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Chapter X THE ANALYSIS OF THE 10.1 The trait. Birthweights were ob- tained for all infants. However, for the reasons given in Chapter VI we shall limit our attention to birthweights obtained on liveborn infants only. Shortly after the initiation of the study it became apparent that there was a remarkable diversity among the practicing midwives in the apparatus used to weigh newborn infants. Ac- cordingly, early in 1949 each practicing mid- wife in the two cities was presented with a simple, spring type scale; prior to distribution, all scales were checked for accuracy. Weight was recorded by the midwives in momme (a Japanese unit of weight; 1 momme = 3.756 grams) and later converted to grams. 10.2 Tire generic argument for irradiation eff ects.-Thus far in our consideration of irradiation effects we have concerned ourselves with only those induced mutations which would, presumably, occasion fairly large departures from the norm among individuals in whom the gene (s) finds manifestation. There exists in addition to these classes a much larger group of induced mutant genes, the so-called "invisibles" or "detrimentals," which give rise to much more subtle changes. These mutants, on the average, reduce the fitness of the organism. This loss of fitness may take the form of a decrease in the life span, a reduction in physical vigor, or similar changes. It seems logical to assume that in most instances a marked reduction in physical vigor would be reflected in certain body meas- urements, among these measurements being the birthweight of an infant. Such a reduction might be manifested as a change in the mean value, an increase in the variance of the measurement, or both. Accordingly, changes in mean birth- weight or in the variance of the weights of newborn infants associated with parental ex- nosure could be interpreted as evidence for irradiation-induced genetic damage. It should be pointed out that radiation-induced genetic 1 . . 131 BIRTHWEIGHT DATA changes in birthweight would, of course, be a function of the extent to which variation in birthweight is under genetic control. The avail- able evidence (Robson, 1955; Morton, 1955) suggests that the component of variation ascrib- able to heredity is small. However, this does not vitiate attempts to determine the effect of irradiation-induced mutations on birthweight. 10.3 Concomitant variables known to affect birthweight. A host of variables are known to, or thought to, influence birthweight. The most important ones, seemingly, are maternal age and parity (inter alla, Karn and Penrose, 1951 ), and maternal nutrition and economic status (inter alla, Millis, 1952~. A word or two regarding these variables seems appropriate. Maternal nutrition and economic status may be considered simultaneously for our purposes since it seems quite possible that the effect of the latter is due largely to the former. While it seems axiomatic that maternal nutrition is im- portant in birthweight, the amount of variation in birthweights attributable to maternal nutri- tion under various circumstances is not ac- curately known. However, there exists evidence (Antonov, 1947, and Smith, 1947) that, bar- ring a totally inadequate diet, maternal nutrition has relatively little effect on body size. It is in the area of marked decrease (near starvation levels) that maternal nutrition seems most im- portant. Unfortunately, maternal nutrition is a variable extremely difficult to measure even under the best of circumstances, and nigh im- possible under the conditions in which the present study was conducted. That conditions in postwar Japan may have been such as to produce maternal nutritional deficiencies cannot be gainsaid. However, there is no evidence to suggest that during the course of this study nu- trition was at near starvation levels for an ap- preciable number of mothers. At no time during the period 1947-1953 was the daily caloric

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132 intake assured by the rationing system less than 1,775 calories per day. The average caloric in- take for adults during the period 1947-1953, as recorded by the Public Health Section of the Hiroshima municipal government, was Calories i947 i,775 948 1,900 949 1,912 950 1,995 1951 2,027 1952 2,050 1953 2,073 This "official" intake was undoubtedly mented, but to an extent impossible to deter- mine, by unofficial ("black-market") foodstuffs. Moreover, the minimal caloric intake available for women Eve months or more pregnant was augmented by approximately 240 calories (70 gms.) of rice. Caloric intake is, admittedly, but one facet of the appraisal of the adequacy of maternal nutrition, but in the absence of more specific information it is the only yardstick by which we can appraise the diets of the mothers involved in this study. Conceivably, some meas- ure of the possible effect of maternal nutrition could be gained by an inspection of the data available on economic status of the parents in- volved in this study, or, in view of the gradual betterment of the diet during the internal of this study, an analysis of year of birth effects might be informative. From the standpoint of the present analysis, it is important to recognize that while the diet of the pregnant Japanese woman may by Western standards have been sub-optimal during a portion of this study, there is no reason to believe that there were dietary differences with respect to radiation categories. Maternal age and parity are variables more readily measured than maternal nutrition and economic status. Their importance is amply attested to by, for example, Karn and Penrose's finding (1951) that as much as a full pound difference may exist between first- and seventh- born children. Moreover, they have shown that maternal age exerts an effect not explicable in terms of the correlation between maternal age and parity. More recently, Millis and Seng (1954), studying infants born in Singapore during the period 1950 to 1951, have extended Karn and Penrose's findings. These workers limited their attention to normal, non-prema- ture, liveborn infants. In two of these respects Millis and Seng's data are not unlike the data Genetic EJects of Atomic Bombs Chapter X here presented. Millis and Seng find that (a) parity has a positive effect, and (b) maternal age a slight negative effect on birthweight. These are findings essentially similar to Karn and Penrose's. Millis and Seng have, however, proceeded one step further, and find that the relationship of parity to birthweight, for fixed maternal age, is cunilinear and fairly consistent over differing age groups. On the other hand, the relationship of maternal age to birthweight, for fixed parity, is neither consistent nor simply stated. In our data, we find that taken conjointly aug- maternal age and parity can be related, fairly consistently, to birthweight by a regression of the form: where y=m+~iX+~2w+53z y = birthweight m = mean birthweight x = parity w = parity squared z= maternal age and Id, [2, and be are, respectively, the regres- sion coefficients associated with parity, parity- squared, and maternal age. Since our interests here are limited to remov- ing the effects of concomitant variation in ma- ternal age and parity, a detailed presentation of the relationship of these variables to birth- weight in Japanese children will be presented elsewhere. To afford the reader some measure of this relationship Figures 10.1-10.2 are presented. 10.4 The dala and their analysis. The ex- tent of the data on the birthweights, and the complexity of the problem posed by their analy- sis, precludes presentation of the raw data in de- tail. It is hoped, however, that the presentation of these data will be sufficiently complete to illustrate the argument underlying the analysis. In Table 10.1 are presented the mean birth- weights in decagrams unadjusted for maternal age and parity and the number of observations on which these means are based for each of the 64 sex-city-mother-father cells. In Table 10.2 are given the results of two analyses of variance seeking to determine whether there exist signifi- cant differences among these means prior to adjustment for maternal age and parity differ- ences. The two analyses differ only with respect to the inclusion or exclusion of the category 1 parents. A perusal of the analysis reveals little

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The Analysis of the in the way of significant differences in mean birthweight between parental exposure cate- gories. The large number of significant inter- actions when the category 1 parents are included attests to the heterogeneity of the data, and vitiates attempts at generalizing with respect to parental exposure. In this connection, it is interesting to note that when these parents, that is, the category 1 parents, are excluded, the bulk of the heterogeneity disappears (see Table 1o.2b). This preliminary analysis of the data does not suggest the existence of large dif- ferences in mean birthweight induced by paren 320t 3'Si 3.0f 30s MEAN BlRrHWElGHT (DECAGRAMS) 3~ 29s 290 285 280 Birthweight Data 133 Hiroshima, and then indicating where the four city-sex cells agree or disagree. In an analysis of these data, we are interested in obtaining answers to the following questions: 1. Is the regression of birthweight on maternal age and parity significant? 2. Are the regressions based on the individual mother-father exposure cells within a given city-sex cell homogeneous? 3. Assuming a significant regression, do the adjusted means differ significantly among pa- rental exposures ? 4. Does there exist significant heterogeneity among the variances in the mother-father cells ? ~ ,-- ~ /," "\ 30, ,, `. ',' , 310 30o . MEAN BIRTHWEI - T MATERNAL AGE (DECAGRAMS) ALL AGES 290 __. AGE 30 PARITY FIGURE 10.1 The distribution of mean birth- weight in decagrams by parity for all maternal ages, and for maternal age 30 only. tat exposure. It seemed pointless, however, to pursue the meaning of the interactions and main effects until adequate compensation had been made for the concomitant variables known to differ among the city-exposure cells. Before we consider the effects of concomitant variables, the reader's attention is called to Table 10.3 which presents the residual mean squares (esti- mated variances) by parental exposure weighted for sex and city differences. The heterogeneity is apparent on inspection. In the analysis in which concomitant variation was to be accounted for, the data were parti- tioned into four parts corresponding to the four possible sex-city cells, namely, males-Hiroshima, females-Hiroshima, males-Nagasaki, and fe- males-Nagasaki. The results of the analysis of these four city-sex cells are presented in Tables 10.4 to 10.24. To present the analytical argu- ment, we shall content ourselves with examining in detail a single city-sex cell, namely, males 28S 28D ~ ~ - LEGEND ~ A. ~._~ . ~ Y 202112324~2621 303233 31,4' 2 - 20 21-23 24-26 2729 3~32 33-35 36~8 39-41 42~44 I~ATERNAL AGE FIGURE 10.2 The distribution of mean birth- weight in decagrams by maternal age for fixed parities (parities 1 and 4~. 5. How heterogeneous are the observations within a mother-father cell ? 6. Assuming the answer to question (5 ) is "appreciable," what are the variables which may account for the within-cell heterogeneity? These questions have been posed in the order in which we shall treat them in the following paragraphs. In Table 10.4 are given the results of the analysis of covariance leading to the determina- tion of the regression coefficients b,, t2, and b3 associated with parity (x), parity squared (w), and maternal age (z) for each of the individual mother-father cells within the males-lIiroshima cell as well as the estimates of b', t2, md b3 based on the pool of the exposure cells. From ~ By "pool" we refer to the results obtained when we sum the sums of squares and cross products of de- viations over all 16 exposure cells, and estimate the regression coefficients therefrom. By "sum" we refer to the results obtained when a regression is fitted to each of the individual exposure cells.

