.6 1429 82.55 134.93 82.51 137 72.10

112.16 145.9 1472 85.03 140.06 85.64 150 78.94

1:3.14 157.7 1548 89.42 154.54 94.50 162 85.26
14.11 169.3 1657 95.72 154.06 94.20 175 92.10

155.14 181.7 1731 100.00 163.53 100.00 190 100.00

 

\

134

 

 

 

 

 

 

 

 

 

 

 

CASE 460M. Ethnic 0rigin--It.; S0ci0-Econ0mic Status-~V
Age Height 7 0f 7 0f 7 of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.
7.09 85.1 1036 68.65 -- -- 66 31.57
8.05 96.6 1077 71.37 -- -- 79 37.79
9.06 108.7 1118 74.08 84.78 59.16 90 43.05
10.06 120.7 1157 76.67 80.86 56.43 104 49.75
11.08 133.0 1198 79.39 105.07 73.32 118 56.45
12.05 144.6 1239 82.10 92.54 64.58 131 63.67
13.05 156.6 1300 86.14 103.35 72.12 144 68.89
14.06 168.7 1393 92.31 102.90 71.81 168 80.37
.15.06 180.7 1463 96.95 128.29 89.5 -- --
115.06 192.7 1493 98.93 142.59 99.51 192 91.85
137.06 204.7 1509 100.00 143.29 100.00 209 100.00
CikSE 474M. Ethnic Origin-~It.; Socio-Economic StatuS--IV
Age Height 7 0f 7 0f 7 of
Years Mos. in mm. Dev. M. Dev. .A. Dev.
(5.81 81.7 1069 65.22 87.41 44.97 77 36.66
"7.77 93.2 1109 67.66 108.11 55.62 89 42.38
23.78 105.4 1156 70.53 110.67 56.93 102 48.57
59.78 117.4 1215 74.13 122.09 62.81 115 54.76
1&0.80 129.6 1265 77.18 129.60 66.67 126 60.00
141.77 141.2 1315 80.23 145.43 74.82 138 65.71
122.77 153.2 1372 83.70 163.92 84.33 149 70.95
143.79 165.5 1436 87.61 162.19 83.44 161 76.67
114.77 177.2 1532 93.47 177.20 91.16 172 81.90
155.78 189.4 1603 97 80 183.71 94.51 184 87.62
1 6. 78 201.4 1622 99.63 191.33 98.43 198 94.28
17.80 213.6 1639 100.00 194.37 100.00 210 100

.00

 

 

 

135

 

 

 

 

 

 

 

CASE 478M. Ethnic 0rigin--NE; S0cio-Econ0mic Status--IV
Age Height 7 0f 7 0f 7 of
Years Mos. in mm. Dev. M.A. Dev. .A. Dev.
7.35 88.2 -- -- 127.00 55.99 89 ~ 39.20
8.37 100.4 1351 75.94 123.49 54.44 102 44.93
9.41 112.9 1397 78.52 111.77 49.27 114 50.21
10.37 124.4 1451 81.56 128.13 56.49 127 55.94
11.40 136.8 1494 83.97 151.84 66.94 142 62. 5
12.36 148.3 1543 86.73 169.06 74.53 154 67.84
13.39 160.7 1653 92.91 194.44 85.72 166 73.12
14.38 172.6 1730 97.24 219.20 96.64 179 78.85
15.37 184.4 1763 99.10 226.81 100.00 195 85.89
175.40 196.8 1778 99.94 222.38 98.04 215 94.70
1:7.37 208.4 1779 100.00 210.48 92.80 227 100.00
ClXSE 479M. Ethnic Origin--NE; Socio-Economic Status--IV
Age Height 7 0f 7 0f 7.0f
Yfiaars Mos. in mm. Dev. M.A. Dev. .A. Dev.
6142 77.0 1108 67.85 72.38 52.15 66 36.26
'7.23 86.8 1161 71.09 77.25 55.66 78 42.85
53.29 99.5 1215 74.40 81.59 58.79 90 49.44
59.24 110.9 1264 77.40 100.91 72.71 103 56.59
1:0.25 123.0 1317 80.64 -- -- 115 63.18
1~1.22 134.6 1352 82.79 99.60 71.77 127 69.77
.122.23 146.8 1391 85.18 110.10 79.33 139 76 36
1:3.23 158.8 1428 87.44 117.51 84.67 150 82.41
14.20 170.4 1476 90.38 121.80 92.09 -— --
fS.22 182.6 1543 94.48 138.77 100.00 -- ——
1<S.25 0 138. 182 100.00

195.

J

1633

13D.

00

45 w 99.

76

136

CASE 483M. Ethnic Origin--NE; Socio—Economic Status--II

 

 

 

 

Age Height 7 0f 7 of 7 of

YEars Mos. in mm., Dev. M.A. Dev. S.A. Dev.
6.33 -76.0 -- -- 72.20 32.91 75 39.26
7.40 88.8 1230 68.14 89.68 42.83 85 44.49
8.41 100.9 1291 71.52 108.97 49.68 97 50.78
9.45 113.4 1345 74.51 105.46 48.08 107 56.01
10.41 124.9 1399 77.50 138.63 63.20 120 62.82
11.41 136.9 1445 80.05 179.33 81.75 130 68.05
12.42 149.0 1502 83.21 169.86 77.44 143 74.86
13.39 160.7 155’ 85.87 165.52 75.46 155 81.14
114.41 172.9 1606 88.97 186.73 85.13 159 83.23
153.42 185.0 1682 93.18 214.60 97.83 172 90.04
163.41 196.9 1755 97 22 218.55 99.63 180 94.23
17'.41 208.9 1805 100.00 219.34 100.00 191 100.00

EQ3SE 488M. Ethnic Origin--NE; Socio-Economic Status--IV

 

b

 

Age Height 7 0f 7 of 7 of
Ykears Mos. in mm. Dev. M.A. Dev. S.A. Dev.
65.13 73.6 1085 69.37 74.33 35.30 67 38.28
65.94 83.3 1133 72.44 166.62 79.13 78 44.57
"7.99 95.9 1189 76.02 117.95 56.01 89 50.85
83.93 107.2 1232 78.77 108.62 51.58 98 56.00
59.96 119.5 1279 81.77 129.06 61.29 104 59.42
l<>.97 131.6 1317 84.20 147.39 69.99 108 61.71
1:1.92 143.0 1356 86.70 165.16 78.43 116 66.28
123.95 155.4 1398 89.38 170.16 80.81 125 71.42
133.91 166.9 1424 91.04 176.07 83.61 135 77.14
11+.93 179.2 1461 93.41 210.56 100.00 148 84.57
3155.92 191.0 1499 95.84 209.14 99.32 161' 92.00
16.92 203.0 1564 100.00 204.01 96.88 175 100.00

 

3
i

137

CASE 526M. Ethnic 0rigin--It.; Socio-Economic Status--V

 

 

 

Age Height 7 0f 7 of 7 of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.
6.15 73.8 1078 65.73 77.49 41.09 69 35.02 1,
7.11 85.3 1133 69.08 85.30 45.23 80 40.60 1
8.11 97.3 1186 72.31 103.13 54.69 93 47.20
9.11 109.3 1246 75.97 99.46 52.74 106 53.80
10.13 121.6 1299 79.20 106.40 56.43 119 60.40
11.10 133.2 1352 82.43 123.87 65.69 130 65.98
12.10 145.2 1402 85.48 134.31 71.23 143 72.58
13.09 157.1 1481 90 30 153.17 81.23 160 81.21
14110 169.2 1575 96.03 164.97 87.49 175 88.83
:15.11 181.3 1619 98.71 188.55 100.00 186 94.41
3 1640 100.00 188.46 99.9 197 100.00

1 6.11 193.

