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OCR for page 164
Chapter XII
THE ANALYSIS OF THE
ANTHROPOMETRIC DATA
12.~1 The me~nremer~ts obtained at nine
months.- As was pointed out in Section 2.6,
one feature of the "9-months" program in-
volved obtaining certain physical measurements
on the infants seen. These measurements were
felt to supply the best index to general physical
vigor obtainable under the circumstances. The
present chapter is concerned with an analysis
of these data. It should be pointed out that be-
cause of scheduling problems, it was not pos-
sible to examine each infant at precisely nine
months of age; the data here presented are
based on babies varying in age from eight to
ten months inclusively. Since the system of
selection for study by terminal registration
digit precludes an age bias with respect to ir-
radiation history, this age variation becomes a
problem only insofar as it may enhance
"within-cell" variation to the point of obscuring
tests on interactions and main effects. We shall
consider this possibility in detail in Section
12.4.3. Caution is also indicated in utilizing
certain aspects of these data for standards of
normality.
The measurements to be analyzed are the
interdependent variables, weight, body length,
head circumference, and chest circumference. In
each city, all measurements were taken by one
of two nurses, both of whom devoted much of
their working time to this procedure. Originally
the weight of the baby was obtained by weigh-
ing mother and (stripped) child together on a
beam-type scale, then weighing the mother
separately, and calculating the weight of the
baby from the difference. During the latter part
of 1952 the practice of weighing the baby di-
rectly in a basket on the same scale was insti-
tuted. Body length was measured by a stadiome-
ter which was wider than the width of the
baby. The readings were taken directly off a
i64
scale on the instrument. Head circumference
was taken with a cloth tape at the maximum
girth of the head in a plane passing through
the nasion. Chest circumference was measured
by means of the same tape, the measurement
representing the chest girth in the plane of the
nipples, taken midway between inspiration and
expiration. This midpoint was estimated after
a brief period of observation.
12.2 The genetic argument for irradiation
ejects.- The genetic argument for irradiation
effects is essentially the same as the argument
advanced for changes in the birthweights of
infants born to exposed parents. The existence
of irradiation-induced changes in body measure-
ments is predicated on the assumptions that (a)
the largest class of gene mutations are the re-
cessive "detrimentals," and (b) the presence
of "detrimentals" would be reflected in changes
in body measurements consequent to abnormali-
ties in growth pattern and rate in the first nine
months of life.
The differences to be expected would be (a)
changes in the multivariate means with chang-
ing parental exposure, (b) a change, quite
possibly an increase, in the generalized variance
with increasing parental exposure, or (c) both.
The likelihood of the occurrence of these
changes would obviously be a function not only
of parental exposure but of the component of
variation in measurements at nine months of
age ascribable to genetic factors. Little informa-
tion is available from which to estimate this
component.
12.3 Concomitant Variables known to affect
growth arid development daring the first year
of life. The concomitant variables affecting
growth and development during the first year
of life are, in some respects, less well known
than the variables which influence birthweight.
OCR for page 165
The Analysis of the Ar~thropometric Data 165
We do not know, for example, whether the ma-
ternal age and parity effects demonstrable at
birth persist throughout the first year of life or
not. That the effects of these two variables on
measurements at nine months would be negligi-
ble would seem to follow from (a) the small
amount of the total variation (approximately
to 12.4 are the means and the number of ob-
servations on which they are based for the 64
sex-city-mother-father cells for the measure-
ments of weight, height, head girth, and chest
girth. Inspection of these data reveals no strik-
ing trends associated with parental exposure.
It should be noted, however, that, save for un.
TABLE 12.1 DISTRIBUTION OF MEAN WEIGHT IN DECAGRAMS AT 9 MONTHS OF AGE BY CITY, SEX, AND
PARENTAL EXPOSURE
(Unrelated parents. The numbers of observations on which the means are based are given in parentheses.)
Hiroshima
^
Males Females
A, ~
vat
cad
1 2
1 ~ 814.35 819.51
1 (2,765) (871)
2J: 808.64 789.89
~ (230) (236)
3 J 820.98 796.66
~ (91) (58)
4_5J 797 27 797.70
l (59) (33)
Mothers
3 4-5
812.03 813.51
(350) (169)
804.36 802.34
(69) (29)
790.38 776.00
(73) (18)
782.95 811.42
(22) (12)
Total
815.20
(4,155)
799.95
(564)
802.42 ,,
(240) =-
796.23
(126)
Tota1 r 813~80 811.97 806.68 809.02 812.43
(3,145) (1,198) (514) (228) (5,085)
Nagasaki
757.27
(33)
Mothers
1 2
1 r 767.39 766.33
l (2,543) (822)
2 r 769.30 756.16
~ (223) (253)
3; 771.45 757.48
~ (100) (52)
4_5J 766.85
~ (48)
3 4-5
766.65 762.46
(331) (153)
758.78 751.00
(54) (26)
755.07 801.71
(67) (17)
796.55 734.88
(22) (16)
Total
766.90
(3,849)
761.44
(556)
765.90
(236)
765.39
(119)
Tota1 r 767~66 763 46 765.51 762.12 766.18
1 (2,914) (1,160) (474) (212) (4,760)
Males
Females
~, ~
Mothers
l
1 2 3 4-5 Total
1 (797.52 794.62 774.13 789.22 795.63
~ (2,074) (1,261) (99) (81) (3,515)
2r788.81 788~79 794.94 762.23 788.64
~ (283) (486) (35) (13) (817)
3 I 782.78 795.63 791.21 774.67 789.38 i,
~ (36) (48) (14) (6) (104) =
4 r 785 22 771.64 768.25 784.60 776.99
~5) (23) (36) (4) (5) (68)
Tota1 r 796 15 792~65 780.34 784.83 793 94
)(2,416) (1,831) (152) (105) (4,504)
3~O) which they account for in birthweights,
(see Table 10.24) and (b) the ever decreasing
correlation between weight at birth and at age
x (by nine months of age this correlation is
0.319 as estimated from these data). For the
purposes of this analysis we shall assume that
the various exposure sub-populations do not
differ significantly as regards any factor in-
fluencing growth and development.