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134 Genetic Ejects of Atomic Bombs Chapter X - c~ 1 ._ ~of Z z ~ _ cn vet ~ cat u, 0 at. P4 .c -; <: ad Ed z ~ x - 04 ~ _ sat EN ~ ~ _ m ~ z at: - cn . cot _ Go ~ ~ ~ ~ 0 ~ 0 it ~ ~ ~ ~ 00up vie ~ 0 ^ ~7 ~\ c<~ cO oo ~ 0 ~ ~ rid cry vie I ~ ~ 0 ~ ~ ~4 so O vie ~ ~ ~ a' oo ~ ~ _1 cry 0 ~ ~ 0 0 ~ ~cry 00 By. ~ lo. ~ ~ ~ ~ ~ so. ~ ~v, ~ ~cry 00 ~ ~ \0 oo ~ ~up vie oo~ ~ u ~ \0 0 ', O" ~4~ ~O ~ ~i ~^ ~ ~ ~ ~c~ v, c~ o~ r~ u~ ~ C;~ ~ ~O oo ~u~ Gs ~ ~r~ ~ ~ - ^ ~i~ 0 ~ ~ O v~ _, ~4 ', ~ ~ 'X ~ IX ~ IX ~ 'X ~ IX - Ct 1 ~ ~r 0 s~auL~o~ r -~ -- -- -~ -^ _ _, ~ _4 ~ _4 ~ v~ ~G~ r~ o ~ ~ GN ~ ~o (-i I_ -^ ~ 0 - . ~ O ~ ~ ~ ~ ~ 00 V~ 00 00 ~ ~ 00 ~ O 'r' ~ O C~ u~ O ~ ~ ~ CO ~G~ ~ G ~d4 ~ cO ~ ~ 00 00 C~ _4 _1 ~ ~ ~ ~ _i C~ ~ O ~ O ~ ~ oo ~ = - oo ~> - 1 GN V~ ~ ~ O a ~ c ~cd O ~d4 ~ ~ ~ u^' ~ ~ ~ ~ _. ._ ~ ~ ~m0 .= G~ V~ r~ ~ u~ ~ v~ \0 G~ ~ ~ C~ v~ ~_I ~ ~O O ~ ~m_l 00 ~ ~ ~ ~ 1 C~ Slaq~ow _ V~ oo ~d -~^o - - o' I =~ ~ e~t' ',-x oo U~ ~ ~o cr, '`. oo C~ o N 00 00 O~ O C~ \0-~ ~ _~ OO O t_ ~ O ~ ~ ~ ~^0 ~ OO Io - g I ~ u~ v~ ~ ~ oo .. ooo ~ G~ v~ ~ o I ~, U~ o o I~ CC C~ ~ o - o oo C~ o o ~ <. o ~ o ~ 'X ~ 1x ~ IX ~ IX ~ IX C~ 1 ~, S]~]O~ 0 ~r~ oo 0 cO oo oo v~ \0 ed ~ ~ O ~ v~ G ~ ~ u~ o ~ ~ ~ ~ U~ c ~r_ o~ c,r, mo C~= ~ o o ~o U~ ~oo ~V~ o oo ~ ~ ~ o o o ~o C ~C ~C~ I_ ~ ~ ~ ~1 1 oo 0 ~00 1 c~,~ c,\ ~ ~ 1 ~ OO O GN 1 0 ~ ~ 1 1 ~ ~- ~ 1 ~ - G~ 1 ~ ~ G~ 1 ~ o 1 cN ~d4 ~ ~ ~1 1 0 C;\ 00 ~ GN C~ ~1 ~1 - . 1 cx c~ ax ~ ~ (- ~o~ r ~o 1 G~ I_ o ~i o ~ O 1 ~ o ~c ~ 1 s]~lon J

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The Analysis of the Birthweigh' Data 135 TABLE 10.2 ANALYSIS OF VARIANCE OF BIRTHWEIGHT BY PARENTAL EXPOSURE AND CITY (Unrelated parents) a. All exposure categories (4 X 4) Sum of squares Sourceof deviations DFMean square Main effects Cities (C) 675.79 1 675.7922.640 Sexes (S) 1,070,650.05 1 1,070,650.049600.077 Fathers (F) 14,154.42 3 4,718.1412.644 Mothers (M) 4,346.49 3 1,448.8311.231 Interactions, first order CS 51.98 1 51.98134.324 CF 12,253.02 3 4,084.3402.289 C M 20,235.97 3 6,745.3233.781 SF 289.84 3 96.61318.467 SM 54,757.96 3 18,252.65210.230 M F 39,647.35 9 4,405.2612.469 Higher orders 19,162.58 33 580.6843.073 Between 1,235,883.20 63 19,617.19410.995 Within 112,097,004.72 62,828 1,784.189 Total 113,332,887.92 62,891 b. Excluding parents with exposure 1 (3 X 3) Sum of squares Source of deviations Main effects Cities (C) Sexes ( S ) Fathers (F) Mothers (M) Interactions, first order CS CF CM SF SM MF 9.64 114,255.51 ....... 2,940.19 5,698.70 DF Mean square 1 2 2 .37 1 8,149.72 2 15,069.70 2 2,018.93 2 8,825.61 2 6,995.23 4 9.638 114,255.511 1,470.096 2,849.350 207.725 57.072** 1.362 1.423 .3695,425.377* 4,074.8612.035 7,534.8523.764* 1,009.4641.983 4,412.8072.204 1,748.8071.145 Higher orders -16 Between 190,786.4935 5,451.043 2.723** Within 17,597,261.258,790 2,001.964 ~- Total 17,788,047.74 8,825 -

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136 Geodetic Ejects of Atomic Bombs Chapter X cx O 00 ~ ~ - = _ _ ~ ~ ~ ~ ~ NO ~ ~ O . . . . . . . . . . . . . . . . 1 1 ~1 1 1 1 ~1 1~ O ~ ~ ~ O cur ~ cat = - ~ ~ ~ ~ O ~ 00 ~ ~ 00 . . . . . . . . 1 1 1 1 1~- 5 cat ~ 0 red ~ ~ Get Cx 00 ~ ~ ~ O 0 - ~ ~ O O ~ Cx ~ ~ AN 00 ~ ~ ~ ~ . . . . . . . . ~ 1 1~ 1 1 ON ~ Cut ~ Cx red oo oo ~ red 0 oo G~ O \0 ~ G~ ~ (;N ~ ~ O x0 ~v~ c~ 1-~ r~ ~ 1- ~ ~ O C~ O a~ 0 ~ ~ ~ r~ ~ ~ ~ ~ ~ 0 0 ~l ~- c~ ~ ~i ~ O ~ ~-~ 1 Cx ~, ~ ~ 1 1 V~ ~ ~ ~ ~ O C~ O ~ ~ ~ ~ ~ ~ ~ C`6 iN O ~ ~ ~ ^ = a~ G~ oo ~ ~ ~ . . . . . . . . . . . . . . . . V~ ~ O ~ ~ ~ ~ ~ ~ ~ ~ ~ oo O oo 00 ~D ~ ~ ~ ~ ~ ~ ~ Cx ~ ~ r~ CN ~ O ~ ~ ~ ~ - = ~ ~ ~ ~ ~ ~ O ~ W -~= ~ =~r ~ 0-~= u-~ r-~-(~, v~ 0 ~ ~ r~ ~ x 0 r~ 0 ~ G~ ~- ~ ~ oo ~ ~ C~ 00 ~ ~ ~ ~ ~ ~ ~ ~ ~ - V~ ~ ~ _` O n ~3 ~ 0 ZE--. - ~: ~ ~ ~ - c .L4 ~ ~ _ ~ ~ o ~ ~ ~ -~= ~: cy . ~ ~ r~ ~ ~ 0,() o o~.