CLASE 530M. Ethnic Origin—-It.; Socio-Economic Status-~IV

 

¥
¥

fl

 

Age Height 7 of 7 0f 7 of
Rhears Mos. in mm. Dev. M.A. Dev. S.A. Dev.
6183 82.0 1131 68.05 85.28 52.34 71 31.27
'7.62 91.4 1175 70.69 97.37 59.76 -- --
£3.70 104.4 1231 74.06 -- -- 100 44.05
59.64 115.7 1269 76.35 111.07 68.17 112 49.33
1&0.67 128.0 1321 79.48 120.32 73.84 123 54.18
131.62 139.4 1370 82 43 125.46 77.00 -- --
3122.62 151.4 1423 85.61 125.66 77.12 -- --
1:3.63 163.6 1488 89.53 140.69 86.34 156 68.72
14.61 175.3 1543 92.83 133.22 81.76 167 73.56
153.62 187.4 1604 96.51 157.41 96.61 180 79.29
16.64 199.7 1637 98.49 153.76 94.37 194 85.46
17.63 211.6 1662 100.00 162.93 100.00 209 92.07
1153.87 226.4 1661 99.93 160.74 98.65 227 100.00

 

 

 

138

 

CASE 534M. Ethnic 0rigin--M3 Socio—Economic Status--III
Age Height 7 0f 7 0f 7 of
‘Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.

 

 

 

6.50 78.0 1129 66.96 75.66 34.70 76 34.08
7.30 87.6 1175 69.69 92.85 42.59 88 39.46
8. 35 100. 2 1234 73.19 107.21 49 . 18 104 46. 63
9.33 112.0 1283 76.-09 118.72 54.46 116 52.01
10.31 123.7 1328 78.76 129.88 59.58 130 58.29
11.34 136.1 1379 81.79 149.71 68.68 141 63.22
12.30 147.6 1449 85.94 172.69 79.22 156 69.95
1 3.33 160.0 1581 93.77 169.60 77.80 170 76.23
14.29 171.5 1649 97.80 188.65 86.54 182 81.61
15.31 183.7 1667 98.87 198.39 91.01 198 88.78
1 6.30 195.6 1682 99.76 191.68 87.93 206 92.37
17.30 207.6 1686 100.00 217.98 100.00 223 100.00
ELASE 542M. Ethnic 0rigin--NE; Socio-Economic Status-—II

 

 

‘
‘

Age Height
Shears Mos. in mm.

7 of

Dev. S.A.

7 0f

Dev. M.A.

7 0f

Dev.

 

 

 

 

7.21 86.5 1123 66.60 94.28 41.61 71 31.27

8.02 96.2 1165 69.09 86.58 38.21 77 33.92

9.09 109.1 1217 72.18 118.91 52.48 89 39.20
10.04 120.5 1262 74.85 126.52 55.84 104 45.81
11.07 132.8 1315 77.99 134.12 59.19 120 52.86
12.06 144.7 1365 80.96 144.70 63.86 134 59.03
13.02 156.2 1465 86.89 149.95 66.18 153 67.40
14.05 168.6 1553 92.11 187.14 82.59 168 74.00
15 .01 180.1 1618 95.96 187.30 82.66 180 79.29
16.03 192.4 1651 97.92 198.17 87.46 196 86.34
17 . 02 204.2 1669 98.99 191.94 84 .71 208 91.62
18 .08 217.0 1682 99.76 206.24 91.02 219 96.47
19.27 213.2 57

llllllllllll

a - .

100.00

227 100.00

 

 

 

 

139

 

 

 

 

 

 

 

 

 

EASE 574M. Ethnic 0rigin--It.; Socio-Economic Status--O
Age Height 7 0f 7 of 7 of
TYears Mos. in mm. Dev. M.A Dev. .A. Dev.
6.41 76.92 -- -- 110.76 44.64 90 44.11
'7.39 88.68 1338 74.04 144.54 58.25 101 49.50
63.45 101.40 1395 77.19 135.87 54.76 113 55.39
59.41 112.92 1446 80.02 156.95 63 25 125 61.27
:1:0.44 125.28 1504 83.23 184.16 74 22 136 66.66
1;1.40 136.80 1541 85.27 206.56 83.25 144 70 58
:122.39 148.68 1587 87.82 221.53 89 28 152 74.50
:124.41 172.92 1670 92.41 240.35 96 87 169 82.84
ILES.44 185.28 1709 94.57 231.60 93.34 179 87.74
1.6141 196.92 1772 98.06 248.11 100 00 190 93.13
.1f7.55 210.60 1807 100.00 231 66 93 36 204 100.00
EQASE 585M. Ethnic 0rigin-—NE; Socio-Economic Status--III
Age Height 7 0f 7 0f 7 0f
Shears M08. in mm. Dev. M.A. Dev. .A. Dev.
'7.64 91.68 1237 70.16 134.76 56.65 78 40.62
53.46 101.52 1278 72.49 165.47 69.56 90 46.50
59.52 114.24 1342 76.12 143.94 60.50 102 53.12
lC>.51 126.12 1386 78.61 156.38 65.73 113 58.85
1:1.48 137.76 1436 81.45 184.59 77.59 125 65.10
122.51 150.12 1481 84.00 210.16 88.34 138 71.87
1 3.50 162.00 1529 86.72 205.74 86.48 149 77.50
114.45 173.40 1575 89.33 195.94 82.37 161 83.80
115.50 186.00 1656 93.93 232.50 97.73 184 95.83
i1éé'i2 198.24 1724 97.78 237.88 100.00 -- --
. 9

a

1763 100.00

222

.47 g 93

w

.52

192

100

.00

140

CASE 599M. Ethnic 0rigin--NE; Socio-Economic Status-~III

 

 

 

 

m 1.1:: J m
Age Height 7 of 7 0f 7 of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.

 

._v V w 1

7.24 86.88 1129 77.70 86.88 48.63 77 45.02
8.14 97.68 1171 80.59 97.68 54.68 89 52.04
9.15 109.80 1210 83.27 107.60 60.23 101 59.06
10.21 122.52 1248 85.89 107.82 60.35 112 65.49
11.16 133.92 1275 87.74 124.55 69.72 124 72.51
12.20 146.40 1318 90.70 140.54 78.67 135 78.94
13.17 158.04 1360 93.59 143.82 80.51 149 87.13
14.19 170.28 1397 96.14 154.95 86.74 —- --

15.19 182.28 1453 100.00 178.63 100.00 171 100.00

 

CASE 620M. Ethnic 0rigin-—NE; Socio-Economic Status--III

 

—' —v v a a v—VV W

Age Height 7 0f 7 0f 7 of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.

7.11 85.32 -- -- 100.68 38.24 72 36.36
8.12 97.44 1245 73.36 112.06 42.56 84 42.42
9.12 109.44 1304 76.84 146.65 55.70 95 47.97
10.14 121.68 1349 79.49 161.83 61.46 108 54.54
11.13 133.56 1386 81.67 157.60 59.86 120 60.60
12.17 146.04 1429 84.20 229.28 87.08 132 66.66
13.15 157.80 1474 86.85 219.34 83.31 144 72.72
14.11 169.32 1514 89.21 225.20 85.53 155 78.28
15.15 181.80 1600 94.28 239.98 91.15 166 83.83
16.17 194.04 1660 97.81 260.01 98.76 180 90.90
17.14 205.68 1697 100.00 263.27 100.00 198 100.00

M1 -1, h 1

 

141

CASE 623M. Ethnic 0rigin-—NE; Socio-Economic Status--O

 

 

w w—

Age Height 7 0f 7 0f 7 of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.

