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On the distribution of anatomic increment data in early childhood.

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BRIEF COMMUNICATION
On the Distribution of Anatomic Increment D a t a
in Early Childhood
HOWARD V. MEREDITH
Iowa Child Welfare Research Station, State University of Iowa,
Iowa City,Iowa
A recent article in this journal discusses three series of frequency distributions
for “number counts” and “size increments” (Garn, Rohmann and Robinow,
’61). The data represent sequential semiannual intervals beginning in infancy and
extending to age 7.5 years. Reference is
made to “the natural skewness characteristic of increment data,” and findings are
stated to confirm “skewness as a general
property of growth increments in the age
range considered.’’
Generalization is a serious and shared
responsibility of scientists. Those who report investigations are obligated not to
sidestep this responsibility and, reciprocally, it is the obligation of colleagues to
take a critical approach toward generalization. The writer has shown elsewhere
that unexamined generalizations “may
lead to the perpetuation of error over long
periods” (Meredith, ’50).
Certain data on file in the writer’s laboratory have been utilized to test whether
in early childhood asymmetry is “a general property” of increment distributions.
These data include semiannual increments for stature and hip width, and annual increments for lower jaw width and
lower jaw depth. The procedures employed in obtaining the data are described
in previous publications (Meredith and
Meredith, ’50; Newman and Meredith,
’56; and Meredith, ’61).
All of the materials subjected to analysis represent North American white males
within the period of childhood between
ages four years and seven years. A detailed discussion of the skewness formula
used, a formula based on the calculation
of moments, is given by Pearl (’27). Suffice to state, in terms of statistical theory
the value denoting symmetry (absence of
skewness) equals zero for the normal or
Gaussian curve.
The statistics obtained are assembled in
table 1. In no instance can the hypothesis
of symmetrical distribution be rejected at
the 1 per cent confidence level. Conversely, the inference of skewness is untenable with respect to the assortment of
increment distributions characterized in
table 1.
It has long been known that at specific
childhood ages some measures of anatomic size are distributed symmetrically
(e.g., stature and head girth), others are
positively skewed (e.g., body weight and
thorax girth).’ Presently it is known that
for specific childhood intervals some anatomic increments are distributed symmetrically (see table l), others are positively
skewed (see Garn, Rohmann and Robinow, ’61).
LITERATURE CITED
Blommers, P., and E. F. Lindquist 1960 Elementary Statistical Methods. Houghton Mifflin, Boston, pp. 210-217.
Garn, S. M., C. G. Rohmann and M. Robinow
1961 Increments in hand-wrist ossification.
Am. J. Phys. Anthrop., 19: 45-53.
Meredith, H. V. 1935 The rhythm of physical
growth. Univ. Iowa Stud. Child Welfare, 11:
no. 3, pp. 50-51.
1946 Physical growth from birth to
two years: 11. Head circumference. Child Develop., 17: 5 6 5 8 .
11x1 this connection, see Blommers and Lindquist
(’60),Meredith (’35,’46), and OBrien, Girshick and
Hunt (’41).
519
520
HOWARD V. MEREDITH
TABLE 1
Skewness statistics f r o m semiannual and annual increment distributions for
North American white males
Increment
variable
Age
interval
Size of
sample
Measure of
skewness
Standard
error
years
Stature
Hip width
Lower jaw width
Lower jaw depth
4.0-4.5
4.5-5 .O
6.0-6.5
6.5-7.0
4.0-4.5
4.5-5.0
6.0-6.5
6.5-7.0
5.0-6.0
6.0-7.0
5.0-6.0
6.0-7.0
1950 The research worker's responsibility for generalization. Physical Educator,
7: 47-48.
study Of change in a manlg6'
dibular dimension during childhood and adolescence. Growth, 25: 229-242.
Meredith, H. v.. and E. M, Meredith 1950 Annual increment norms for ten measures of
physical growth on children four to eight years
of age. Child Develop., 21: 141-147.
Newman, K. J., and H. V. Meredith 1956 Individual growth in skeletal bigonial diameter
80
107
95
87
75
102
96
83
67
67
67
67
0.02
0.13
0.01
0.20
0.06
0.17
0.15
0.01
0.00
0.31
0.28
0.20
0.14
0.12
0.13
0.13
0.14
0.12
0.13
0.14
0.15
0.15
0.15
0.15
during the childhood period from five to eleven
years of age. Am. J. Anat., 99: 157-187.
OBrien, R., M. A. Girshick and E. P. Hunt 1941
Body measurements of American boys and
girls for garment and pattern construction^
u. s. Bureau
^. Home Econ., Mist. Pub. no. 366,
PP.
Pearl, R. 1927 Introduction to Medical Biometry and Statistics. W. B. Saunders, Philadelphia, pp. 266278.
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