= ~ [=, ~ ~ E ~_ 1 GC v~ o cx v~ ~ ~ 0-= ~ r~ ~ ~ N~ r~ Cx~ c~ ~ O C~ G~ oo ~ O ~ ~ ~ ~ ~ ~ ~ ~ 00 00 3 x t~, ~ <~3 ~ ~ 00 c~, ~ ~ O O 0 ~4 ~ ~ v~\ O ~W ~ ~ 0~= - ~ - ~ ~ - = ^= O ~ ~ ^~40~0 ~ ~ ~r~ ~: ` ~ ~ > C~ Cx '` ~ cc r~ co ^-0 ~-~ 0 Cx~ r~= =- o ~V~ r ~ ~ ~ ~ ~ 0O-OO~,O~=OO=~=O=~^ -= ~ G~_ ~ ~ O ~ ~ ~-1 r~;r ~ ~ c;xo ~ ^^ - ~ - r~ ~ =~= ~ ~ ~U j ~ o~ ,^ ~ ~ x X ~ _, ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 1 1 ~ = ,_ mo r_ 0 c~ ~ ~o~o~ ~ 0 c~a)= oo ~ >-c ~ ~o ~ O ~ ~ c4 ~ ~ ~ 0 ~ r~ r~ ~ ~ . U ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ . . . . . . oo oo '` ~x Cx c~ ~ GN~ CC ~ 00 ~ ~ ~ ~ ~ ~ ~- ~ D,,C _ . o ~. ^ ~ ~W ~ +^ ~ O. ~ O ~ ~ ~ ~ ~d4 ~ Cx ~P c<~ O q X \0 C<~ oo GN ~O (~l ~ it N CN ~ ~ ~ ~ ~-~ ~ ~ ~ O ~ ~ ~ O 1 -I O 00 ~4 ~ ~ CO O Cx C~= \0 C~ 1-X 1-~0 ~ ~m ~ ~ ~ ~ g O oOo ~ ~ ~ ~ ~ ~, ~ ~ g o ~ ^^ ~ ~ 0 ~ ~w ~ ~ ~ ~ ~ ~ ~ O. ~ ~ ~ ~ O c< ~ _~ ~ (~ 0 ~ ~ v~ O ~ ~00~ 00 ~, ~ I_ ~ oo r~ O [L CN \0 ~-~ ~a r~ ~oo u~\ ~ _ co _ * ^_ ^_ ^ ^ * z O O =~0 ,`= ~v~= 00 ~ O cx~ ~ ~d4 '< cc ~ V~ Cx Cx _~ oo ~ 1-~ ~ C~ ~ ~ 1_ ~O :d x ~ ~ ~ oo ~ ~ ~ ~ ~ ~ ~ cx oo v~ l- I_ . ~ ~ C~ ~ ~ ~W tr~ 0 trN (~ O ~ ~ ~ ~ ~! c~ ~^ (~ oo C V~ o~ ~ - ^ ~ r- ~ <} 11 (-) I ~ r- - ~~- ~ ~ X CtN ON ~~ 00 ~ ~ Cx 0 v~ ~ O ~- <) ~ ~ ~Oo -~ ~c~ ~ mo~-oov~a~V-~-oo~ c ~V~ 1 ~ ~ ~ ~ ce ~ G~ ~ ~ \0 =~-Cx 00^ ~ ~o c~ , ~r~ ~ ~ ~r '~ ~ ~ ^= ~ ~ ~ ~ ~ 3 ~r ~ ~ ~ ~o ~ ~ ~ % GN ~ . _ 4 ~ ~ ~d4 ~ ~ ~ 4 ~- N ~ ~ ~_~ D ~ == mo~-xr c~ ~ o~ 0 - = ~ 11 11 ~N ~ ~_ o r_ O -I Cx ~ ~P r~ ~ ~ ~I_ 0 3 '` ~ ~, ~ ~ ~> ~ :` x _ r' ~ r~ ~c~ 0 0~= 0 r`= 0 a,= 0 ~ oo ~ ~ 0 ~ c~ ~ c~ ~ ~ ~ ~ ~ ~ ~ c~ _4 m _ ~ ~ ~ ~ c~ ~ ~ ~ ~ cx c~ ~ ,_ c~ ~ c~= oo ~0 ~r r~ ~ ~ I-~ Cs ~ ~ r~ x O =\ ~ ~ ~ ~ 00 ~ ,~ ~ v~ ~ ~ O ~ O 3 ~ ~ ~ ~ ~ ~ c~ 0 ~ c~ ~o ~ ~ 0 ~ a' oo ~ r~ ~ ~o ~ O ~ ~ ~ ~ ~ ~ r~ 0 G~ oo ~ ~ co 0 ~ - . ~ ~ ~ 0 ~4 C4 ~ ~ ~ u~ ~r _4 ~ ~ ~ c~ r~ V~ V~ ~ Cx~ ~ cc C~ ~ ~ ~ a v~ ~ ~ 0 ~ ~ ~ ~ c~ cx ~ cx ~ ~ c~ ~ ~ ~ ~ cx ~ ~ ~ ~ I- V:) ~ V) -~ CS ~ cx 3 ~, ~ ~ ~ ~ c~ =, a~ ~ ~ cc ~ ~ ~ ~ ~ 0 W =^~^ ~ c~ l-~ ~ 0 ~o 0 0 ~o cc ~- ~ ~ oo ~ r~ cx ~o _ ~ _ ~c ~ v~ _I v~ ~ _ r~ ~ ~o ~ ~ ~ 0 ~ _ == ^0= ~ CN' ~ ~11 ~ Cx ~ O C~ G~ ~ ~ C~ ~ ~- ~ I_ oo ~ ~ ~ ~ ~-~ ~ ~^ aw v~ ~4 ~ ~ ~ I

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The Analysis of the Birthweight Data 137 Table 10.5a we note that the estimates of b,, t2, and be based on the pool remove a significant amount of variation from the birthweights. In the light of the work of other investigators this is not an unexpected finding. However, if we return to Table 10.4, we note on inspection considerable heterogeneity among the b's asso- ciated with the various exposure cells. That this variation is significant is borne out by Table 1o.5b. At this point, it is of interest to inquire into the amount of variation in the birthweights ac- counted for by variation in the individual re- gressions after removing the portion associated with the common regression (see Sec. 6.3~. From the data in Table 10.5, we form the mean anticipated from irradiation, variation, account- able for on other grounds, of as small as 3 per cent could be sufficient to obfuscate irradiation differences. For the analysis of variance on the adjusted data set out in Table 10.6, adjustment was to the common regression because adjustment to the individual exposure cell regressions removed a seemingly negligible additional amount of variation (for a discussion of the computational procedure see Wishart, 1950~. For the reader not familiar with covariance analysis it might be pointed out that the computations in Table 10.6 effectively transform through the pooled regression the observed array of exposure cell means into the array of exposure cell means TABLE 10.5 TESTS OF THE SIGNIFICANCE AND HOMOGENEITY OF THE REGRESSIONS OF BIRTHWEIGHT ON MATERNAL AGE AND PARITY: MALES, HIROSHIMA (a) Test of the significance of the regression based on within-cells (pooled) regression coefficients Source SS DF Variation removed by regression 761,262.72 Residual within cells (pool) 28,264,084.66 16,178 MS F 2 253,754.240 145.246* * 1,747.069 (b) Test of the homogeneity of the regressions (all exposure cells considered) Source SS Differences in regressions 116,630.11 45 Residual within cells (sum) ....... 