 

i f

7.19 86.28 1212 68.24 -- -- 66 29.07
7.98 95.76 1267 71.34 88.09 44.90 79 34.80
9.05 108.60 1325 74.60 122.72 62.56 93 40.96
10.00 120.00 1388 78.15 117.60 59.95 106 46.69
11.03 132.36 1435 80.79 131.04 66.98 119 52.42
11.98 143.76 1495 84.17 142.32 72.56 133 58.59
12.98 155.76 1602 90.20 160.43 81.78 157 69.16
14.01 168.12 1703 95.88 154.67 78.85 176 77.53
14.97 179.64 1741 98.02 163.47 83.33 191 84.14
15.99 191.88 1755 98.81 168.85 86.08 207 91.18
17.99 215.88 1776 100.00 181.34 92.44 227 100.00
19.23 230.76 1768 99.54 196.15 100.00 227 100.00

m1 fij 1 7‘fi 11"—

 

 

QASE 626M. Ethnic 0rigin--NE; Socio—Economic Status--III

 

 

w 1— 1 1

Age Height 7 0f 7 0f 7 of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.

7.24 86.88 1129 67.76 -- -- -~

8.05 96.60 1171 70.28 97.57 43.71 88 40.74
9.09 109.08 1236 74 18 136.35 61.08 101 46.75
10.07 120.84 1280 76.83 116.01 51.97 113 52.31
11.07 132.84 1334 80.07 164.72 73.79 126 58.33
12.06 144.72 1376 82.59 164.98 73.90 139 64.35
13.08 156.96 1432 85.95 167. 5 75.2 152 70. 7
14.03 168.36 1513 90.81 178. 6 79.9 166 76. 5
15.06 180.72 1592 95 55 177.11 79.34 179 82.87
16.08 192.96 1638 98.31 189.10 84.71 191 88.42
17.07 208.84 1657 99.45 210.93 94.49 204 94.44
18.06 216.72 1666 100.00 223.22 100.00 216 100.00

w—w

142

CASE 630M. Ethnic 0rigin—-NE; Socio—Economic Status--I

 

 

m 1
Age Height 7 0f 7 0f 7 of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.

 

6.20 74.40 -- -- 77.37 30.35 71. 33.80
7.01 84.12 1214 68.85 96.73 37.95 86 40.95
8.06 96.72 1285 72.88 136.85 53.69 96 45.71
9.00 108.00 1334 75.66 148.50 58.26 108 51.42
10.30 120.36 1391 78.89 186.55 73.19 119 56.66
11.04 132.48 1443 81.84 192.09 75.37 132 62.85
12.01 144.12 1504 85.30 210.41 82.56 146 69.52
13.01 156.12 1582 89.73 226.37 88 82 161 76.66
13.98 167.76 1688 95.74 248.28 97.42 175 83.33
15.00 180.00 1735 98.41 232.20 91.11 190 90.47
15.99 191.88 1759 99.77 254.24 99.76 199 94.76
16.99 203.88 1763 100.00 254.85 100.00 210 100.00

mm: 1 1: - 1J1 Vfi‘

 

CASE 645M. Ethnic 0rigin--J; Socio-Economic Status—-III

 

 

Age Height 7 0f 7 0f 7 of
Years M08. in mm. Dev. M.A. Dev. S.A. Dev.

 

6.40 76.80 1118 65.95 95.23 39.02 77 60.62
7.36 88.32 1183 69.79 106.86 43.79 89 70.07
8.38 100.56 1239 73.09 128.71 52.74 102 80.31
9.38 112.56 1289 76.04 152.51 62.50 114 89.76
10.39 124.68 1339 78 99 174.55 71.53 127 100.00
11.38 136.56 1390 82.00 189.81 77.78 -- --
12.39 148.68 1454 85.78 205.17 84.08 -- --
13.36 160.32 1553 91.62 232.46 95.26 -- --
14.37 172.44 1636 96.51 229.34 93.98 -- --
15.35 184.20 1687 99.52 225.82 92.54 -- --
16.37 196.44 1691 99.76 238.67 97.81 -- --
17.38 208.56 1695 100.00 244.01 100 00 -- --

143

CASE 648M. Ethnic 0rigin--NE; Socio-Economic Status--II

 

‘

 

Age Height 7 0f 7 of 7 of
Years M03. in mm. Dev. M.A. Dev. S.A. Dev.

 

6.95 83.40 1168 69.19 100.91 42.29 77 41.17
7.76 93.12 1216 72.03 125.71 52.69 87 46.52
8.80 105.60 1275 75.53 140.44 58.86 101 54.01
9.75 117.00 1322 78.31 133.96 56.15 113 60.42
10.78 129.36 1371 81.22 178.51 74.82 125 66.84
11.75 141.00 1412 83.64 176.95 74.17 131 70.05
12.76 153.12 1457 86.31 195.99 82.15 139 74.33
13.76 165.12 1482 87.79 196.49 82.36 150 80.21
14.76 177.12 1526 90.40 218.74 91.69 156 83.42
15.78 189.36 1572 93.12 213.01 89.28 166 88.77
16.75 201.00 1630 96.56 234.16 98.15 179 95.72
17.75 213.00 1688 100.00 238.56 100.00 187 100.00

m 1 v m

 

CASE 661M. Ethnic 0rigin--NE; Socio-Economic Status-~IV

 

 

W :11 111 v 1

Age Height 7 of 7 0f 7 of
Years M08. in mm. Dev. M.A. Dev. S.A. Dev.

 

.45 77.40 1166 66.21 58.82 26.10 78 37.68
.26 87.12 1216 69.05 87.12 38.66 89 42.99
.31 99.72 1273 72.28 105.70 46.90 102 49.27
.28 111.36 1321 75.01 124.16 55.10 114 55.07
.31 123.72 1372 77.91 124.95 55.45 125 60.38
.26 135.12 1416 80.40 135.12 59.96 132 63.76
.25 147.00 1466 83.24 159.49 70.78 145 70.04
.27 159.24 1514 85 97 157.64 69.95 156 75.36
.24 170.88 1550 88.01 153.79 68.25 161 77.77
.26 183.12 1591 90.34 174.87 77.60 168 81.15
.26 195.12 1654 93.92 188.29 83.56 174 84.05
.26 207.12 1732 98.35 202.97 90.07 180 86.95
.50 222.00 1761 100.00 225.33 100.00 207 100.00

t—‘i—‘F—‘l—‘F—‘D—‘Hl—‘l—J
CDNmU'l-P—‘UUMi-‘OKOOD‘IO

144

CASE 669M. Ethnic 0rigin--NE; Socio-Economic Status-~11

 

 

m 1 1 - w 1

Age Height 7 0f 7 0f 7 of
Years M08. in mm. Dev. M.A. Dev. S.A. Dev.