12.4 The data. Presented in Tables 12.1
Mothers
~..
1 2 3 4-5 TOta1
1 r 753~03 749.06 763.16 744.29 751.70
W(1,845) (1,168) (106) (80) (3,199)
2-r 750.17 738.09 736.21 708.13 741.33
~ (264) (482) (47) (16) (809)
3; 749.14 720.85 734.35 694.50 731.34
~ (29) (40) (17) (4) (90)
4 r 735~89 708.69 791.00 774.00 734.67
~51 (27) (16) (4) (4) (51)
TOta1 r 752 41 744692 753.71 737.95 749 03
1 (2,165) (1,706) (174) (104) (4,149)
common exceptions, infants
· ., i. . ~
born to parents
one or both of whom are In exposure category
1 are larger in all measurements than infants
born to parents both of whom were exposed.
Let us turn now to the questions to be asked
of these data, namely:
1. Are there significant differences between the
multivariate means associated with parental
exposure ?
2. Are there significant differences between ex
OCR for page 166
166 Genetic Effects of Atomic Bombs Chapter XII
TABLE 12.2 D~sTR~suT~oN OF MEAN HEIGHT IN MILLIMETERS AT 9 MONTHS OF AGE BY CITY, SEX, AND
PARENTAL EXPOSURE
(Unrelated parents. The numbers of observations on which the means are based are given in parentheses.)
Hiroshima
~-
cat
cat
cut
Males
~.,
Mothers
_
1 2 3 4-5 Total
1 (698.20 698.85 696.14 699.16 698.20
~ (2,765) (871) (350) (169) (4,155)
2 r 697~21 693~31 693.94 697.86 695.21
1 (230) (236) (69) (29) (564)
3; 699.07 691.59 691.93 691.00 694.49 .,
~ (91) (58) (73) (18) (240) 3-
4_5 r 691.34 693.21 697.50 705.58 694.26
~ (59) (33) (22) (12) (126)
Total r 698.02 697.25 695.30 698.69 697.59
~j(3,145)- (1,198) (514) (228) (5,085)
Females
Mothers
_ ~
1 2 3 4-5 Total
683.83 682~84 681~92 684.02 683.46
1 (2,543) (822) (331) (153) (3,849)
2 r 682.65 681.11 681.67 676.81 681.58
(223) (253) (54) (26) (5S6)
r 683.88 681.31 684.42 685.35 683.57
31 (100) (52) (67) (17) (236)
4_51 681.77 687.36 696.32 667.00 684.02
~ (48) (33) (22) (16) (119)
Total { 683.71
682.52 682.77
(1,160) (474)
Nagasaki
, ~
Males Females
~,, ~
681.96 683.25
(212) (4,760)
Mothers
_ ~
1 2 3 4-5 Total
1 r 696.86 695.36 694.31 692.12 696.14
:(2,074) (1,261) (99) (81) (3,515)
2 r 695~92 691.85 695.54 694.92 693.47
~ (283) (486) (35) (13) (817)
3; 696.44 693.71 691.93 693.83 694.42
~ (36) (48) (14) (6) (104)
4 r696.13 694.25 690.00 686.00 694.03
~5) (23) (36) (4) (5) (68)
-
Tot lr 696.74 694.36 694.26 692.27 695.58
1(2,416) (1,831) (152) (105) (4,504)
Mothers
~-
4-5 Total
1 r 682.05 679.94 683.01 684.03 681.36
~ (1,845) (1,168) (106) (80) (3,199)
2 r 680.56 677.76 677.28 676.06 678.61
~ (264) (482) (47) (16) (809)
3; 675.24 677.65 680.82 670.75 677.17
l (29) (40) (17) (4) (90)
4r 678.41 676.81 697.75 673.7S 679.06
~51 (27) (16) (4) (4) (51)
,
679.24 681.59 681.90 680.70
(1,706) (174) (104) (4,149)
Total{ 681 73
OCR for page 167
The Analysis of the Ar~thropometric Data 167
TABLE 12.3 DISTRIBUTION OF MEAN HEAD GIRTH IN MILLIMETERS AT 9 MONTHS OF AGE BY CITY, SEX, AND
PARENTAL EXPOSURE
(Unrelated parents. The numbers of observations on which the means are based are given in parentheses.)
