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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Suggested Citation:"THE ANALYSIS OF THE ANTHROPOMETRIC DATA." National Research Council. 1956. Effect of Exposure to the Atomic Bombs on Pregnancy Termination in Hiroshima and Nagasaki. Washington, DC: The National Academies Press. doi: 10.17226/18776.
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Chapter XII THE ANALYSIS OF THE ANTHROPOMETRIC DATA 12.1 The measurements 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 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 effects. — 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 and development during 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. 164

The Analysis of the Anthropometric 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 Mothers Females Mothers * 1 2 3 4-5 Total 1 2 3 4-5 Total ,/ 814.35 ( 819.51 812.03 813.51 815.20 767.39 766.33 766.65 762.46 766.90 1(2,765) t (871) (350) (169) (4,155) (2,543) (822) (331) (153) (3,849) - f 808.64 804.36 r 789.89 802.34 799-95 769.30 756.16 758.78 751.00 761.44 I (230) (236) (69) (29) (564) (223) (253) (54) (26) (556) I 1- , / 820.98 3 1 (91) 802.42 g (240) •£• K £ 796.66 (58) 790.38 (73) 776.00 (18) 771.45 (100) 757.48 (52) 755.07 (67) 801.71 (17) 765.90 (236) r 797 27 797.70 782.95 811.42 796.23 4-5 / 766.85 757.27 796.55 734.88 765.39 -^ 1 f 59 ^ (33) (22) (12) (126) (48) I (33) (22) (16) (119) Total/813'80 811.97 806.68 809.02 812.43 Total/ 767.66 763.46 765.51 762.12 766.18 3 1(3,145) (1,198) (514) (228) (5,085) (2,914) (1,160) (474) (212) (4,760) Males Mothers Nagasaki Females Mothers 1 2 3 4-5 Total 1 2 3 4-5 Total . / 797.52 794.62 774.13 795.63 f 749.06 789.22 753.03 763.16 744.29 751.70 \(2,074) (1,261) (81) (3,515) \ (99) (1,845) (1,168) (106) (80) (3.199) , f 788.81 788.79 794.94 762.23 788.64 f 736.21 750.17 738.09 708.13 741.33 1 (283) (486) (35) \ (13) (817) (264) (482) (47) (16) (809) , / 782.78 I (36) 789.38 g (104) •£• K u 795.63 (48) 791.21 (14) 774.67 (6) 749.14 (29) 720.85 (40) 734.35 (17) 694.50 (4) 731.34 (90) _c - 3 til cC x,/ 785.22 771.64 768.25 784.60 776.99 735.89 708.69 791.00 774.00 734.67 I (23) (36) (4) (5) (68) (27) (16) (4) (4) (51) Total/ 796.15 \(2,416) 792.65 (1,831) 780.34 (152) 784.83 (105) 793.94 (4,504) Total/ 752.41 (2,165) 744.92 (1,706) 753.71 (174) 737.95 (104) 749.03 (4,149) 3%) 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 common exceptions, infants 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-