 

6. 6 72.73 1201 67.39 58.90 29.19 77 33.92
6 5 82.20 1240 69.5 101.10 50.11 89 39.20
7. 1 94.92 1299 72.89 105.36 5 .22 101 44.49
8.87 106.44 1364 76.54 92.07 45.64 114 50.22
9.90 118.80 1420 79.68 114.04 56.53 125 55.06
10.90 130.80 1475 82.77 116.41 57.70 137 60.35
11.89 142.68 1543 86.58 133.40 66.12 151 66.51
12.87 154.44 1616 90.68 146.71 72.72 162 71.36
13.85 166.20 1710 95.95 156.22 77.44 180 79.29
14.87 178.44 1755 98.48 178.44 88.45 203 89.42
15.86 190.32 1755 98.48 201.73 100.00 215 94.71
16.86 202.32 1782 100.00 188.15 93.26 227 100.00

 

ifivfi—v *— +7

CASE 685M; Ethnic 0rigin--It.; Socic-Economic Status—~III

 

—"""‘ w

 

 

Age Height 7 0f 7 0f 7 of

Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.

 

V v v v v

6.39 76.68 1114 66.94 66.71 34.65 71 31.27
7.20 86.40 1171 70.37 82.08 42.63 83 36.56
8.25 99.00 1232 74 03 83.16 43.19 93 40.96
9.22 110.64 1276 76 68 98.46 51.14 111 48.89
10.25 123.00 1321 79.38 111.93 58 14 124 54.62
11.20 134.40 1363. 81.91 112.89 58.64 135 59.47
12.19 146.28 1420 85.33 122.87 63.82 --
13.21 158.52 1475 88.64 144.25 74.93 159 70.04
14.18 170.16 1559 93.68 151.44 78.66 168 74.00
15.20 182.40 1619 97.29 147.74 76.74 180 79 29
16.21 194.40 1650 99.15 159.40 82.80 199 87.66
17.21 206.52 1652 99.27 175.54 91 18 221 97.35
18.44 221.28 1664 100.00 192.51 100.00 227 100.00

145

CASE 699M. Ethnic Origin--NE; Socio—Economic Status--IV

 

Height 7 of

v— fi fi—

 

 

 

 

 

 

Age 7 0f 7 of
Years Mos. in mm. Dev. M.A. Dev. .A. Dev.
7.77 93.24 1285 71.38 93.24 48.68 89 39.20
8.76 105.12 1336 74.22 103.01 53.78 102 44.93
9.75 117.00 1393 77.38 122.85 64.14 113 49.77
10.74 128.88 1438 79.88 121.14 63.25 123 54.18
11.71 140.52 1491 82.83 115.22 60.16 132 58.14
12.10 152.40 1542 85.66 134.11 70.02 145 63.87
13.71 164.52 1618 89.88 138.19 72.15 156 68.72
14.67 176.04 1722 95.66 153.15 79.96 176 77.53
15.70 188.40 1763 97.94 165.79 86.56 192 84.58
16.70 200.40 1779 98.83 172.34 89.98 216 95.15
17.70 212.40 1794 99.66 176.29 92.04 227 100.00
.18.71 224.52 1800 100.00 170.63 89.09 227 100.00
:19.95 239.40 1800 100 00 191.52 100.00 227 100 00
(EASE 721M. Ethnic 0rigin--NE; Socio—Economic Status--IV
Age Height 7 0f 7 0f 7 of
‘Years Mos. in mm. Dev. M. Dev. .A. Dev.
7.78 93.36 1259 70.13 109.23 56.64 77 38.88
8.75 105.00 1302 72.53 126.00 65.33 90 45.45
9.74 116.88 1360 75.76 118.36 61.37 101 51.01
lC>.73 128.76 1414 78 77 135.20 70.10 114 57.57
11..70 140.40 1450 80.77 143.91 74.62 126 63.63
142.73 152.76 1490 83.00 169.56 87.92 139 70.20
153.71 164.52 1554 86.57 161.23 83.60 151 76.26
14.67 176.04 1637 91.19 161.96 83.98 162 81.81
155.72 188.64 1724 96.04 166.00 86.08 173 87.37
163 4 200.88 1769 98.55 192.84 100.00 185 93.43
17’ 75 213.00 1795 100.00 191 40 198 100.00

.70 . 99.

146

CASE 1801M. Ethnic 0rigin--NE; Socio-Economic Status--IV

 

 

 

Age Height 7 of 7 of 7 of
Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.

 

7.49 89.88 —- -- 94.37 50.25 -- --

8.50 102.00 1228 71.93 -- -- 90 40.54

9.51 114.12 1273 74.57 118.68 63.19 103 46.39
10.52 126.24 1315 77.03 122.45 65.20 117 52.70
11.51 138.12 1367 80.08 146.40 77.95 129 58.10
12.55 150.60 1407 82.42 161.14 85.80 139 62.61
13.52 162.21 1472 86.23 147.63 78 61 150 67.56
14.49 173.88 1565 91.68 158.23 84.25 163 73.42
15.53 186.36 1652 96.77 169.58 90.30 180 81.08
:16.56 198.72 1689 98.94 172.88 92.06 192 86.48
17.53 210.36 1707 100.00 185.11 98.57 211 95.04
:18.63 223.56 1699 99.53 187.79 100.00 222 100.00

 

(EASE 2848M. Ethnic 0rigin-—NE; Socio-Economic Status--II

 

 

b

Age Height 7 0f 7 0f 7 of
'Years Mos. in mm. Dev. M.A. Dev. S.A. Dev.

6.05 72.60 1106 62.73 87.84 40.22 62 31.95
6.83 81.96 1160 65.79 105.72 48.41 71 36.59
'7.90 94.80 1225 69.48 127.03 58.17 83 42.78
€3.86 106.32 1289 73.11 114.82 52.58 94 48.45
59.89 118.68 1339 75.95 145.97 66.84 106 54.63
lC>.98 131.76 1390 78.84 152.84 69.99 118 60.82
11.86 142.32 1433 81.28 162.24 74.29 130 67.01
122.86 154.32 1482 84.06 168.20 77.02 145 74.74
133.83 165.96 1545 87.63 187.53 85.87 156 80.41
14.86 178.32 1634 92.68 196.15 89.82 168 86.59
155.85 190.20 1716 97.33 214.92 98.42 181 93.29
163.85 202.20 1763 100.00 218.37 100 00 194 100.00

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

 

APPENDIX B

148

 

 

 

 

 

 

 

 

 

CASE 4M
Height Skeletal Age Mental Age

K1 1410 156 174
r1 .2687 ..1713 .3654
11 24.23 20.76 6.19
K2 261 88 16
r2 .813 .2770 .7907
12 -102.29 -15.91 -97.36
t2 143.93 110.61 141.76
K3 1671 224 190
t3 18.3 27.65 18.27

.Average

error of

equation 9 .85 l .807 7.25

CASE 15M

. Height Skeletal Age Mental Age

K1 ; 1574 128 140
r1 '.1530 .4152 .4211
i1 31.92 4.34 -0.80
K2 253 102 49
r2 .8536 .3418 - .4000
12 -92.86 -20.39 -29.93
t2 126.04 102.75 111.65
K3 1827 230 189
t3 16.48 23.50 22.07

Average '

error of

equation 8.72 2.59 . 4.40

 

'\ #:3- 7 J 1 I: x—~ #_ —-——" W

 

 

 

 

 

149

 

 

 

 

 

 

 

 

 

 

 

 

CASE 37M
Height Skeletal Age Mental Age

K1 1610 156 166
r1 .2211 .2300 .4077
i1 25.66 16.29 9.15
K2 243.6 96 77
22 ..945 .3370 .6873
12 -123.61 -30.33 -64.90
t2 146.3 133.70 115.85
K3 1853.6 252 243
t3 17.60 26.29 17.08

Average

error of

equation 11.01 2.85 5.49

CASE 56M

Height Skeletal Age Mental Age

K1 1514 144 127
r1 .2487 .2623 .4255
11 19.21 11.02 8.03
§K2 230.0 102 78
r2 .7693 .3650 .4358
12 ~92.62 -30.08 -33.44
t2 139.54 122.76 110.53
K3 1744 246 205
t3 18.26 24.22 20.93

AVerage

erfiror of 6.44 1.759

5.878

a fi ~—v

ggggation

CASE 60M

 

‘—:—
1.