Hiroshima
Males
~1 ~
cot
a)
Mothers
, ~ . ~
1 2 3 4-5 Total
444~63 444.28 443.88 443.79 444.46
(2,765) (871) (350) (169) (4,155)
r444.05 442.04 444.22 442.38 443.14
2: (230) (236) (69) (29) (564)
3 r 447.10 443.69 441.67 445.72 444.52 V
(91) (58) (73) (18) (240) =-
r441.47 442.18 444.91 448.33 442.91
4-55 (59) (33) (22) (12) (126)
. ~,
To al r 444.60 443.75 443.66 444.00444.28
t 1 (3,145) (1,198) (514) (228)(5,085)
Nagasaki
Males
Females
Mothers
/ --- A
3 4-5
1 r433.82 433.38 434.11 433.10
1(2,543) (822) (331) (153)
2 r 434.65 433.38 435.19 431.27
(223) (253) (54) (26)
r 435.53 431.63 430.85 438.94
31 (100) (52) (67) (17)
4_ r433.04 433.58 439.91 426.00
51 (48) (33) (22) (16)
1 2
T tat {433.93 433.31 434.04 432.81
° ~ (2,914) (1,160) (474) (212)
Females
Total
433.72
(3,849)
433.97
(556)
433.59
(236)
433.51
(119)
433.74
(4,760)
Mothers
~,
1 2
1 r 452.48 452.50
j(2,074) (1,261)
2r452.40 452.82
(283) (486)
r451.42 453.73 454.86 460.67 453.48
3l (36) (48) (14) (6) (104)
4 5 {451.91 449.44 449.25 447.20 450.10
~ ~(23) (36) (4) (5) (68)
v'
so
con
3 4-5 Total
450.23 450.69 452.38
(99) (81) (3,515)
455.46 454.23 452.81
(35) (13) (817)
Total r 452.45 452.56 451.83 451.53 452.45
(2,416) (1,831) (152) (105) (4,504)
Mothers
~ _
1 2 3
1 r 441.22 441.27 441.97
~ (1,845) (1,168) (106)
2 r 440.17 439.82 441.74
(264) (482) (47)
r 440.28 439.73 443.47
3) (29) (40) (17)
4 5~438.48 435.50 449.75
~ 1~ (27) (16) (4)
435.50
(16)
4-5 Total
438.03 441.18
(80) (3,199)
438.94 440.03
(16) (809)
439~75 440.61
(4) (90)
440.50 438.59
(4) (51)
Total r 441.05 440.77 442.23 438.33 440.92
)(2,165) (1,706) (174) (104) (4,149)
OCR for page 168
168
posure cells in the generalized variances, that
is, the determinants of the variance-covariance
matrices ?
3. Does there exist demonstrable within-cell
(exposure cell, that is) heterogeneity which
would limit or augment the conclusions which
can be drawn from these data?
Genetic Ejects of Atomic Bombs Chapter XII
the cell numbers are unequal and disproportion-
ate. The analysis of dispersion is, of course,
merely the multivariate equivalent of the analy
. , .
sits ot variance.
As in the case of birthweights, we shall dis-
cuss in detail only one of these analyses and
then summarize the information from the two
TABLE 12.4 DISTRIBUTION OF MEAN CHEST GIRTH IN M~IMETERs AT 9 MONTHS OF AGE BY CITY, SEX, AND
PARENTAL EXPOSURE
(Unrelated parents. The numbers of observations on which the means are based are given in parentheses.)
Hiroshima
, ~.
Q)
con
Males
~it,
Mothers
_ A _ ~
1 2 3 4-5 Total
1 or 427.32 428.92 427.51 427.18 427.67
)(2,765) (871) (350) (169) (4,155)
2 ~ 425.41 423.38 427.12 424.34 424.71
al (230) (236) (69) (29) (564)
r430.70 426.09 423.29 420.83 426.59
3] (91) (58) (73) (18) (240)
4 5 I 422.59 429.85 421.59 432.17 425.23
~ (59) (33) (22) (12) (126)
Total ~ 427.19 427.72 426.60 426.58 427.23
(3,145) (1,198) (514) (228) (5,085)
Nagasaki
Females
Mothers
, ~
1 2 3
1 r 416.96 417.39 416.38
)(2,543) (822) (331)
2 r 417.74 415.34 418.56
~ (223) (253) (54)
3; 418.82 419.21 413.64
~ (100) (52) (67)
4 5:415.42 415.45
~ (48) (33)
426.77
(22)
- ~
=5 Total
415.96 416.96
(153) (3,849)
415.46 416.62
(26) (556)
422.94 417.73
(17) (236)
415.13 417.40
(16) (119)
Total r 417.06 416.96 416.72 416.40 416.97
1(2,914) (1,160) (474) (212) (4,760)
.
Males
a'
cad
Mothers
1 A Total
1 r 439.23 438.44 434.36 437.21 438.76
)(2,074) (1,261) (99) (81) (3,515)
2 ~ 438.14 438.75 441.97 432.38 438.58
~ (283) (486) (35) (13) (817)
3 r 433.19 438.31 442.21 439.67 437.14
~ (36) (48) (14) (6) (104)
4 r436.00 431.75 446.00 432.20 434.06
~5: (23) (36) (4) (5) (68)
Totai{438~98 438.39 437 14
~ (2,416) (1,831) (152)
436.51 438.62
(105) (4,504)
12.4.1 The maltivar~a~e means.-The
analyses of the multivariate means are given in
Tables 12.5 to 12.11. Tables 12.5 to 12.8 cover
the analysis when all categories of parental ex-
posure are considered but variation in age at
examination is ignored. Tables 12.9 to 12.11
present a comparable analysis save for the ex-
clusion of all parents of exposure category 1.