166 Chapter XII Genetic Effects of Atomic Bombs TABLE 12.2 DISTRIBUTION 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 Males Mothers Females Mothers 1 2 3 4-5 Total 1 2 3 4-5 Total J 698.20 698.85 696.14 699.16 698.20 . / 683.83 682.84 681.92 684.02 683.46 H (2,765) (871) (350) (169) (4,155) 1(2,543) (822) (331) (153) (3,849) 9/ 697.21 693.31 693.94 697.86 695.21 - / 682.65 681.11 681.67 676.81 681.58 H (230) (236) (69) (29) (564) I (223) (253) (54) (26) (556) H r 691.59 691.93 691.00 694.49 g ,/ 683.88 681.31 684.42 i H 699.07 685.35 683.57 (91) (58) (73) (18) (240) -S- I (100) (52) (67) (17) (236) b 4 5/ 691.34 693.21 697.50 705.58 694.26 "" 4 ,/ 681.77 687.36 696.32 667.00 684.02 (59) (33) (22) (12) (126) I (48) (33) (22) (16) I (119) Toal/ 698.02 697.25 695.30 698.69 697.59 Total/ 683'71 682.52 682.77 681.96 683.25 ° a \ (3,145) (1,198) (514) (228) (5,085) 10tal\(2,9l4) (1,160) (474) (212) (4,760) Nagasaki Males Mothers Females Mothers 1 2 3 4-5 Total 1 2 3 4-5 Total / 696.86 695.36 694.31 692.12 696.14 I/ 682.05 679.94 683.01 684.03 681.36 1(2,074) (1,261) (99) (81) (3,515) l\ (1,845) (1,168) (106) (80) (3,199) , f 695.92 691.85 695.54 694.92 693.47 7/ 680.56 677.76 677.28 676.06 678.61 I (283) (486) (35) (13) (817) H (264) (482) (47) (16) (809) jj -f 696.44 693.71 691.93 693.83 694.42 £ ,f 675.24 677.65 680.82 670.75 677.17 H (36) (48) (14) (6) (104) -£H H (29) (40) (17) (4) (90) £ 4 f 696.13 I (23) 694.25 (36) 690.00 (4) 686.00 (5) 694.03 ^ (68) 4-5{ 678.41 (27) 676.81 (16) 697.75 (4) 673.75 (4) 679.06 (51) Total/ 696'74 Iotal\(2,4i6) 694.36 (1,831) 694.26 (152) 692.27 (105) 695.58 (4,504) Total/ 681.73 (2,165) 679.24 (1,706) 681.59 (174) 681.90 (104) 680.70 (4,149)

The Analysis of the Anthropometric 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 Mothers Females Mothers 1 2 3 4-5 Total 1 2 3 4-5 Total / 444.63 444.28 443.88 443.79 444.46 , f 433.82 433.38 434.11 433.10 433.72 1(2,765) (871) (350) (169) (4,155) \(2,543) (822) (331) (153) (3,849) ,/ 444.05 442.04 444.22 442.38 443.14 ,/ 434.65 433.38 435.19 431.27 433.97 I (230) (236) (69) (29) (564) I (223) (253) (54) (26) (556) g , f 447.10 443-69 441.67 445.72 444.52 g , / 435. 53 431.63 430.85 438.94 433.59 3l (91) (58) (73) (18) (240) f' I (100) (52) (67) (17) (236) 433.04 433.58 439-91 426.00 433.51 (48) (33) (22) (16) (119) Total / 433.93 433.31 434.04 (2,914) (1,160) (474) 432.81 433.74 (212) (4,760) Nagasaki Males Mothers Females Mothers 1 2 3 4-5 Total 1 2 3 4-5 Total . / 452.48 452.50 450.23 450.69 452.38 J 441.22 441.27 441.97 438.03 441.18 \(2,074) (1,261) (99) (81) (3,515) H (1,845) (1,168) (106) (80) (3,199) _ / 452.40 452.82 455.46 454.23 452.81 2/ 440.17 439.82 441.74 438.94 440.03 I (283) (486) (35) (13) (817) H (264) (482) (47) (16) (809) fi ,/ 451.42 453.73 454.86 460.67 453.48 g 3r 440.28 439.73 443.47 439.75 440.61 I (36) (48) (14) (6) (104) iH 3t (29) (40) (17) (4) (90) * x_« f 451.91 449.44 449.25 447.20 450.10 ^ 1 5*- 438.48 435.50 449.75 440.50 438.59 I (23) (36) (4) (5) (68) ' 'I (27) (16) (4) (4) (51) Total/ 452.45 452.56 451.83 451.53 452.45 Total/ 441.05 440.77 442.23 438.33 440.92 >la \(2,416) (1,831) (152) (105) (4,504) (2,165) (1,706) (174) (104) (4,149)