 

 

 

 

 

 

Height Skeletal Age Mental Age

K1 1566 117 111
r1 .1457 .3423 .3450
11 28.77 7.00 18.00
K2 200 108 69
r2 .826 .2317 .3738
12 -111.62 -8.27 -25.71
t2 153.0 99.27 108.13
K3 1766 225 180
t3 18.93 30.31 22.67

Average

error of

equation 16.26 2.51 4.80

CASE 68M

Height Skeletal Age Mental Age

K1 1523 143 170
11 30.64 15.45 -3.67
K2 247.0 95 56
r2 .7036 .2848 .4437
i2 -85.56 -19.70 -4l.69
t2 146.91 120.89 127.16
K3 1770.0 238 226
t3 19.13 28.00 22.10

Average

error of

equation 10.24 6.07 4.76

x
X i Vfi

CASE 69M

 

w

Skeletal Age

Mental Age

 

 

 

 

 

 

Height

K1 1612 159 150
rl .1759 .2310 .2279
i1 25.47 14.05 12.97
K2 188.3 72 35
re .8850 .2827 .8335
i2 -1l9.07 -19.93 -103.13
t2 151.18 122.60 141.40
K3 1800.3 231 ,185
t3 18.37 28.27 18.45

Average

error of

equation 6.35 2.748 7.16

CASE 81M

Height Skeletal Age Mental Age

K1 1525 154 180
r1 .1792 .2570 .3208
i1 26.73 15.27 10.80
K2 175.3 53 66
re .8958 .2132 .4233
i2 -125.20 -6.27 -37.12
t2 156.20 98.50 122.48
K3 1700.3 207 246
t3 18.71 32.15 22.27

Average

eI‘ror of

eCluation 5.24 2.18 3.203

W

 

CASE 82M

 

Mental Age

 

 

 

 

 

 

 

 

Height Skeletal Age

K1 1547 166 116
r1 .1665 .1911 .2750
11 28.19 17.82 23.07
K2 237.8 73 61
r2 .6053 .2972 .6900
12 -70 88 ~20.69 -79.20
t2 141.43 119.18 136.13
K3 1784.8 239 177
t3 20.22 27.11 18.74

Average

error of

e quation 6. 21 2. 25 6. 230

§;ASE 83M

Height Skeletal Age Mental Age

K1 1519 157 116
r1 .1722 .2382 .2344
i1 29.15 12.82 19.22
K2 212.5 68 36
r2 .7426 .3097 .5980
12_ —90.67 -22.15 -58.44
t2 141.93 119.08 122.35
K3 1731.5 225 152
t3 18.70 26.41 18.73

Average

eI‘ror of

equation 7.77 .83

7.590

153

 

 

 

 

 

CASE 94M
Height Skeletal Age Mental Age
K1 1528 157 135
r1 .1600 .2117 .2294
11 27.88 13.86 16.35
K2 208.2 31 52
12 -95.78 -31.86 -54.43
t2 161.5 126.46 137.08
K3 1736.2 188 187
t3 20.92 26.66 21.54
Average
error of
equation 9 . 39 l . 68 6.200
SLASE 108M

 

w

 

m

4.
J- —

Mental Age

 

Height Skeletal Age

K1 1653 184 127
r1 .1768 .1728 .3491
$1 2:503 19.23 20.;3
r: .5488 .3775 .4770
12 -71.62 -35.76 -43.41
t2 157.34 133.75 139.53
K3 1808.0 238 184
t3 22.41 24.67 20.86

Average

error of

equation 9.80 5.31

9.010

.2 Q0.

..v..:v.-.

’c

d. 7. ‘

~._o..~1_.

. I . .
. . . g

P? T .oo. 51::

 

154

 

 

 

 

 

 

 

 

 

 

 

 

CASE 119M
Height Skeletal Age Mental Age

K1 1605 157 182
r1 .1716 .1953 .3600
11 26.42 17.27 2.33
K2 221.9 70 50
re .8659 .2971 .4495
12 -1l7.08 -19.80 -42.13
t2 152.22 116.22 126.49
K3 1826.9 227 232
t3 18.58 26.87 21.9

Average

error of

equation 6.67 1.49 7.06

_§@SE 123M

Height Skeletal Age Mental Age

K1 1596 160 140
r1 .1877 .2423 .3207
i1 25.65 15.30 8.24
12 163 84 49
r2 1.063 .2616 .7041
12 -140.79 -18.29 -75.28
t2 146.30 126.22 127.83
K3 1759 244 189
t3 16.99 30.03 17.90

Average

error of

equation 5 . 18

5.16

4.06

 

 

155

 

 

 

CASE 150M
Height Skeletal Age Mental Age

K1 1492 200 168
r1 .1740 .1716 .1768
11 28.48 14.41 18.39
K2 226 60 60
r2 .9583 .3353 .7225
12 -98.51 -l7.57 -66.90
t2 118.16 96.33 112.98
K3 1718 260 228
t3 15.17 23.55 16.48

.Average

error of

equatinn 7.72

4.03 5.06

 

 

 

 

 

 

ggfiE 162M
Height Skeletal Age Mental Age

K1 1488 140 143
rl .1566 .2362 .3505
11 29.58 14.52 10.98
K2 230.7 108 85
r2 .7164 .2863 .3875
12 -82.65 -17.98 -26.37
t2 135.92 114.25 106.06
K3 1718.7 248 228
t3 19.12 27.35 22.02

Average

error of

equation 6.06

\
\

1.69 3.20

 

CASE 166M

 

 

 

 

 

 

 

 

 

Height Skeletal Age Mental Age

K1 1596 138 135
r1 .1585 .2338 .2646
11 28.20 12.88 15.72
K2 219 93 75
re .9025 .2346 .4240
12 -131.14 -l2.24 -36.01
t2 161.62 114.96 119.66
K3 1804 231 210
t3 20.03 31.34 22.01

Average

error of

equation 8.78 1.53 7.71

CASE 203M

Height Skeletal Age Mental Age

K1 1531 154 153
r1 .1666 .2546 .2708
11 28.25 15.09 15.32
K2 189 90 67
re .785“ .3554 .5345
12 -91.42 . -30.02 -53.15
t2 135.15 125.91 126.99
K3 1720 244 220
t3 17.76 24.86 20.13

Average

error of

equation 7.57 2.69

7.75

 

 

 

157

 

 

 

 

 

 

 

 

 

 

 

CASE 227M
Height Skeletal Age Mental Age
Kl 1635 144 170
r1 .1608 .2700 .2650
21.8: 148?, ӣ3
2 .
r: 1.010 .2246 .5045
i2 ~132.32 -8.20 -50.05
t2 145.5 102.09 128.40
K3 1851.8 251 282
t3 17.18 31.24 20.82
Average
error of
equation 10.37 1.71 4.21
SQASE 232M
‘ i a ' 1 _ w w W
Height Skeletal Age Mental Age
K1 1678 159 182
r1 .1804 .2235 .2961
11 12131 18.63 21.34
K .
r: 1.395 .2512 .4178
12 -191.23 -11.12 -35.14
t2 1S7.64 102.91 119.36
K 1 39.1 229 279
t; 15.96 28.90 22.17
Average
error of

e quati on

\
\

 

6.15

2.09

10.05

158

 

 

 

 

 

 

 

 

CASE 250M_
Height Skeletal Age Mental Age

K1 1544 142 148
11 29.39 20.37 13.62
K2 240.6 64 57
r2 .6857 .2606 .6171
12 —82.89 -9.16 -53.03
t2 142.36 91.67 109.80
K3 1784.6 186 205
t3 19.30 27.23 17.42

.Average

error of

equation 10.14 1.46 5.80

CASE 255M

 

 

r12.