In both instances, analysis has been by Rao's
(1955) analysis of dispersion for the case when
Females
,
1 2
1 I 429.07 428.75
](1,845) (1,168)
2 J 428.91 427.69
(264) (482)
~3 I 428.69 421.95
=~1 (29)
{ (7)
Total{ (4228.98 428.22
(i.e., with and
Mothers
3 4-5
430.50 424.20
(106) (80)
430.13 417.38
(47) (16)
428.76 425.75
(17) (4)
421.44 431.50 431.50
(16) (4) (4)
Total
428.88
(3,199)
428.03
(809)
425.58
(9o)
424.41
(51)
430.25 423.49 428.58
(174) (104) (4,149)
without category 1 parents)
sources regarding differences in the multivariate
means. In Table 12.5 are given the data appro-
priate to the analysis of the first order (two-
factor) interactions. Inspection of the mean
squares for the individual analyses of variance
reveals that in most instances the interaction
mean squares are smaller than the within-cell
mean squares. Because of these low values
Wilks' test (cf. Rao, 1952), which tests the
OCR for page 169
The Analysis of the Ar~thropometric Data 169
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OCR for page 170
70
significance of the ratio of two determinants,
say, OWN and ~W+Q~ where AWN is the error
matrix (within cells) and ~Q~ is the matrix due
to any other category, was not performed (this
ratio is, of course, the multivariate analogue of
the L statistic used in Chapter X). It may be
that the variation in age at examination has
inflated the within-cell mean squares to the
point where small interactions would be ob
Genetic Ef]:ects of Atomic Bombs Chapter XII
clearly given in Tables 12.7 and 12.8, to which
we now turn.
For each class of father's exposure, mother's
exposure, sex, and city, there can be assigned a
constant estimated in a fashion such that a com-
parison of two constants from differing classes
of a single classification reflects differences be-
tween these classes in any one of the four meas-
urements. These estimates are derived from a
TABLE 12.6 ANALYSIS OF D~sPERs~oN
(All exposure cells)
(a) Sums of squares and cross products of deviations for main effects and additivity
, A
Between
Source cells Fathers MothersSexCityResidual a
(DF) (63) (3) (3)(1)(1)(55)
.849,154 854 949558,451261,03712,392
x2 1,063,755 12,890 8,069 978,425 18,163 31,591
Z2 1,123,123 3,496 1,577 475,161 577,066 28,252
w2 11,840,022 227,141 55,354 9,567,378 1,327,332 451,750
yx 676,905 2,119 1,850 739,190 -68,857 9,435
yz 941,068 1,518 1,045 515,125 388,118 11,066
yw 1,753,375 10,554 6,643 2,311,473 -588,628 43,488
xz 587,612 6,064 984 681,843 -102,379 124,722
xw 3,412,827 52,788 18,096 3,059,570 155,270 69,818
zw 1,333,236 27,420 6,821 2,132,146 -875,191 92,923
(b) Mean squares for individual analyses of variance
Source
(DF)
Between
cells Fathers Mothers
(63) (3) (3)
ye 13,478.63** 284.67 316.33
x2 16,885.00* * 4,296.67* * 2,689.67* *
z° 17,827.35** 1,165.33** 525.67
we ............... 187,936.86** 75,713.67** 18,451.33
(on main effects and additivity)
SexCity
(1)(1)
558,451 * *261,037* *
978,425**18,163**
475,161**577,066**
9,567,378* *1,327,332* *
(c) Analysis of dispersion, Wilks' test (using Bartlett's approximation)
Significant
%2 (by inspection)
(DF) .............
~ Sum of interaction terms.
Residual a
(55)
225.31
574.38
513.67
8,213.64
Significant for
sex and city Not significant
40.5** 24.0* (by inspection) (by inspection)
4
12 12
scored. For the moment, suffice it to say that
at this stage there is no evidence for the non-
additivity of the main effects. The significance
of this evidence is, of course, limited if there
exists within-cell heterogeneity.
Turning now to Table 12.6 we note evidence
from 12.6c that the multivariate means differ
significantly between (1) sex-city-mother-father
cells, (2) categories of paternal exposure, (3)
categories of maternal exposure, (4) cities, and
(5) sexes, but the pooled interactions ("Re-
sidual" in Table 12.6) are not significant. The
precise nature of these differences are more
linear model assuming additivity of the main
effects, and specifying, without loss of gener-
ality, that the constant associated with the high-
est class within a given classification is zero;
for example, the constant for father's exposure
category 4~5 (f4, 6) is assigned the value zero.
Comparison of the difference between two con
~ It is convenient when only two classes exist for
a classification to indicate their difference rather than
the constants associated with each of the two classes.
For example, in Table 12.7, the constants designated
(N-H) and (d :) are in fact the difference
between N and H. and males and females.
OCR for page 171
s"
o 0)
c~ ~
~ . -
.s >=
~ - ~
c.
-
o ~ c~
·s ·-
x c)
O ,o ~
=1 1 ~
1 ,,=
o ~
~. ~ -
c ~(d
o
cO ~
z ~
~ .C ' I
~ o ~
c
~:
3 ,,
C~
~N ~
E-. O oo
Z ~
~ ._
O _
C~
~X ~
~U~ ~
Oi
m ~o
The Ar~alysis of ~he Anthropometric Da~a 171
c ~stants from a given classification with the vari
m~ Oo ~ ~° ° ~ance of the difference affords a test of the
i ~ ~ ,,~ <', o ~ ~ ~ o significance of the difference. For example if
~ ~ r ~ ~ ~ ~
8 g Oo g g 0 we were interested in testing whether there
° ° ° ° ° ° existed evidence for a significant difference in
the mean of the w measurement (weight) be
tween father's 2 and father's 3, the test would be
o'
~o r~ v~
<
u~
O O O
O O O
. . .