168 Chapter XII Genetic Effects of Atomic Bombs 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? the cell numbers are unequal and disproportion- ate. The analysis of dispersion is, of course, merely the multivariate equivalent of the analy- sis of 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 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 Mothers Females Mothers 1 2 3 4-5 Total 1 2 3 4-5 Total . / 427.32 428.92 427.51 427.18 427.67 tf 416.96 417.39 416.38 415.96 416.96 1(2,765) (871) (350) (169) (4,155) H (2,543) (822) (331) (153) (3,849) 2 (-425.41 423-38 427.12 424.34 424.71 2f 417.74 415.34 418.56 415.46 416.62 I (230) (236) (69) (29) (564) I (223) (253) (54) (26) (556) 1- , / 430.70 3\ (91) 426.09 (58) 423.29 (73) 420.83 (18) 426.59 g (240) •£' '{ 418.82 (100) 419.21 (52) 413.64 (67) 422.94 (17) 417.73 (236) & «{o« 429.85 (33) 421.59 (22) 432.17 (12) 425.23 (126) «{ 415.42 (48) 415.45 (33) 426.77 (22) 415.13 (16) 417.40 (119) Ma"'> 427.72 (1,198) 426.60 (514) 426.58 (228) 427.23 (5,085) Total/ 417.06 (2,914) 416.96 416.72 (474) 416.40 (212) 416.97 (4,760) Nagasaki (1,160) Males Mothers Females Mothers 1 2 3 4-5 Total 1 2 3 4-5 Total . f 439.23 438.44 434.36 437.21 438.76 . r 429.07 428.75 430.50 424.20 428.88 \(2,074) (1,261) (99) (81) (3,515) H (1,845) (1,168) (106) (80) (3,199) ,f 438.14 438.75 441.97 432.38 438.58 ,/ 428.91 427.69 430.13 417.38 428.03 \ (283) (486) (35) (13) (817) I (264) (482) (47) (16) (809) E , / 433. 19 438.31 442.21 439.67 437.14 g , f 428.69 421.95 428.76 425.75 425.58 _c - 3\ (36) (48) (14) (6) (104) £- t (29) (40) (17) (4) (90) HI «{«£» 431.75 (36) 446.00 (4) 432.20 (5) 434.06 (68) K "{ 424.07 (27) 421.44 (16) 431.50 (4) 431.50 (4) 424.41 (51) iMSSS 438.39 (1,831) 437.14 (152) 436.51 (105) 438.62 (4,504) Total/ 428.98 (2,165) 428.22 (1,706) 430.25 (174) 423.49 (104) 428.58 (4,149) 12.4.1 The multivariate 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 (i.e., with and 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 Wilks1 test (cf. Rao, 1952), which tests the

The Analysis of the Anthropometric Data 169 o «» 2 a>a " OJj .2 K § "S is s ^~ ° UJ^ "g g« & a enox'-*Om *r* rH o * ST ^ **£ 1 1 « tL. ocT ^ ~ o" X^T1 K•* i rt% ^^ , Xen tNfN s^^r-i^-t - X * c° 2 ^? ^ ° 0s in ! i **% O I"- a, » in p sO jy iSsi -s I •-* V '3) « « g slil!.l :g y u, UH 00 00 Os • *fl" CTs m f^ ^- r-t *s I I I

170 Chapter XII Genetic Effects of Atomic Bombs significance of the ratio of two determinants, say, |IF| and \W+Q\ where \W\ 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- 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 DISPERSION (All exposure cells) (a) Sums of squares and cross products of deviations for main effects and additivity Source (DF) Between cells (63) 849 154 Fathers (3) 854 Mothers (3) 949 Sex City (1) 261 037 Residual ' (55) 12 392 y> (1) 558451 1,063,755 12,890 8,069 978,425 18,163 31 591 Z« 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 vx . 676 905 2,119 1,850 739,190 — 68857 9,435 vz . , 941,068 1,518 1,045 515,125 388 118 11 066 1,753 375 10 554 6,643 2 311 473 — 588 628 43488 xz 587 612 6064 984 681 843 — 102 379 124 722 xw , 3,412,827 52,788 18,096 3,059,570 155,270 69,818 1.333.236 27.420 6.821 2.132.146 —875.191 92.923 (b) Mean squares for individual analyses of variance (on main effects and additivity) Between Source cells Fathers Mothers Sex City Residual • (DF) (63) (3) (3) (i) (1) (55) y2 • 13,478.63** 284.67 316.33 558451** 261 037** 225 31 x" 16,885.00** 4,296.67** 2 68967** 978 425** 18 163** 574 38 z1 17.827.35** 1.165.33** 525.67 475.161** 577.066** 513.67 w" 187,936.86** 75,713.67** 18,451.33 9,567,378** 1,327,332** 8,213.64 (c) Analysis of dispersion, Wilks' test (using Bartlett's approximation) Significant for sex and city (by inspection) Significant (by inspection) Not significant (by inspection) x' (DF) ...... 40.5** 12 24.0* 12 4 • Sum of interaction terms. scured. 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, B) is assigned the value zero.1 Comparison of the difference between two con- 1 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 (c? — ?) are in fact the difference between N and H, and males and females.