A...[.‘ -
3 9
. f.
p,

r.

y] L :D .A “4.1””... 1.1:. A... .. ..V
. 13.32.13). Iqw sf. .i 3’7yl'tl‘J-n'

W

 

{'1’

 

 

Height Skeletal Age Mental Age

Kl 1627 182 149
r1 .2015 .1952 .2761
11 25.61 14.15 11.73
K2 177.6 62 72
r2 .8208 .5619 .4020
12 -84.04 -52.22 -31.23
t2 120.33 119.14 114.32
K3 1804.6 244 221
t3 16.24 19.01 22.23

IXVerage

error of

equation 9.50 3.18 7.23

\
V

159

 

 

 

 

 

 

 

 

 

 

 

 

CASE 269M
Height Skeletal Age Mental Age

K1 1546 172 155
r1 .2281 .2070 .2121
11 19.25 13.95 15.88
K2 178.0 62 43
r2 .8592 .3631 .4380
12 -116.21 -34.31 -36.68
t2 152.39 135.05 117.37
K3 1724.0 234 198
t3 18.64 25.32 21.44

Average

error of

equation 6.99 1.15 9.99

CASE 280M

- , .
Height Skeletal Age Mental Age

K1 1658 170 118
r1 .1823 .2237 .2100
11 26.98 17.50 22.68
K2 183.8 74 58
r2 .7854 .2658 .4683
12 -89.85 -16.57 -45.94
t2 133.0 117.75 129.55
K3 1841.8 244 176
t3 17.59 29.02 21.69

Average

eI‘ror of

7.98

e quation

\__
\

w—Y

3.29

9.79

160

 

 

 

 

 

 

 

CASE 288M
_ , 2 .
Height Skeletal Age Mental Age

K1 1629 168 170
r1 .1570 .2180 .2515
11 27.96 16.46 19.01
K2 224.3 54 100
r2 .8046 .3560 .7254
12 -106.05 -30.40 -87.02
t2 150.1 126.76 140.26
K3 1853.3 222 270
t3 18.85 24.90 18.73

Average

error of

equation 10.9 3.005 9.63

gm: 319M

Height Skeletal Age Mental Age

K1 1686 160 183
r1 .2095 .2761 .7723
11 24.01 11.73 -30.36
K2 207.6 72 67
r'2 1.251 .3450 .2440
12 -157.34 ~25.41 -9.80
t2 137.54 116.34 100.53
K3 1893.6 232 250
t3 15.54 24.49 29.30

Average

error of

equation 5 . 21 1 .039

6.00

 

CASE 343M

 

 

 

 

 

 

 

 

 

Height Skeletal Age Mental Age

K1 1568 210 164
r1 .1701 .1319 .2565
11 27.31 18.78 14.15
K2 166 60 73
r2 .9299 .4002 .4335
12 -131.66 -39.04 ~45.85
t2 157.42 134.35 139.74
K3 1734 270 237
t3 18.60 23.95 23.42

Average

error of

equation 5.09 2.76 5.87

CASE 350M

m

Height Skeletal Age Mental Age

K1 1604 188 158
r1 .2106 .1837 .3230
11 22.41 15.78 11.24
K2 169.6 57 55
r2 1.115 .3860 .5018
12 -145.86 -36.83 -49.59
t2 144.02 133.57 128.17
K3 1773.6 245 213
t3 16.58 24.36 20.85

Average

error of

6.03

equation 4.11

‘

1.52

. {tr-3..»

C ASE 368M

162

mm

 

 

 

 

 

 

Height Skeletal Age Mental Age

K1 1552 142 106
r1 .2128 .1795 .5994
11 24.46 19.13 ~8.l7
K2 158.3 44 64
r2 .4811 .5028 .5725
12 -5o.91 -42.59 -55.35
t2 136.43 114.00 122.41
K3 1710.3 186 170
t3 21.98 19.65 19.12

Average

error of

equation 12.19 4.519 4.93

SQASE 371M

:7 1L m

Height Skeleta1 Age Mental Age

Kl 1464 182 117
r1 .1804 .2000 .4215
11 26.34 13.52 5.15
K2 194.6 61 65
re 1.162 .4621 .5885
12 -148.14 -44.69 -68.14
t2 140.10 128.58 140.81
K3 1658.6 243 182
t3 16.06 21.76 20.41

.Average

error of

1.46

equation

 

 

9.57

2.40

 

-

——

‘fi

_-——‘ mfifi‘

163

 

 

 

 

 

 

 

 

 

CASE 372M;
Height Skeleta1 Age Mental Age

K1 1557 165 145
r1 .2280 .2620 .2690
11 22.78 11.49 20.98
K2 168.5 67 25
r2 1.198 .4350 .9055
12 -168.90 -44.94 -132.49
t2 155.8 137.17 162.58
K3 1725.5 232 170
t3 17.31 23.17 19.18

Average

error of

equation 4.57 2.37 11.315

CASE 373M

Height Skeleta1 Age Mental Age

K1 1391 184 123
r1 .2167 .1837 .2520
11 21.47 12.48 16.80
K2 191.7 64 60
P2 .8331 .6041 .4588
12 -101.78 -66.62 -51.53
t2 139.85 134.66 144.42
K3 1582.7 248 183
t3 17.78 19.67 23.16

Average

error of

equation 8.71 3.46 4.76

-===========

.3 .3. ’9’... 5.

2.1 :3. .1...

1 . . 0:...

"I

164

 

 

 

 

 

 

 

CASE 380M
m
Height Skeleta1 Age Mental Age

K1 1534 192 139
r1 .1794 .1539 .3284
11 27.78 16.72 12.89
K2 202.3 59 64
r2 .8531 .3630 .5838
12 -91.89 -20.58 ~63.04
t2 124.97 97.27 133.21
K3 1736.3 251 203
t3 16.39 22.17 19.84

.Average

error of

equation 6.30 3.47 6.28

, . . ' .' ' .
CASE 402M
Height Skeletal Age Mental Age

K1 1597 150 130
r1 .2223 .2883 .3287
il 21.50 11.45 7.44
K2 139.7 83 61
r2 1.450 .4020 .4469
12 -196.12 -35.05 -40.23
t2 145.41 123.83 122.98
K3 1736.7 233 191
t3 15.64 23.02 21.67

Average

error of

equation 4.61 2.25 7.43

. ' ........ 2 ' ; a ,T ‘ ' ‘ ‘ Z ’ ' ‘

 

165

 

 

 

 

 

 

 

 

 