O O O
1` ~ ~ 00 G~
U~
cr~ ox
~ ~ 00 \0
o0 ~ ~ ~ V~
- ~00
C~ ~ \0 ~ U~
O O ~ ~ ~
O O O O O
O O 0. 0 O.
O 0 000
* *
* *
00
O
O
I ~
**
* *
00
G~ 00
O
* *
* *
r~
~ V~
ax
00
V~
O
1~
~ O
V~ ~ ~
N0 0 0 0
r~ u~
00
.
SD
O ~
GN O
~0
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. . .
_4 _
~ O
U~
V~ V~ _.
U~
. . .
O Ol Ol
o
**
00 ¢\ G~
O r~ ~ O
G~ oo 00 r~ 0 0
I_ V~
O. r~ G~
O ~ O O
=~::
Z~O f~f
00 ~4 00
oo CC r~
O - ~
0 \0 - - O
1_ ~ I_
O O O
O O O
. . .
O O O
~r
_4
O
-= ~r 0
oo
0 0 0
0 0 0
. · .
O 0 0
~ ~o
oo r~
~o ~ ~
00 ~ `_
~ ~ 0
o~ ~
. . ~
~D
V~
r~ ~
r~ 0
0 ~4 ~
. . .
oo oo
r~
0
V~ 0
V~ CO
V~
. . .
~ 0 0
1 1
00 G~
~ V~
om ~
0
oo
G~
0
· ·
.
t- Wf2-Wf3
~ ~w~ (~f2 + ~f3 -2~f2f3)
where wf2 and W~3 are the w constants for
father's exposure categories 2 and 3, aW2 is the
variance of w (obtained from "within-cell"),
and c~f22, af32, and a.~2f3 are respectively the
variances of the f2 and f3 constants and their
covariance. The results of all possible contrasts
for the data here presented are given in Table
12.8. It should be noted that in all instances
where a significant difference exists it consists
of a contrast involving the comparison of in
fants from category 1 parents with some other
·= class of parental exposure. We shall return to
1 ~the implication of this finding, but first let us
consider some explanations for the significant
findings in Table 12.6. The findings requiring
some statement are the differences between the
cities and the parental exposure classes.
We note first that the cities differ with respect
to all four measurements, with Nagasaki infants
~being shorter and lighter but greater in circum
Z ferential measurements than their Hiroshima
1 ~counterparts. This difference while not pre
Z cisely unexpected was not predicted. The find
ings are, however, compatible with Matsumura's
and Hasebe's (see Hulse, 1943) classification
of the Japanese. These authors recognize four
physical types of Japanese, namely, the Ishi
kawa, Chikuzen, Okayama, and Satsuma. Only
the Okayama and Satsuma types, whose centers
of distribution are respectively the shores of
the Inland Sea (and central Japan), and south
~ ern Kyushu (presumably including Nagasaki
prefecture), concern us. The Okayama type is
described as an individual taller than the aver
~age Japanese, and possessing a head shorter than
<, usual but of average breadth. The Satsuma type
is described as a short individual with a broad
head of average length. Granted the reality of
this distinction and the distribution ascribed to
these types, the city differences are readily
explicable. As an historical aside, it might be
pointed out that Kaempfer (1728; 1906 edi
OCR for page 172
172 Genetic EJec`s of Atomic Bombs Chapter XII
lion, Vol. II, p. 372) commented on the rela-
tively small stature of the inhabitants of Hizen
(an area which then included Nagasaki).
The findings with respect to parental ex-
posure are less simply resolved. As has been
repeatedly stated, to assert, without qualification,
that a given change is the consequence of ir-
radiation would entail at least the demonstration
that (1) a difference exists between the preg-
nancies occurring to " 1" and "non-1" parents,
and (2) differences exist among "non-1" par-
ents consistent with increasing exposure. Let us
consider to what extent these requirements are
TABLE 12.8 A SUMMARY OF THE SIGNIFICANCE OF
FOR EACH PARENT WITH RESPECT
grated to Hawaii were appreciably larger than
their neighbors who remained in Japan. It is
reasonable to assume that similar selection
would have occurred among the migrants to
Korea, Manchuria, and elsewhere in eastern and
southeastern Asia in the years preceding World
War II. The repatriation of the Japanese mi-
grants to Korea, etc., following the war, was
both forcible and almost exhaustive since the
Japanese had become unwelcome throughout
much of Asia. As a consequence of this repatria-
tion, there may well have been settled in Hiro
shima and Nagasaki in the years immediately
TESTS COMPARING ALL POSSIBLE PAIRS OF EXPOSURE
TO THE VARIABLES W. X, Y. AND Z a
F1 F2 F3 F4.6 F1 F2 F3 F4,6
~,
y J
Variable y Variable z
, ~ . ~, ~
F1 ~ x t~ n.s. n.s. n.s.F1 ~ ~ ~ \ * n.s. *
F2 ~ ** n.s. n.s. F2 J D J ** n.s. n.s.
Fs .~- n.s. n.s. ~n.s. Fin ,] * n.s. \
F4,6 ~ n.s. n.s. n.s. ~F4,6 ~ ~ * * n.s. n.s.