The Analysis of the Anthropometric Data 171 OS ON *•' tn. •-* 0o ^S • Os P » §§§ TT 00 sO ^ IT 21 ^* r- o m sO ON fN tN o o o o 00 sO ON 00 *"-i 00 rN [*--. —i i-* sO rt-s 'N O •«• 00 sO r*- vs o ' *-* sO sO M *•**._ vs trs ers O sOXf-^O ES ^- *-H •-. 'N 8i8 d o d > fN 888 odd fv ^| *^ 00 Os X^ w^ -** C| ifs Os Os Os 0| O\ oo vs oo sO os oo sO sO i-* trs rsi *-. *^ tr« rcs * (N *sI sO *^ *rs §O 3 O O O O O O . o o o o o v-s 'X •— •^ O irs rr-1 sO Xf - sss §o o q o odd x ^ <n — 00 N rr 00 00 00 IS * * * * oo *rs O\ 00 fN ' * * » » ON IT* ON trx oo r- fN O rfs *s"s rfs r-i •^ fTs tN in r^ oo sO *n oJ sO sO ** ^r r- *o os o 'N r- ^ sO i^s t^ rfs O *^ ff^ « o r- ^ oo oo w-* M rn r-* o r- \O "^ r*"i —I —i O rMr^-soo •^•^•i^o ^ ^ ^ ir. oo XT oo irs m sO *n ^H •s °T — 00 I I c o U >*0 ^O * * 00 Os 00 00 o tfs irs • os oo oo r- o o fN Os r^ "^ "-"* 00 *N "i r-os or^os fNOs1^ Kd i-Idd rHd*-* B ^O ** •^ t/^ *TS 11 .a V g 1 sr I stants from a given classification with the vari- ance of the difference affords a test of the significance of the difference. For example, if 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 /=- where wlz and wf3 are the w constants for father's exposure categories 2 and 3, *7w2 is the variance of w (obtained from "within-cell"), and «7/2a, *7/g2, and *7/?/3 are respectively the variances of the /2 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 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- ferential measurements than their Hiroshima counterparts. This difference while not pre- 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-

172 Chapter XII Genetic Ejects of Atomic Bombs tion, 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 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 TABLE 12.8 A SUMMARY OF THE SIGNIFICANCE OF TESTS COMPARING ALL POSSIBLE PAIRS OF EXPOSURE FOR EACH PARENT WITH RESPECT TO THE VARIABLES w, x, y, AND z • F, F, F. F,,. F, F, F, F... Variable y Variable z M, M, M-, M,, M, M. M. M,.. Variable y Variable z Mi M. M, M,,B n.s. = not significant * = significant at 5% * * = significant at 1% * These tables are designed so that the entries above the diagonal refer to tests on the variable above the diagonal, whereas entries below 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-1" 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 mi- 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

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174 Chapter XII Genetic Effects of Atomic Bombs J 21 9 Q 53. >* 1 I I J; i 00 sO CO sO I t 'N 'N C ' , .-., _ "* • A —j sO 00 i S so .n', O CT\ Q , H fN « ' —- os . s •*- so • •9 •a R *S ^!^£ § 1 ;$; J- 000° •C -JC* .fi ^. • _J i- r*< 'r^ trs Os •-• rt s*^' *Q xj* fsj M LiH sO 00 *—' |^°s^ |ciogg; *- 3- » » * * . sO so r- o TT 'N 00 00 . fN 'N GO Os It -— CL C 2 .a> -S I I I I I I o en r- » * » * o oo r- •— _, r*"i Os 00 m •^ 'N sO^ 0_ O^ _o -p 2 so O Ks H M" Q > "X V."N S [j^ ~ ?i Q