CASE 407M
Height Skeletal Age Mental Age

K1 1691 150 150
r1 .2121 .3721 .2602
11 24.84 6.47 14.03
K2 143 98 80
r2 .9178 .2879 .5062
12 -114.68 -17.42 -46.99
t2 141.00 121.04 121.92
K3 1834 248 230
t3 17.31 27.04 20.25

IXverage

eerror of

eequation 6.88 2.29 5.18

_§@SE 412M1

Height Skeletal Age Mental Age

K1 1701 192 113
P1 .1684 .1775 .2764
11 27.26 14.15 10.98
K2 183 57 45
re .75“ .14280 .4421
12 -90.56 -42.60 -42.85
t2 139.64 133.94 130.24
K3 1884 249 158
t3 18.40 23.09 23.40

Average

error of

equation 8.62 2.04 5.03

§ .4 - fl --1

166

 

 

 

 

 

 

 

 

 

 

 

CASE 417M
Height Skeleta1 Age Mental Age

K1 1585 168 160
r1 .1612 .1908 .3108
11 28.83 16.27 11.10
K2 205.6 35 36
22 .5887 .3657 .5796
i2 -72.74 -34.03 -61.15
t2 148.58 133.33 130.91
K3 1790.6 203 196
t3 21.05 25.07 19.72

Average

error of

equation 15.59 1.48 5.64

.... . ., 3 3 213 . ... _
CASE 442M
Height Skeletal Age Mental Age

K1 1646 159 130
r1 .1785 .2350 .3393
11 26.79 15.40 4.92
K2 231 .7 53 46
r2 .5890 .4030 .5014
12 ~62.27 -35.03 -47.78
t2 130.7 123.47 124.67
K3 1877.7 212 176
t3 19.55 22.96 20.57

Average

error of

equation 7.59 9.802

‘

 

v—v i V- —' vef r— w w w *7 fl Vfiv w w fi—v

CASE 444M

 

Height

Skeleta1 Age

fi—v

 

 

1r-

 

 

 

 

 

 

Mental Age
K1 1636 136 121
r1 .1608 .2895 .3092
11 29.45 14.97 15.16
K2 206.3 96 96
re 1.445 .2910 .4981
12 -195.22 -l5.35 -50.45
t2 145.20 103.36 130.85
K3 1842.3 232 217
t3 15.63 26.16 21.15
Average
error of
equation 9.04 1.61 7.39
CASE'456M
Height Skeleta1 Age Mental Age
Kl 1591 155 148
r'1 ~1957 .2722 .2463
11 25.82 11.90 13.66
K2 232.4 60 27
r2 1.038 .3665 .5213
i2 ~137.14 -27.56 -44.21
t2 146.31 115.38 113.06
K3 1823.4 215 175
t3 17.11 23.54 19.21
Average
error of
5.62 3.80

equation

W

........

1.317

 

 

4"
1

CASE 460M

 

 

 

 

 

 

 

 

 

 

 

 

Height Skeleta1 Age Mental Age

K1 1388 136 108
r1 .1570 .2883 .2735
11 28.36 8.56 11.92
K2 184.7 96 47
r2 1.004 .3345 .6439
12 -129.22 -26.78 -81.32
t2 143.37 124.09 149.16
K3 1572.7 232 155
t3 17.03 25.61 20.36

Average

error of

equation 6.33 3.119 5.23

CASE 474M

Height Skeleta1 Age Mental Age

K1 1508 154 130
r1 .1209 .2310 .5875
11 30.84 14.97 11.95
K2 235.8 84 65
22 .9755 .2479 .6993
12 -129.11 -14.42 -81.36
t2 147.45 117.58 137.40
K3 1743.8 238 195
t3 17.52 30.39 18.75

Average

errorof

equation

¥

1361

1.66

‘ 6.77

169

 

 

 

 

 

 

 

 

 

 

CASE 478M
Height Skeleta1 Age Mental Age

Kl 1637 518 131
11 26.92 14.40 14.46
K2 191 96 98
r2 1.265 .3304 .9454
12 -164.48 -26.27 -109.11
t2 141.66 124.09 130.99
K3 1828 254 229
t3 15.84 25.79 16.32

Average

error of

equation 5.33 2.57 9.49

CASE 479M

Height Skeleta1 Age Mental Age

Kl 1572 148 101
r1 .1500 .2371 .1934
11 29.25 13.76 25.81
K2 165.5 56 42
r2 .6423 .3300 .4833
12 —84.74 -22.68 -38.82
t2 154.86 113.36 110.80
K3 1737.5 204 143
t3 20.85 24.91 19.79

Average

error of

equation 12.17 0.83 3.13

0000000

f

 

CASE 483M

 

 

 

 

 

 

Height Skeleta1 Age Mental Age

K1 1679 148 155
11 27.82 18.88 5.77
K2 214.6 60 68
22 .5792 .2619 .7572
12 -70.51 -11.50 -86.31
t2 147.16 100.15 133.43
K3 1893.6 208 223
t3 21.07 27.84 17.86

Average

error of

equation 9.12 1.49 9.73

CASE 488M

 

 

 

Height Skeleta1 Age Mental Age

K1 1512 111 174
r1 .1562 .4146 .2345
11 29.38 6.35 13.93
K2 120.6 88 51
r2 .3796 .2988 .4134
12 ~35.48 -21.58 -29.42
t2 132.30 121.51 106.79
K3 1632.6 199 225
t3 24.46 27.21 21.25

Average

error of

equation 7.27 1.20

.
W—XX

 

13.007

W

 

 

171

 

 

 

 

 

 

 

 

7.08

 

 

CASE 526M
Height Skeleta1 Age Mental Age

K1 1506 158 116
r1 .1571 .2205 .2622
11 29.52 15.58 19.63
K2 208.9 56 84
r2 1.043 .3966 .3512
12 -125.75 ~3l.37 -21.73
t2 134.68 116.23 103.81
K3 1714.9 214 200
t3 16.11 22.56 23.19

Average

error of

equation 10.5 1.97 4.58

CASE 530M

Height Skeleta1 Age Mental Age

K1 1551 137 127
rl .1676 .3357 .3088
11 27.36 6.74 14.83
K2 178.0 94 37
re .570 2682 .7214
12 -63.43 -16.49 -85.12
t2 137.1 116.40 138.41
K3 1729 231 164
t3 20.38 28.74 18.61

Average

error of

equation 3.31 3.69

W

 

172

 

 

 

 

 

 

 

 

CASE 534M
Height Skeleta1 Age Mental Age

K1 1554 155 162
r1 .1730 .2553 .3323
11 27.66 13.49 1.65
K2 192.7 87 65
r2 1.436 .2940 .5300
12 -187.29 -18.25 -56.77
t2 140.68 112.17 134.90
K3 1746.7 242 225
t3 15.27 26.71 20.87

Average

error of

equation 6.08 1.41 13.80

CASE3542M

Height Skeleta1 Age Mental Age

K1 1501 _ 195 152
r1 .1781 .1747 .2769
i1 26.50 13.88 13.47
K2 232.2 48 66
re .7853 .4912 .3710
12 ~93.71 -51.60 ~32.20
t2 138.08 135.03 126.49
K3 1733.2 243 218
t3 18.00 21.65 24.30

Average

error of

equation 6.11 3.35

6.17

 

#

 

 

 

 

 

 

 

173

 

 

 

 

 

 

 

 

 

CASE 574M
Height Skeleta1 Age Mental Age

K1 1729 164 190
r1 .1608 .2227 .2678
11 29.49 17.85 15.62
K2 144.9 68 63
r2 .6819 .2262 .5314
12 -87.49 -11.43 -37.33
t2 149.90 115.64 97.96
K3 1873.9 232 253
t3 19.98 32.21 17.76

Average

error of

equation 14.07 1.63 4.85

CASE 585M‘ _‘ . .