M1 M2 M3M4,5 M1 M2 M3 M4,6
~' ~
Variable y Variable z
~, ~
Ml(X (~ n.s. n.s. * Mark (~ n.s. nuts. ~
MiJ I, | * * ~ n.s. n.s. ~ D | n.s. ~ n.s. n.s.
M3 ~ ~ ~ n.s. n.s.~ n.s. Me ,~ ~ n.s. n.s. ~n.s.
M.,6 1~> tn.s. n.s.n.s. ~ ~=5 ~ Cn.s. n.s. n.s.
n.s. = not significant
* = significant at 5~%
* * = significant at 1~%
a These tables are designed so that the entries above the diagonal refer to tests on the variable above
the diagonal, whereas entries loelow the diagonal refer to the variable below the diagonal.
satisfied within the Japanese anthropometric
data. From Tables 12.7 and 12.8 we have evi-
dence that "1" terminations differ from "non-1"
terminations. However, from Table 12.10 we
note no demonstrable differences between the
"non-l" terminations. The absence of changes
between exposure categories 2, 3, and 4-5
could be interpreted as evidence that the ob-
served differences, when all categories of ex-
posure are considered, are not due to irradiation.
That this is the most likely interpretation stems
from the following considerations:
1. In the main, exposure category 1 parents
are repatriates from Korea, Manchuria, and
elsewhere, and migrants from the rural areas
surrounding Hiroshima and Nagasaki. Shapiro
(1939) has shown that the Japanese who m~-
following the bombings a group of non-exposed
persons appreciably larger than the natives.
Whenever possible, repatriates were settled in
the areas from which they or their families origi-
nally stemmed.
2. Another factor of possible importance is
nutrition. To what extent a differential in nu-
trition may have contributed to the observed
differences is admittedly a matter of speculation.
However, it seems likely that migrants from the
rural areas adjacent to these cities may have had
an opportunity, not available to other urban
dwellers, to supplement their diet with food-
stuffs from the family farm.
However, it may be argued that the require-
ment that a demonstrable difference obtain
among the remaining exposure classes when the
OCR for page 173
The Analysis of the Anthropometric Data 173
by_
~ =_ ax Do a) Go fat ~ Go ~
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V~ _ ~ c4 no ~ ~ ~ 0 en cot
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OCR for page 174
OCR for page 175
OCR for page 176
OCR for page 178
OCR for page 179
OCR for page 180
OCR for page 181
OCR for page 183
Representative terms from entire chapter:
exposure category
174
Genetic Ejects of Atomic Bombs Chapter XII
- ~ O O up r
cat _ cot car I_ _ =~ ~ ~ ~ vet
Ox ~ c<, ~ ~ DO cO
~1
- ~- Do ~ I~ ~ up ~ ret ~ up
~ _ ~ _4 _l c<~ ~ Or
_4 ~- 00 ~ ~ O~ ~ ~ ~ ~
c<, 00 lo. ~ _I ~ ON aN ~ up
5 ~ c~ ~ ~ _1 ~ ~ I ~
- c<~ ~ _4 00 c<) - -~ ~N
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= 0 - ~= ~=
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_ - .
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c^. ~ ~ oo oo oo ~ r~ G~ o
~ ~ 0 oo O~ ~ ¢N 0 ~ ~ 0
·- _4 ~ ~ ~ ~ ~ ~ ~ ^ ~ ~s4 -
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cd
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CC
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0 ~ 0
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<
The Analysis of the Ar;`hropometric Data 175
"1" terminations are removed becomes too re-
strictive in practice, and that because of the
great preponderance of parents one or both of
whom are "1," exclusion of the "1" parents
may so reduce the sample size that we could not
detect differences of the magnitude expected
even if such differences did, in fact, exist. This
consideration would favor drawing inferences
regarding irradiation effects from the "1" vs.
"non-1" contrast, however, only if there existed
no ~ priori basis for viewing this contrast as
biased. We have advanced arguments in the
preceding pages which suggest that this contrast
may well be biased. Accordingly, we are unwill-
ing to draw inferences regarding the effects of
irradiation in the absence of demonstrable dif
TABLE 12.11 ESTIMATES OF CONSTANTS AND
(Linear model assuming
covariance matrices associated with the exposure
cells are significantly different, then the general-
ized variances are most probably significantly
different (or heterogeneous). To infer signifi-
cance, of course, assumes that the elements to be
tested are chosen on an a priori basis. It may
be pointed out also that if the elements chosen
for testing are not significantly different it does
not follow that the generalized variances are
not. The elements of the exposure cell variance-
covariance matrices with which we shall concern
ourselves are the variances of weight (w),
height (x), head girth Ail, and chest girth (z).
Moreover, in view of the problem of the com-
parability of " 1" and "non-1" terminations, we
shall routinely perform four tests, namely, a
, THEIR VARIANCES FOR TEST OF EQUALITY
only main effects)
Internal w x y ~
variancesR 7,720.44 402.27 163.31 358.39 Variance covariance
matrix of estimates for any
Constants character without a2
~, - ~
H N 14.047595 2.337845 -8.682824 -12.413078 0.00193378
........ 44.24880 13.117449 11.420425 9.823059 0.00169194
F2 ............ 0.855447 -3.012068 0.456508 -0.231801 0.00569837 0.00481708
F3 ............ -1.261074 3.104190 0.121017 -1.071249 0.00481708 0.00734644
F4 6 0 0 0 0 0 0
Ma 2.488047 1.058013 - 0.797087 0.691081 0.00698914 0.00604162
Ma 6.372319 2.733161 0.607450 2.376684 0.00604162 0.00845267
Me 5 O O O O O O
N = Nagasaki
a Mean square (within cells) .
ferences among the "non-1" terminations. Be-
fore pursuing this matter further, let us con-
sider the data with regard to the generalized
variances, and the effects of within-cell hetero-
geneity among the observations.