28,147,454.55 16,133 MS F 2,591.780 1.485 * 1,744.713 (c) Test of the homogeneity of the regressions (only those cells in which both parents were exposed are considered Source SS Difference in regressions 38,429.76 Residual within cells (sum)3,473,234.85 square ratio of the "mean square residual (pool ) " to the "mean square residual (sum) ." The value obtained is 1.001350. Accordingly, we may assert that the variation in regressions accounts for 0.14 per cent of the variation in birthweight not accounted for by the common regression. This value obviously attains per- spective only if we know the amount of varia- tion in birthweight accounted for by the com- mon regression. The latter we obtain from the mean square ratio 28264084.66+ 761262.72 16181 (1747.069) which is 1.02674. The common regression, then, accounts for 2.7 per cent of the variation in y. It is natural to inquire here whether this amount, 2.7 per cent, is of importance. To this we can only answer that in view of the small eRects DF MS F 24 1,601.240 1.124 1,929 1,800.536 which one would obtain if each exposure cell had the same maternal age and parity distribu- tion. The mean squares obtained following this transformation are wholly analogous to those obtained in a simple analysis of variance, and may be interpreted in the same sense. Inspection of this table fails to reveal significant differences among maternal or paternal exposure categories or evidence from the interaction mean square of nonadditive effects of parental exposure. The adjusted birthweight means are given in Table 10.7. The next question to be asked of these data was, "Does there exist significant heterogeneity among the variances in the mother-father cells ?" The residual mean squares for the sixteen ex- posure cells within males-Hiroshima are given in Table 10.8. Bartlett's test (cf. Rao, 1952) of the heterogeneity of the variances is not

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138 Genetic Effects of Atomic Bombs Chapter X vat ~ ~_ [~=,` ox ~ 1 1 1 1 1 vat x in 0 rat ~^ cat ~ O ~ 0 ~ ~ x l_ 65!~ X ~ ~1 1 1 1 ~ cat X 0 ran 0 ~ ~. ret 4J cat ~ ~0 R ~ rat I I I I ~ I_ 7 c', on 1-A\ C;x At; ~ ~ ~ 1 1 1 1 1 8 ~O ~ ~ ~ ~ Q ~ ~ ~ ~ ~ o ~ ~ o ~oo ~ ~ X ~ c,\ - To , ~ ~ ~ma, ,, ~ . ~ ~ ~ o o ~ ~x-= ,a ~ -~- ~-~- ~ on ~ ~ ~ ~ = - Cal O ~ X O no ~ to 0,) 7 1 1 1 1 ~ ~ ~ red TO To =^ = X X x a = 0-~ ~<~- ~. ~ <, .< .- ~ ~ ~ oo r ~ ~ ~ ~ c 1~,- _ C~ ~ O ~ ~ C~ ~ ~ O _ 11 I! ~ ~ ~ ~ ~ ~ ~._ _ D I | | | ~~^ - - ~ A ~ ~ \0 ~ \0 ~-~- ~11 11 11 x cx v~ ~r ~ ~ ~ ~ ~ ~ ~ ~ ~X ~o ~ O ~ v~ oo ~CO r<~ ~ v ~ ~ l~ v~ ~ ~ ~ x ~ ~ ~ ~ 0^^ ~ a ~ ~ 00 ~ ~ ~ Oo O O O 0 - 0 ~10 ~ ~ ~O O O O mc`~= 1 1 r~ ~ ~ r~ ~ O ~ 00 ~ ON ~ ~ ~ . ~O ~-~ CO ~ ~ +0 - ~ O ~ ~ oo ~ O4 r<\ 1-CO ~ ^^^ ^^ ^^~ ~_~ cO _~ v~ r- ~ 00 0 oO a - \0-X ~ r~r~ ~ m ~ ~ ~ ~ -~, ~ ~ ~ ~ ~ ^0= ^^ ~ 0~~ r ~ ~ w ~- o^m o^~~o== 8 B ~ ~ ~ ~ | I - ~Cx ~CN Ov~1- - 0,0 ~ O x ~ ~ ~ O X ~ oo td {~3 ~T~ 9 x - ~ ~ ~= ~ ^ - ~ v ~ w -~ ~ ~ ~ ~ ~ ~ ~c ~ _. _ _ _ .2 X ~ ~o oo G~ ~v~ E ~ o ~ c~ 0 oo ~ 0 ~o ~ ~ ~ ~ ~ ~ ~O ~ ^~0 -~= ~a - ~0OO~= ~ z N ~ oo ~ ~ ~ ~ 1- ~ ~0 1 1 ~ C~ t) Z ~ ~ ~ X ~ ~ ^ ~x ~ ~ o ~ a~ r~ r~ - W ~ ~ m. ~ ~ c;` ~ ~ r~ \ ~ _ c~ C7~ ~ 0\ - 0 C ~; X ~ O C~ ~ x~xo r~ a)- O ~a'c~x~ ~0 _ < ~ 0 ~ O ~ ~ _ ~A ~ ~ ~ ~ ~ ~_ - W \ ~ C~ -~ ~ c~ ~.o {~. t.A, _ ~ 0 ~ ~ - ~ o~ ~C` ~r.1 ~ ~ oo '_] oo r~ o ~ v~ r~ ~ c~ l- ~ 3~ ~ ~ ~ ~ ~ om ~ ~ ~ ~ ~ ~ ~ W ~ ~?- <~ ~ ~-` O~ I_ ~ ~Ci~ ~ ~ ~ CN ~ ~ ~a' o ~.... ~ ~ ~ ~ ~ ~ o ~ C" uA, . . . . er1 K ~ a) ~ ~ v~ ~ 0 ~ ~ O ,_1 ~ ~ ~ ~ O 0 0\ o0 S L4 W ~ X ~ \0 Cx ~ ~ 0^ ON ~A, . ^~4 ~Y ~ ~ oo~ 0_ ~ c;` ~t ~ ~o~o ~ ~_ ~ _ I_ ,= N~ ~ o~ o~ ~ ~ o ~ -~ N c~ ~^ ^ ^^ ^^ ^ ^ ^ Ct W ~ ~ ~ ~ ~ O -' \0 V~ r~ . . . . . . . . - ~ O ~ _ O '~ ~ ~ ~ ~ ~ ~ ~ ." ' R~ ~C. - D 11 11 : ^x 1 1 v~ ~\ c~ ~ IOl o O O ~ c~ ~o C~ ~\ Gs cx _ ~ r~ I 00 G~ cr ~v~ r~ ~0 o oo oo aN U~ r~ ~ 00 oo Io oo o ~ ~V~ ~, ~ G ~- o ~ o - . . ~A. . . o - . . X . . . a' . . ~V~ =:::: + o 4 | l~e t) IN ~ 1 1 1 - x B N 1 ___ 11 11 11 a 1 x 1 ._ ,^ cr, G~ o. . ~ ~,~ Ol O 11 11 11 c ~ ~ ~