7 7 77 777 Height 7 Sk7e17eta177Agve 77 7 Mental Ag7e
K1 1645 168 187
rl .1785 .1805 .3790
11 25.72 16.22 7.02
K2 193.6 47 53
22 .7725 .3262 .5088
i2 -108.18 -23.93 -41.37
t2 159.1 118.51 110.25
K3 1838.6 315 240
t3 19.86 25.53 19.21

Average

error of

equation 6.69 0.83 10.37

V:

a

e3:*fi

I m

9‘ 1m

4 1 If

. q‘.f

o. 00.4.9 9’.

4

’9. .-

2 7.1..

o
\: Cc

 

174

 

 

 

 

 

 

 

 

CASE 599M
Height Skeleta1 Age Mental Age

K1 1388 150 129
r1 .1831 .2264 .3310
11 29.86 14.12 10.48
K2 109 41 54
r2 .666 .5050 .5985
12 -72.09 -47.78 -89.52
t2 130.36 123.78 125.58
K3 1497 191 183
t3 18.52 20.42 19.05

Average

error of

equation 5.01 1.54 4.43

CASE 629M

Height Skeleta1 Age Mental Age

K1 1590 160 178
r1 .1667 .1905 .3842
11 28.17 16.04 1.89
K2 191.2 53 86
P2 .704 .3287 .7890
12 -94.23 -25.10 -11.01
t2 154.70 121.17 132.12
K3 1781.2 213 264
t3 20.15 25.63 17.48

Average

error of

equation 5.54

1.83

iJ-fi“,
‘—:A——

W

10.96

Vj fi wv

Vifi

028E 623M

 

a if 4

 

 

 

 

 

 

 

Height Skeleta1 Age Mental Age
K1 1629 132 157
r1 .2015 .3323 .2880
11 24.16 4.97 7.85
K2 190 102 41
re 1.095 .4042 .2770
12 -134.89 -34.46 -51.84
t2 136.63 121.69 92.92
K3 1819 234 198
t3 16.04 22.77 17.4
Average
error of
equation 8.13 1.14 7.77
CASE 626M
Height Skeleta1 Age Mental Age
K1 1538 160 178
r1 .1732 .2441 .3110
11 26.52 11.51 5.20
K2 186. l 75 55
P2 .9385 .2955 .4662
12 -123.47 -22.09 -30.35
t2 147.25 124.60 142.79
K3 1724.1 235 233
t3 17.71 27.66 22.85
Average
error of
1.44 10 69

equation 5.31

 

W1

’ .

a . y

CASE 630M

 

 

—v

 

vfiv—V— w

 

 

 

 

 

 

Height Skeleta1 Age Mental Age

K1 1618 154 207
r1 .1847 .2309 .3200
11 26.93 15.69 6.57
K2 206 73 54
re 1.105 .3547 .4331
12 -141.35 -26.59 -23.21
t2 141.2 116.49 104.08
K3 '1824 227 261
t3 16.38 24.10 20.46

Average

error of

equation 9.96 1.70 5.17

CASE 645M

Height Skeleta1 Age Mental Age

K1 1542 143 210
r1 .1781 .2726 .2496
11 27.21 13.83 12.85
K2 225 61 41
r2 .8203 .3647 .3935
12 '95.15 -24.37 -106.24
t2 133.90 107.21 96.41
K3 1767 204 251
t3 17.38 22.93 21.01

Average

error of

equation 3.82

. O. 7 .93.

j V v fi fi—

177

 

 

 

 

 

 

 

 

 

 

CASE 648M
Height Skeleta1 Age Mental Age
K1 1607 147 195
r1 .1650 .2540 .3119
11 27.09 13.00 9.44
K2 167.7 53 47
r2 .620 .3395 .8017
12 -85.83 -28.83 -65.83
t2 162.19 128.30 150.89
K3 1774.7 200 242
t3 21.75 25.73 18.94
Average
error of
equation 9.47 2.07 5.39
'QASE 661M
Height Skeleta1 Age Mental Age
K1 1638 151 159
P1 .1469 .2761 .2688
i1 29.27 12.28 11.82
K2 190.6 36 85
r2 .4844 3270 .5004
12 -6l.70 -2l.48 -39.35
t2 157.78 110.73 , 160.99
K3 1828.6 187 244
t3 23.68. 24.84 23.62
Average
error of
18.48 5.61

equation

a a > a

- a

CASE 669M

 

 

 

 

 

 

 

Height Skeleta1 Age Mental Age

K1 1661 166 126
r1 .1638 .2173 .2145
11 28.95 16.62 26.76
K2 194.7 79 58
r2 1.283 .3914 .4675
12 -164.12 -32.21 -25.46
t2 139.39 119.92 115.67
K3 1855.7 245 184
t3 15.59 23.04 20.5

Average

error of

equation 11.45 1.84 9.88

CASE 685M

Height Skeleta1 Age Mental Age

K1 1553 176 117
r1 .1665 .2050 .2870
11 28.19 15.22 14.48
K2 175.3 68 65
22 .9608 .2996 .3350
i2 -124.77 -25.53 -80.31
t2 145.10 134.37 119.97
K3 1728.3 244 182
t3 17.40 27.68 25.24

Average

error of

equation

3.16

 

42...;
‘ v

8

A... R‘L'O.
'. O. ‘ . a

7 '3' xww nrm‘:

CASE 699M

 

 

T

 

 

 

 

 

 

 

Height Skeletal Age Mental Age

Kl 1661 158 129
r1 .1771 .2400 .3183
i1 27.04 13.13 10.47
K2 191.3 83 51
r2 .7125 .4208 .6575
12 -85.30 -43.88 -54.16
t2 140.39 139.28 144.54
K3 1852.3 241 180
t3 18.84 23.74 19.81

Average

error of

equation 9.16 2.43 4.77

CASE'721M‘

Height Skeleta1 Age Mental Age

K1 1655 172 148
r1 .1608 .2077 .3150
11 27.89 12.61 12.81
K2 213.2 46 50
P2 .7802 .3370 .5362
12 —104.62 -31.21 -64.56
t2 152.9 136.32 133.51
x3 1868.2 218 198
t3 19.29 26.51 20.23

Average

error of

equation

4.70

1.3999

3 7.53

I . 3.5111152 #1th “5' E“

fl
;

180

 

 

 

 

 

 

 

 

CASE 1801M
Height Skeleta1 Age Mental Age

K1 1553 167 150
11 26.43 8.53 18.17
K2 217.3 76 42
r2 .8746 .3993 .7065
i2 -116.93 ~45.53 -90.64
t2 150.53 150.91 149.16
K3 1770.3 243 192
t3 18.38 25.36 19.65

Average

error of

equation 5.89 1.375 5.93

CASE 2848M

Height Skeleta1 Age Mental Age

K1 1622 143 170
r1 .1583 .2235 .3060
i1 28.09 15.54 12.33
K2 232.7 75 51
r2 .8421 .3034 .9925
i2 —1l2.77 -20.15 -133.65
t2 151.40 114.96 149.50
K3 1854.7 218 221
t3 18.76 26.41 17.60

Average

error of

equation 7.28 1.236 3.94

m -11 _. a - 11..- -fi

R

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