The Analysis of the Anthropometric 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 a 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- 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 (y), 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 TABLE 12.11 ESTIMATES OF CONSTANTS AND THEIR VARIANCES FOR TEST OF EQUALITY (Linear model assuming only main effects) Internal variances* w 7,720.44 x 402.27 163.31 358.39 Constants Variance — covariance matrix of estimates for any character without a' H — N . . . 14.047595 2.337845 13.117449 —8.682824 11.420425 — 12.413078 9.823059 0.00193378 0.00169194 *? — ? .... 44.24880 Fi . .. 0.855447 —3.012068 —3.104190 0 0.456508 0.121017 0 —0.231801 —1.071249 0 0.00569837 0.00481708 0 0.0048170 0.0073464 0 F, — 1.261074 F«-« 0 M. 2.488047 1.058013 2.733161 0 —0.797087 0.607450 0 0.691081 2.376684 0 0.00698914 0.00604162 0 0.0060416 0.0084526 0 M, 6.372319 M4 5 0 •Mean N = N square (within cel agasald Is). H = Hiroshima 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 variances. — 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- 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 w, 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-

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178 Chapter XII Genetic Effects of Atomic Bombs TABLE 12.16 TESTS OF THE HOMOGENEITY OF THE VARIANCES OF THE ANTHROPOMETRJC 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 both only one All parent is parents are parent is exposure exposure exposure exposure Variable cells (DF=15) category 1 (DF = 8) category 1 (DF = 6) category 1 (DF=5) 15.201 7.390 7.712 4.096 x 18.675 6.073 11.627 10.223 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 one or where neither both only one All parent is parents are parent is exposure exposure exposure exposure Variable cells (DF=15) category 1 (DF = 8) category 1 category 1 (DF=5) w 12 716 8.751 3.182 2.529 X 12.581 7.305 1.395 1.621 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 oneot where neither both only one All parent is parents are parent is exposure exposure exposure exposure Variable cells (DF=15) category 1 (DF = 8) category 1 (DF=6) category 1 (DF=5) 11.978 7.012 2.516 2.330 x 16.186 6.279 9.328 8.907 14.373 5.947 8.086 15.940 9.476 4 917 4.854 (b) Females — Nagasaki -*«7*, 1 Cells * Cells where Cells where one or where neither both only one All parent is parents are parent is exposure exposure exposure exposure Variable cells (DF=15) category 1 (DF = 8) category 1 (DF = 6) category 1 (DF— 5) w 15.743 I 1 Q2, 1 2 7*(C* UQCQ* x 14 577 6 345 1 J* I 2O -ojy* 23.280 sj- j~t j 15.003 7 664 41 7 A X . . 13.595 4.821 / *vwt • J .- i 7. in? £ nsn

The Analysis of the Anthropometric Data 179 cant" findings in Table 12.17b 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=80,00 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 Af = N loge\sit\ - 2 (vt loge\stlt\) i where sljt is the unbiased estimate of the vari- ance or covariance, atil, between the /'* and ;'* variable in the /'* sample based on v, degrees of freedom, and suppose /=1, . . ., k, and sis is the average variance or covariance, that is, and N = 2fj. i Now Box (1949) has shown that M/b is dis- tributed as F with «t and nt degrees of freedom where 6(k-\) 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 Summary. —• Analysis of the multivari- ate means and the generalized variances asso-

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The Analysis of the Anthropometric Data 181 o u a, O >• I o o o X I a t; 1 1 ~ & c _O _rt O •r C 1 0, sr •3 fi 3 a ^ oo oo o o o oo 1-_ o M_ oo_ T_ U sO op" --" r-T -3 in o? KC «< -^" oo" r-^ Os m 00^ fN^ tN^ T3 1 8 *-* ^ " . r* r* w-C oT ^T oo r-" 'N" o" oo" in O - ' r*-r*-infNfTimrtso I- — 0OO0O'N•^00'N - -- > , ST o m so" irs r-" o" so" « oo 15 2 ° -; r4ooinominoo'fl'Ox * » * „ • • » e » » * * * * * «^ o r^ O m " , R -e § G ^ 2 «»»• **** 5 o 5". Hoo *8 § oa

182 Chapter XII Genetic Ejects of Atomic Bombs oooo oooo oo o

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.* P. F, F, F"., F, F, F, F,,. Variable y Variable z M, M, M, M,,. M, M, M,.. Variable y Variable z M.I M,J M.1 M...I n.s.= not significant * = significant at 5% ** = significant at \% •These tables are designed so that the entries above the diagonal refer to tests on the variable above the diagonal whereas entries below the diagonal refer to the variable below the diagonal. dated 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.

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