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The Analysis of the Birth weigh Data 139 significant. Thus when all exposure cells within the males-Hiroshima cell are considered, the only evidence for an association of birthweight with parental exposure is the heterogeneity of the individual cell regressions. But, this associa- tion is neither consistent nor does it persist to a significant extent when the category 1 parents are excluded (see Table 10.5c). Before we summarize and consider the possi- ble interpretations of the findings on the males- Hiroshima data let us turn to the remaining three sex-city cells. Tables corresponding to those for males-Hiroshima are given for fe- males-lIiroshima (Tables 10.9-10.13), males TABLE 10.8 THE RESIDUAL MEAN SQUARES FROM THE INDIVIDUAL CELL REGRESSIONS: MALES, HIROSHIMA (The degrees of freedom are given in parentheses.) Mothers 1 2 1 J1,747.87 1,649.29 )(8,669) (2,711) 2 {1,777.14 1,783.05 =O ~ (740) (894) 5 311,849.41 1,957.12 ~ (291) (186) 4_512,382.73 1,968.26 ~ (195) (110) Bartlett's test for between-cell mean squares: %2_ 20.43 3 4-5 1,768.00 1,595.93 (1,061) (537) 1,738.38 1,876.84 (215) (104) 1,798.85 1,764.54 (252) (44) 1,598.47 1,609.30 (73) (51) heterogeneity of DF 15 Bartlett's test for between-cell heterogeneity of mean squares when category 1 parents are excluded: %2 2.12 DF 8 Nagasaki (Tables 10.14-10.18) and females Nagasaki (Tables 10.19-10.23~. In none of these three sex-city cells does the analysis of variance on the adjusted data reveal significant differences as regards mean birthweight between maternal or paternal exposure categories or evi dence of heterogeneity as judged by the interac tions. In Table 10.24 are set out the principal findings with regard to the four sex-city cells. From this table when all exposure cells are considered we note (a) significant heterogeneity in the individual father-mother regressions in two of the four sex-city cells, (b) a reasonable measure of constancy in the amount of variation removed by the common regression in each sex city cell, and (c) significant heterogeneity be tween the residual mean squares within a sex _~ 0 ^m coo ^~m arm om O ~ 0 ~ O 00 ~ ~ O _ ,_ ~ ~ x ~ ~ m^~m ~ ^m ~ - _ m=m D~ o ~ in ~4 ~ ~ ~ ~ So ~ lo O _. . . . . . . . . . . . . . . . . 1 1 1 1 1 1 1- 1- 1 1 Vat Cut 1 so ~ ~ to ~ ~ O Vet ~ ~ ~ ~ ~ ~ ~ X O oo (X\ ~ m ~ ~ ~ C:x ~ ~ Go- ~C4 ^' ~ ~ Cat- ~ -~ Cat Go O X x ~ ~ ~ ~ ~ ~ 0 ret ~ ~ ~ ~ 0 0 ~so ................ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 _ ~ _ ONE ~ ~ ~ vet ~ = - O red cat cat O ran ~ Cat \0 ~ O ~ O ~ ~ ~ ~ _ ~ Cx ~0 ~ a ~ Van ~ Van ~ O O ~ ~ Cal _ I_ Van _ X C; ~ ~ ~-I O tm Cx 1_ ~ X ~-~4 O \0 1-X ~ ~ of red ~ oN no (~ ~ (~ A - ~ _ _ ~ ~4 A: - o ~0 CC O Van ~-\0 CN ~ ~- ~ ~ Cx ~ ~ Vet red O X ~ ~ ~ Van O O WE \0 ~ Cx ~ X ~ O _ van -~ X X Hi ~ 1- Cx ~ Van ~ X ~ ret X O Ox m~ X\O ~ O red _ ~ _ _ JO van - ~ - - - -~ - m=~0 00 =~0= Or No ~ ~ _ rut ~-O ret ~ ret O rat ~ ~ Cut van ~ X ~ ~ vet vet ~ vet ~ so ~ ~ van I_ X ~ X _ v- - ~ ~ ~ ~ ~ _ _ _ ~ ~ _ _ _ 0 ~ ~ ~ vet ~ ~ red ~ ~ cat 0 0 ~ ~ O so or-~ ~ ~ ~ vet vet ~ O O ~ ~ _ . . . . . . . . . . . . . . . 