12.4.2 The equality of the generalized
var~ar~ces. The term "generalized variance"
was coined by Wilks (1932) and is defined as
the determinant of the variance-covariance ma-
trix. The generalized variance plays the same
role relative to the generalized mean (multi-
variate mean) as that played by the variance
relative to the univariate mean. The hetero-
geneity of a series of generalized variances may
be ( 1 ) demonstrated directly by the multivariate
analogue of Bartlett's test, or (2) inferred from
tests on elements of the variance-covariance
matrix.
Let us consider first the latter of these two
approaches. It may be argued that if randomly
chosen, corresponding elements in the variance
H _ Hiroshima
test on the homogeneity of the variances when
(1) all exposure cells are considered, (2) only
those exposure cells in which both parents were
exposed are considered, (3) only those exposure
cells in which one or both parents are in ex-
posure category 1, and (4) only those exposure
cells in which only one parent is in exposure
category 1. In Tables 12.12 to 12.15 are given
the mean squares and mean products of devia-
tions (the elements of the mean product [MP]
matrices) for each exposure cell for the four
city-sex cells. Inspection of the first four col-
umns of these tables (corresponding to the esti-
mates of the variances of Hi, x, y, and z) reveals
no striking evidence of heterogeneity. In Tables
12.16 and 12.17 are set out the results of test-
ing these estimates for heterogeneity by Bart-
lett's method (cf. Rao, 1952). From the latter
tables emerges little that can be construed as
evidence for the heterogeneity of the general-
ized variances. A comment on the two "signifi
176
Genetic Efects of Atomic Bombs Chapter XII
AN Ov ~ ~ ON Vet ~- ~ ~ ~ ~ _ _ 00 00 or ~ ~ oo CN ~ ~ ~ ~ ~ ON O 00
~ ~ ~ ~ ~ ~ ox ~ do us ~ _ 0 ~ ox up ~ ~ vat ~ ~ oo ~ US ax ~ ¢` ON oo ~ O _
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Tl~e Analysis of the Ar~thropometric Data 177
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178 Genetic Effects of Atomic Comics Chapter XII
TABLE 12.16 TESTS OF THE HOMOGENEITY OF THE VARIANCES OF THE ANTHROPOMETRIC MEASUREMENTS
OVER ALL EXPOSURE CELLS, AND SUBDIVISIONS THEREOF FOR SPECIFIED SEX AND CITY ( HIROSHIMA
(The tabular entries are chi-squares.)
(a) Males Hiroshima
Cells
Cells where Cells
where one or where
neither 60th only one
All parentis parents are parentis
exposure exposure exposure exposure
cells category 1 category 1 category 1
Variable (DF= 15) (DF=8) (DF 6) (DF 5)
w 15.201 7.390 7.712 4.096
x 18.675 6.073 11.627 10.223
y 23.041 7.593 14.965* 11.773*
z 13.472 3.971 9.272 7.411
(b) Females Hiroshima
.
Cells
Cells where Cells
where ore or where
neither both only one
All parent is parents are parent is
exposure exposure exposure exposure
cells category 1 category 1 category 1
Variable (DF = 15) (DF = 8) (DF 6) (DF = 5)
w 12.716 8.751 3.182 2.529
x 12.581 7.305 1.395 1.623
y 23.908 15.472 4.678 1.462
z 9.580 3.284 5.875 5.951
TABLE 12.17 TESTS OF THE HOMOGENEITY OF THE VARIANCES OF THE ANTHROPOMETRIC MEASUREMENTS
OVER ALL EXPOSURE CELLS, AND SUBDIVISIONS THEREOF FOR SPECIFIED SEX AND CITY (NAGASAKI)
(The tabular entries are chi-squares.)
(a) Males Nagasaki
Cells
Cells where Cells
where one or where
neither tooth only one
All parent is parents are parent is
exposure exposure exposure exposure
cells category 1 category 1 category 1
Variable (DF-15) (DF = 8) (DF 6) (DF_ 5)
w 11.978 7.012 2.516 2.330
x 16.186 6.279 9.328 8.907
y 14.373 5.947 8.086 5.525
z 15.940 9.476 4.917 4.854
(b) Females Nagasaki
Cells
Cells where Cells
where one or where
neither tooth only one
All parent is parents are parent is
exposure exposure exposure exposure
cells category 1 category 1 category 1
Variable (DF = 15) (DF _ 8) (DF _ 6) (DF = 5)
w 15.743 1.193 13.736* 12.859*
x 14.577 6.345 8.413 5.910
y 23.280 15.003 7.664 4.124
z 13.595 4.821 7.102 6.050
The Catalysis of the Ar~thropometric Data 179
cant" findings in Table 12.l7b is necessary.
Box (1949) has shown that Bartlett's X2 test
overestimates significance, particularly when
the degrees of freedom are large. An alternative
F test which Box has shown to be relatively
unbiased fails to confirm the significance of the
two starred entries.