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B 0 W B W a cat ~ ~ ~ ~ ~ ~ 0 0 Van ~ or ~ _ 0 co so ~ m . . . . . . . . . . . . . . oo co ~ ~ red ~ red ~ ~ US 0 0 of ~ 0 Al-or:) C\~ v~mo 1 ~ ^~m cut oo ~ 0 cat ~ ~ 0 ~ rat ~ I ~ ~ 0 o ^~ - ~ + - mm 1 _ van ~ r-~ C;` ~ O cut ~ ~ 0` 0 0 1-~ ~ ~ ~ Cat ~ ~ O ~ ~ ~ ~ O O O ~ ~ O rut x ~ oo of ~ ran 0 ~ ~ In so ~ ~ ~ fir t_ of oo 0 _ ~ rut 0 ~ ~cat W~ ~ ~ ~ ~ ~ ~ ~ ~ ~ so or o. cat ~ 0 _ . ~ ~ ~ ~ l~ ~ cO ~ ~ 1-~ ~ ~ ~ ~- ~ Vet 0 X 0 ~ Pro ~ ^^o ~ ^~ COO of ~ ~ 0 ~ 00 ~ ~ No ~ ID 1-~ van _ I_ 0 oo van rot ~ x co co ~ ~ ~ Cow \ O _ O V-0 Vet - Cot - ^m 0 X ~ ~ Cat _ ~ ~ ~ ~ ~ ~ ~ ~ ~1 ~ _ ~ _ ~ ~ to ~ ~ ~ ~ r`~ ~ 00 ~0 ~ X ~ O 00 C;` ~ ~ ~- ~ ~-beg ~ 1- _ ~ ~ van 0 ~ ~ ~ ~ ~ _ c4 ~ X ~ O oo I ram _ cow Fix 00-~ ~ ~ ~-~ ~ ~ 1 - _ \0 ~ red \ rut ~ rut ~ red oo 0 ~ _ ~ Cx ~ t~l Cut W\ A ~ _ ~ rip ~ 1 ~ . 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' cut vet l ~van van _ Ci' ~ ~ ~ ~ ~ _ Hi ~ ~ ~ ~ I ~ ~ ~ ~ ~ ~ ~ ~ I I I

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140 o _ . a: m .0 0 ~ - - - V) - ._ o no, ~2 CO I c o ._ Cal 0c 4 o C C = V' o 1 z o ~ C.~ O Ed O - [Z4 Z- O Z O PA Z ~ ~ `.Y z _ ~ Z ~ ~ En _ A: 5! X En o En Cal lo - o - * * \0 ~c' 1 Cal - C o V, - in X - - - V, o ._ as Vet 00 O I ~ Vat \0 .O C . . o :: ~ . . O . . 0 "S . _ . it, U) ~ 0 0 0 D V) ~ ~ ~ 7 D o o.= - C~ ~ ~ q) .~ ~ B .0 cd cd ~ - >= 0 ~ ~ 00 V) oo e~ ~ o~ G~ 0^ ~ O GN ~ 1 00 V) r~ 1 . G~ ~ 0 C~ r~ ~ o^ - 00 v~ - ^ 0 : . _ .~ 8 ~ ~ ~ ~ o =7 <,, o -.5 ~ cn Ces CJ- Ccd ~ ~ - ~ Q" ~ ~ Gerzetic Efects of Atomic Bombs Chapter X O1 1 1 1 1 c ~ ~0 c'' . _~ ~ O _ 2; x0 _ v~ \0 v~ c~ Q V~ ~ o. 1 ~4 V~ . . C~ oo oo ~ _1 X C~ o x cn ~ 1 1 1 ~: Gs 00 C~ . . ^+ 1 1 1 1 - ~ ~ l l l l o . . c~ z E" ~ oo moo x \ ~ oo ~ f~ ^ ~ ~ mmm ~ WO ~ C' ~ w ~ xoo ~ z w~= o z w w . ~ - 4 c~ - ^ . . v) o ~ - v) ~ ~ =, 7 ~ c) c 0 ~ ._ cn ~ ~ ._ ._ a) ~ c~ Q) ~ I: ~ c~ - - - o - m ~ w O ~ r- m ~ ~ O \0 .` x ~ _. ~ r~ x 00 v~ _, - - O 00 G~ ~ ^ ~ 0~0 _ O q. O ~4 ~ O ~.. ~ x ;^ ~ ~ x ^ r~;r ~ ~ ~ ~4 ~ Cx' ;~ oO ~ O W ~ ~ I_ O - = O oo O ~ _ ~ ~X X 1_ V~ e _d _ P W ~ ~ ~ Q V~ ~ o o V~ . . . . . C o V) _ C C) C C ~ ~ ~ ~ ~ c m ~ . . . 1 1 1 1 c o . 1 1 1 1 1 ~ OC c' ;^ ~Q P O ~; v ~ O q) c I_ , ~ V4 v) c~ 00 ~ ~_ O :' ~, x ~ O ~ c~ ~c \0 0 ~ r~ cx ~ .` O v, =~ - ~ 1111 r~ C~ '! O ~ ~ ~ . . . . . \0 \ v~ ~ ~ O ~ O x ~ m^m ~ 00 ~D ~0 \0 ~ \0 ~ ~ ~4 ~ cx ~ r~ r~ 0 o~ V~~ r~ 0\ cx x - - _ ~ ~ _~ _1 v~ ~ v~ v~ v~ x - - 0 r~ x ~ x x O 00 0 ~ ^ ~ ~ ~ ~ O r~ O ,_ r~ cx ~r v~ oo ~ a' v~^ c~ x ~ r~ oo _ ~ c) r~ oo \0 :: ~_ 00 ~ ~ ~ v, c4 c _` ~ ~ c, . ~ ~ CN CN k0 td ~ =~ - c`E o-~~ 11 11 ~o ~ ~o ~ P o ~ mo Cs C~ V~ A _ ~ _ ~0 ~ V~ V~ C~ X X V~ Cs V~ ^- ~ _ _ _ ~_ Ox \0 0 \0 ~ C~ \0 1-~0 C~^ ~ +~0 Cx X ~ ~ - ~4 X ~-\0 ~ V~ ~ ~ ~ V~ O ~ c4 0 ~ ~- X ~ V~ _' O ~ ~ r~ ~ X =~ 00 _4 r~ 00 C~ ~ C~ O ~ O ~ O Cx ~ O O ~ O O O O ~^ ~ V~ _I . . . . . . . . m~_ ++~+ ~c 0 . B ;^ , ~ ~ ~ . _ - C~ 1111 :^ X

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The Analysis of the Birthweight Data TABLE 10.12 THE ADJUSTED BIRTHWEIGHT MEANS: FEMALES, HIROSHIMA x w z Ax Aw 141 - y y /`z unadjusted adjusted R Father's exposure 1 2.413 7.942 26.991 - .138 - 1.023.397 303.374 303.769 2 3.157 13.548 28.979 +.606 +4.583+1.591 304.619 302.899 3 3.068 12.710 29.124 +.517 +3.745+1.736 303.424 301.959 4 + 5 2.852 11.138 28.573 +.301 +2.173+1.185 306.350 305.543 Mean 2.551 8.965 27.388 303.615 303.615 Mother's exposure 1 2.414 7.910 27.074 - .137 - 1.055 - .314 303.539 303.929 2 2.771 10.694 27.913 +.220 +1.729 +.525 304.324 303.727 3 2.779 10.623 27.870 +.228 +1.658 --.482 303.088 302.362 4-t 5 2.694 10.117 27.724 +.143 +1.152 +.336 302.176 301.805 Mean 2.551 8.965 27.388 303.615 ay adjusted _y unadjusted-box-b2/`w-buzz. b1 _ 8.620 Ax = (xt - x) b2 - 0.662 low two - w be - 0.295 ^2 = (~ z) TABLE 10.13 THE RESIDUAL MEAN SQUARES FROM THE INDIVIDUAL CELL REGRESSIONS: FEMALES, HIROSHIMA (The degrees of freedom are given in parentheses.) Mothers 1 2 3 cat cot Let 1;l,617.30 l(7~995) 2 J1,645.67 ~ (696) 3 t1,769.35 l (262) 4 5il,s60.2s ~ (171) 1,566.69 (2,424) 1,782.13 (870) 1,300.74 (177) 1,277.68 (114) Bartlett's test for between-cell heterogeneity of mean squares: 4-5 1,621.86 (522) 1,733.04 (85) 1,569.98 (51) 1,417.02 (54) 1,678.38 (1,028) 2,210.23 (194) 2,155.90 (242) 2,151.95 (71) %a=51.216** DF=15 Bartlett's test for between-cell heterogeneity of mean squares when category 1 parents are excluded: %2=26.156** DF 8 x = parity w_ parity squared z = maternal age

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142 _ ~ tic rut O x 0 0 c _ _ ~ _ ~ us vat ~ ~ Gs ~ X ~ l_ vat O ~ ~ ox x _ coo ml~= or mo us_ five Gs O ~ ~ ~ ~ V~ CN ~ ~- 00 ~ V _ m~ ~ ~ ~ O . . . . . . . . . . . . . . . . 1 1-~ 1 ~ 1 ~ 1 ~- ~ ~ oo x ~ ~ oo c~ ~ ~ ~ ~r oo v~ CO ~\ ~ -~ ~ ~ ~ X 1-~ ~r - ^ _ ~ O x O ~ _ -= ~ ~ ~ ~ ~ O - 00 ~ mx ^~ - ~ 00 0 - ~_= . . . . . . . . . . . . . . . 1 1 - 1 1 1 1 - 1 -~ 1 - 1 x ~ 00 u~ 0 0 r~ ~ ~ v~ ~ ~ ~ ~ ~ ~ ~ l_ ax v~ _ ~ O ~ O O O ~ ~ ~ c m ~ ~ ~ O ~ ~1 -- 1 - 1 ON v~ - x Genetic Effects of Atomic Bombs Chapter X r~ 1 c~ x 1 u~ _~ - l_ _ - - x ~ 0 +~r ~ ^w ~ ~ mmo ox'-0 - ~r~ ~ ~0 0 . . . . . . . . . . . . . . . .. m x V~ = oo r~ ^ \0 ~ X t-~ ~ = 1- ~cO ~ _ 0 r~ ~ ~ r~ oo ~ ~r x c~ ~ ~ ~ ~F4 1 e ~ ~r ~ x ~ ~r ~ x-x r~ \ ~ ~ o v ~c: W m\ x ~V~o ~xo-~-o~o ~eq ~a' v~ 1` _ 1-r~ ~ oo ~ x 0 _ ~ 0- - 1-~ r~ r~ ~X _ r~O ~ _4 ~O ~ _ ~ X ~ X ~ ~ -- ^= ~ ~ ~ ~ O - ~ - ~ 0 ~ m~ ~ X" ~ ~ ~ XO ~ cr~-- ~r 0 0 _ oo O - = ^xo~ ~ ~O c ~X O ~ G~ O ~ ~r ~D ~ O ~ ~ ~ ~ ~r ~t r ~0 o~ 0 r~ m~ ^--~r _= r ~_ c~ , ^ , ~a~ v ~4 - N ~1 00 0 - - - ~O s~ ~r rn ~e~ 0~ 0 ~-~-0m 0 v--_ ~ 0 Z o ~ ~ ~ _ ~ x cs ~ ~ ~ ~ ~ 0\ ~ O v ~O _ X ~ ~ O X ~ ~ ~ _ O l_ _ _ CJ cn ~ :^ a~0xo ~ ~-+ r~ V~ X a~ ~ c~- ~r ~ t4 c ~ W ~ ~ ~ ~-X- 1 ~ ~ ~ ~ ~ ~o mm.~^ m~ 1 ~ 1 ~ ~ v ~o ~C ~ ~ c ~ ~p: ~_ X r~ C~ ~ ~ X ~ ~ O CS ON X ~ V~ X O ~- C. ~V V > ~- - a) x ~ ~ - ~ m_m ~r~ ^~r 0 ~ ~ Z x ~x_r`xo~~`o~rx - - ~11 I' E ~u W oo c\! ~ ~ o ~ v~ ~- 1 ~ ~ ~- 1 v ~ ~ ~ CO p v~ _ ', ~ ~ ~ _ _ ~ I t~, N [.14 ~C _ ~O a' V~ ~ r~ V~ _ CN ~ ~ r~ ~ ~ ~ ~ X O m _ ~ ~ ~ +- ~ ~ ~ ~ ~ ~ -= O ~ - = m ~ c~ x x _ m ~ x 0 - ~ _ ~c ~N C~ ~ ~ ~- ~ _ ~ \~ ON ~ ~ O ~ O Z O W X r~ ~ ^~0 ~ r^ - X X 0~^ ~ ~ ~ ~r ~`~; _ o r~ x ~x ~ _ c~ r~ v ~ ~ ~~ ~v, 7 S! c~d ~=~ - oo~ooox~a)cx= - <~ O a ~ _ ~ ~x =-0 ^00 +~=x += ~ ~ ~ ~== - ~ 0 ^~= mo o ~ +0 ~ ~c <: x x v~ ~ x x 00 ~ ~ ~o ~-~ ~ 0 ~ ~v ~ ~0 O W x 0 0 x ~ ~ ~o-~ ~ ~ ~ ~r ~Z V mO _ v ~ -t 0 ~ ,~ ~ 0 r~= ~ ~ ~ ~= ~ 0 mx-- ~ Z c ~ x ~ _ ~ ~ v~ O ~ ~ ~ ~ ~ \0 v~ ~, _ ................ . . c ~x ~ ~ ~ ~ ~ ~ ~ 0 0 c~ ~ ~ ~ _ x `^ . v p: ~, ~--~OO-=~mmmm ~_ - - = ~-x ~ 1 r`~ - ~ ~=, ~ o~~0~m ~ - m 1 _ ~, Z ~o O ~ ~ ~4 ~D C ~ ~ 1` ~-X X ~ ~ 0 ~14 ~ ~ v~ ~ ~1 0 ~Ct ~ r~ 0 0N X ~ ~ 0 \0 ~ ~ ~ oO ~ ~ \0 ~ X ~uc - 1 ~v-~ 1~ l_ ~ V~ 0 C~ ~ m ~ ~ O ~ O ~ ~ ~ O ~ = - ~ ~ ~ ~ ~ ~ m" ~p _ - W ~~~ V~ o^-I_ V~ X ~ ~ ~ ~ ~o-~ V ~u4 C~ X ~ ~ O ~ ~ ~ - - _ r^~ ~ ~._ _. ~ _ _ r~ cs ~ ~ ~4 O c. _ ~cn ~: x a' ~ ~ ~ _ ~ ~ x ~ ~ ~ X v~ ~ ~v, ,,^~= ~ cr`~r ~ ao 0 ~ - = 1-r^= ~ rx O t.Z.] r ~. . . . . . . . . . . . ~ . . . ~r . ~ X ~ ~ =4 Q ~ O ~ ~r ~ X X 0: ~ _ 1- ~CN ~O ~ - 1- = - O ~ O ~ ~ O ~- ~ ~ - W ~ ~-~ ~ ~ I~ O-V~ _ l- ~ O" ~ _ ~ ~ ~ r_ V~ ~ _ v~ v~ ~ ~ r~ _ ~_. v, ~o O ~ Cx r ~O _. ~ ~_ ~ ~ ~ ~ \ r~ r~ X r~ ~ X X ~ N ~ ~ eO ~.:.l _ =~ xo=~-or~o~v~mr ~cd . . . . . . . . . . . . . . . _ C~` ~ 0 ~ ~ ~ r~ ~ X ~ ~ I_ ~ c~ ~ _ . _ ~ ~ O ~ ~ X v~ X 00 ~ u~ oo v~ ~ rrY 1 ~ v~ O ~ ~ ~ ~ _ ax _ ~ e~ 1-Gs ~ G~V~-0= mo~r x o~ _m t_ _ ~. 00 ~ x0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ _ 00 ~ c~ ~ ax o" _ ~ ~ oO~ O ~ ~O t~v-` co ^ c~ I~ ~,~ (~ c= c~ == 1 =O - - G~ \0 v) ~ oo ~ ~ ^~ ~ ~o c . - ~, ~r oo ~ v) o - == c~ ~ - ~ ~ oo - o o v ~ve oo ~c c~ oo ~o r' ~ ~ - -~ <, ~- u, a~ ~ ~ ,1) -, . . ~ . . . ~ . . o . . . . .- 41~ c~ v, ~ - o ~ ~ c -c o ~ me=.~ ~o c Cd ~ _ ._ ~ ~ ~ _ ~= 1 cO ~ GN ^ o~ oo c;x ~, ~ ~ m~ ~ a) . . ~ oo v, v~ c7~ ~ : . . . : _ 0 ._ v, _ ~ ~ c 0 c {~, m ~ Q~