Let us, therefore, turn now to the other of the
two approaches listed above, a direct test of the
homogeneity of the generalized variances. The
basic theory for the generalized test of homo-
geneity was advanced by Wilks (1932~. The
test employed on the data presented here pro-
ceeds from Wilks' original considerations of the
problem. Briefly the test is as follows: The test
The results of testing the generalized vari-
ances in this fashion are presented in Table
12.18. In no one of the sex-city cells can the
generalized variances be shown to be signifi-
cantly different. There is then no evidence that
parental irradiation has significantly altered the
variances associated with these measures of
physical vigor.
12.4.3 Within-cell heterogeneity. We
have previously indicated that there may exist
extraneous sources of variation which could lead
to the observations within an exposure cell hav-
ing dissimilar expectations with respect to the
multivariate mean and the generalized variance.
In other words, the observations within an ex
TABLE 12.18 TEST OF THE GENERALIZED VARIANCES OF THE ANTHROPOMETRIC MEASUREMENTS BY
SPECIFIED SEX AND CITY
(The tabular entries are F-values. All tests are against the alternative that the variance increases with
increasing parental exposure.)
Only those exposure cells
where both parents were
City-sex All exposure cells exposed
Hiroshima males .............. F = 1.128 DF= 150, 00 F = 1.003 DF = 80, 00
Hiroshima females F ~ 1.000 DF = 150, 00 F < 1.000 DF = 80, 00
Nagasaki males F = 1.109 DF = 150, 00 F < 1.000 DF = 80, Oc
Nagasaki females F = 1.222* DF-150, 00 F = 1.283 DF = 80, 00
criterion, M, is the generalized form of Bart-
lett's criterion for the univariate case, and
M = N 10ge~s~j~-~ (vie 1°ge~Siiz~ ~
1
where sij7 is the unbiased estimate of the vari-
ance or covariance, Fiji, between the its and josh
variable in the lth sample based on vie degrees of
freedom, and suppose 1=1, . . ., k, and Sij is
the average variance or covariance, that is,
ski = (TV, jib) /N
1
and N = PHI.
1
Now Box (1949) has shown that M/b is dis-
tributed as F with n~ and n2 degrees of freedom
where
b al
A, = ~ (`k-1 ~ p (p+ 13/2
n,+2
2 A2-A, 2
A= 2P2+3P-1 -~1 1
6(`k-1) (p+1) Rev, N
(p-1) (p+2) I 1 1 ~
A - ~ __
~6(`k-1) Ivy- N2
and where p is the number of variates.
posure cell may be heterogeneous in the sense
that they do not represent observations drawn
from the same parent population. The most
apparent possible extraneous source of variation
which should be considered is difference in age
at examination. To "control" the age variation
we elected to recognize another way of classifi-
cation, namely, age at examination. Three age
groups were defined; these age groups were
7.5-8.5, 8.5-9.5, and 9.5-10.5 months at ex-
amination. The results of analyzing the data
following this further partitioning are given in
Tables 12.19 to 12.22. As might be surmised,
the within-cell variation is reduced. However,
aside from the demonstration that weight,
height, head girth, and chest girth vary with the
age of the infant, the results of the analysis are
essentially unchanged from those results ob-
tained when the age variation was ignored. That
is to say, we still find significant differences be-
tween sexes and cities, no evidence for inter-
action, and that the exposure differences are
explicable in terms of the differences between
the "1" and "non-1" parental exposure cate-
gories.
12.5 Sammary.-Analysis of the muItivari-
ate means and the generalized variances asso
180 Genetic Efects of Atomic Bombs Chapter XII
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182
Genetic Ejects of Atomic Bombs Chapter XII
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. . Cl
The Analysis of the Anthropometric Data
183
TABLE 12.22 A SUMMARY OF THE SIGNIFICANCE TESTS COMPARING ALL POSSIBLE PAIRS OF EXPOSURE FOR
EACH PARENT WITH RESPECT TO THE VARIABLES X, Y. W. AND Z AFTER ALLOWANCE IS
MADE FOR AGE AT EXAMINATION.a
F1 F2 F3 F4 5
~ ,
Variable y
F1 F2 F3 F4 5
~,
Variable z
F1 ~ x r n.s. n.s. n.s. F: r 3 r n.s. *
F2J C J ~- n.s. n.s. F2 ~ 4~ n.s. n.s.
F3 ] ~ ~ n.s. n.s. ~ n.s. F3 .~ * n.s. n.s.
F`,~ Hi, Ems. n.s. n.s. ~ F.] ~ ~> * ~n.s. n.s~
M1 M2 M3 M4.5 M1 M2 MB
v ,
Variable y Variable ~
M' ~ xn.s. n.s. * M1 ~ 3 ~n.s. n.s. *
M2JDJ **~ n.s. n.s. MiJ Q| n ~ __ n.s. ~
M31 ~ 1 n.s.n.s. ~M31 ~ 1 n.s. n.s. ~n.s.
M4,5 (> ~n.s. n.s. n.s. ~6 :> ~ 5 n.s. n.s.
n.s.= not significant
*- significant at 5~%
** significant at 1~%
a These tables are designed so that the entries a/oove the diagonal refer to tests on the variable above the
diagonal whereas entries 6elow the diagonal refer to the variable below the diagonal.
ciated with the anthropometric measurements
fails to reveal differences between exposure cells
which are unequivocally due to parental irradia-
tion. The only significant differences to emerge
involve those contrasts utilizing infants born
to parents whose exposure category is 1. These
differences are in the direction of genetic ex-
pectation. In view of the numerous differences
known to exist between the "1" and "non-1"
parents, these differences are not thought to
constitute unbiased evaluations of parental
exposure.