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The Analysis of the Bintweight Dam 143 Vet Vat ,, _ m ~ o Cal . . . ~ ~ _4 or ~ vet 'I ~ X CZ,, ~ ~ Cx en. Cat L Cal o of o - ~ _ ~ C`3 ~ ~ 1 1 1 . . ~ 1 1 1 1- x . . CO C~= C] ~ V~ ~ W ~ ~ ~ ~ ~ W P ~ ~ W ~ F o ~: X ~ V~ X ''- W -mm o ~: 1 1 1 1 1 1 1 1 o ~ 1 1 1 1 1 C C) oo C~ _' _ ~ mm :^ . .. . . ~ ~ X 1 V~ _' ~:- ~ 00 ~ =~= 0 3 cx c~ OX c~ c~ c~ v) ~ O V~ Gs . 00 cN v4 v O ~ r~ oo _ ~ ~ ~ ^ ~ c~ r~ ~ 0N- :' 0O 00 x x ~. 0- ~ x- l_ ~ r~ ~ r~ 11 11 cr, v ~I ~r 0 o 0 X ~ ~ X 0 0 ) ~o ~ C~ ~ ~ _ ~ Cx 0 ~4 ~ C~ ~ O X ~ ~ ~^ ~ ~ ~ _ ~ ~ 0 ~ oo _ _d ~ ~ _ _ _ _= r~ _ 0 ~ `= r~ ~ 0 ~ >- ~ ~ ~4 X -0+ W ~ ~ _ ~ o - m _ O >q c~ ~ O \0 ^ w I ~ ~ r~ ~ O O N W ~ -~ X ! W - . ~ G~ ~ o om ~O ~ ~ W _ ~ ~ . . . . C o o ~ ~ ~ .~ ~m C m~ 1 _4 C~ ~: V ~: - C~ ~ ~ t_ _ C;N r~ c4 o- ~o ~ cO tC mo ~ ~ o x ~ ~~ a~r _ V~ V~ ~ ~ ~ CJ V~ ~ Ct~ c~, X ~ (~ ~ oo ~ oo X _ _. _ _ ~ V) - ~C C~ ~ ~ o~ ~ ~ ~ (~, ax \C, ~_ ~ ~., 4) td Ct r. ~ t_ c~ - l- ax l_ oo oo ~ - ~= 11 11 oo ~ ~ '. '' r~4 r-~ N \0 V~ ~ ~ V~ V~ r~ ~ ~ ~ V~ ~r ~r x ~r 1~ X ~ C;~ X ~ O ~r~ ~ mx r~ r~ ~ ~ _ _4 _ _ _ X ~ 0 - - ~r o== r~ c~x~r 0 -~ X 1 - 0\ V~ O ~ O ~ G~ 00 ~ ~ ~ ~ l_ cc ax ~ ~ ~ r~ _ ~ ~ ~ ~ ~ S C ~ ~ ^ ^ ^ ^ ^^ - 1- a~ cx ~ G~ _U ~r - ~= ~C O X ~ O C ~4 ~ O D C~ ~ ~ ~ ~ ~ ~ 1 ~ 1 _ x CN~ ~ ~ 11 11 oo ~ ~-~ ~ -O ~-~- ;^ X ~r 0 x a> - v~ ~ r~ \0 _ ~ _4 _ . . . . . . . . . . : ++++ I G~ ~ ~ C ~N ~ ~ N o ~ ~ ^ 0 v ~ ~ oo ~r . . . . . ~, ~ U~ C~ oo \ o V~ N~ ~ _~ 00 V~ . . . 1 ~ ~ ~ . . Z ~ a E~ ~ ~ c~ x E~ Io U~ o x ~ ~ r~ 1 G~ V~ oo oo o o o oo C~ ~ C~ ~ a~ ~ oc ~o ~ ~ 00 ~ U~ ~r X .... ~. . . ~ . . o X . V) . . ~. . . :+ ~ , - = 11 1 1 1 1 1 ~ o ~ o 1 o. ~ ~ o. 1 - I x 13 IN 1 1 1 1 1 X ~ ~ 1 ___ -~ ~o~ ~ 11 11 11 ~ oO GN 0Or~ _ ~ ~ N ~ ~ ~ 00~ `: a a a - ~m ~ 1 x v~ ~00 oo v~ . . . .. ~ ~ ~ _,~ I ~ ~ r~ o C~ . . . . . =:: V, . . o ~: C) . U~ ,. . . . + o ~ ~ ~ ~ I ~r o . 4 - . cd c V~ Il a~ ~c~ ~ 1' ~ 0 0 . G~ : ~ 11 11 11 C ~ ~ ~= `

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144 Genetic Effects of Atomic Bombs Chapter X cut v, a: ._ ~ ~ 1 > em a) ~ o a:: - 0,0 0 ^ ~ _ Go ~ 0 ~ O _ up of ~ 00 O _ ^ _ 00 ~ ~ cut ~ ~ 0 - idle DO ~ ~ _ ~ _ o . 0 ~ ~ ~0 - aN ~ ~ _ 0 _ vet _ . ~ a_ cut ^ ~ =4 0 ^ ~ _ Go ~ ~ ~ O ~ O 0 ~0 0 0 or ~ 00 ,_ ~ _,^ ~ ~ ~ _ _ HI _ ~_4 e<, Or , ~ so - C~ % =~ oo~-~ O ~ a) ~ 0 ~ ~ ~ oo ~ ~ c~ ~ ~ ~ r~ ~ ~ ~ 0 X 0 Oo ~ ~ ~ v ~ed r~r v~ ~ ~ ~ v~ O ~ ~ 1- ~ v~ I ._ ~ e4 r ~^ ^ ^ ^ ^ ^ ~I r~ ~ 1-~ ~r ~ ~ ~_ - = - = 11 ~ ~ ~ ~,.~ C r~ 0 ~ ~ ~ ~ oo ~ ~ oo O ~ ~ ~ ~ ~- c.~ r~ O ~ ~ ~ ~ ~ ~ ~ ~ O ~ ~ ~ N0 ~t~ cd . . . . . . . . . . . . . . . . _ ~ ~ u~ ~ ~ ~ ~ ~ ~ ~ ~ ~ O v~ ~ ~ ~ ~ ~ . x ._ ~ oo 1-~ 0 c~ ~ ~4 ~ ~ ~ v ~11 1 r^T r~ ~ 00 ~ ~ ~ ~ ~ v~ ~ C~ ~ 00 ~ I ~I I ^ ^ ^ ^ ^ ^ 1 1 ^ ^ ^ 1 1 ' ~3 N 0 +~r c~= m~ ~o mo ~ =- ~c~ 0 ~ ~ ~ ~ 0 ~ ~ ~r ~ ~ 0 ~ ~ ~ ~oo . . . . . . . . . . . . . . . . O ~ ~ ~ O m~ ~ ~ ~ ~ ~ \0 u~ ~ v~ ~ 1_ 00 ~ ~ ~ ~ ~ 00 ~00 l_ ~ v~ ~ ~ ~ ~ ~ ~ v~ O 0 ~ ~ ~r ~ ~ ~ u~ ~r _t N~ . . ~ ~ C~ W ~ 1- r~ ~ ~ ~ C~ ~ ~ ~ r~ I_ ~ ~ ~ ~ ~ ~ -1 ~- ~ C~ ~ \- N~ ~ ~r ~ ~ c~ ~ ~ r~ ~ ~o ~i ~ ~ ~ 0 ~ CC c~ C4 ~ ~ ~ v~ ~ ~ v~ ~r h~ ~ ~ r~ V~ 0 ~ oo 0 ~ _. VS o^ U~ 0 +, u~ Cx ~ I~ ~ G~ v~ Cs ~ ~ ~ ~ 0 ~ ~ ~ ~ ~ 1- . . . . . . . . . . . . . . ~r ~ ~ x ~ ~ ~ 0 oo O Cx ~ O ~ Cx 00 ~ ~ - 00 c~ ~ 0 0 I_ ~o r" ~ ~ ~ oo 0 ~ - ~xr ~ cx~ ~ ~ - = ~ ~ ~ CN X 1 1 ~ ~ 1 1 1 G~ ~ ~ ~ ~ o v~ r~ ~ 1_ ~ r~ ~ ~ ~r ~ ~ r~ 0 ~ ~ r~ ~ O . . . . . . . . . . . . . . . X ~ ~ ~ ~ ~ ^ - 0 0 . ~ 0 0 ~ ~ ~ r~ 0 V~ 0 I 0 ~ c~ oo ~ ~ ~ ~ ~ a: r~ cx ~ v~ ~ _ ~ ~ ~ v~ = X _~ ~ ~) ~c C`.D o 3 ;~ ~,~ ~ G~ ~ C~ \o 11 11 X ~r

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The Analysis of the 13irthweight Data 145 ~ ~ fir 00 0 0 =0~ . . . ~ ~4 ~ 0 r`= ~ vet cot . . ~0 O of on - E~ ~cat v ~ a: 0 m ~0 0 cat Z e,.o cot v ~ =4 4 ~ X C C~ [L. O ~= O ~ C ~.= ~V, C~ ~4 o ~4 r ~ ~- * * co m~ 1 0 - v~ G~ 0 - 4~ ~ _ - - o X - Ct - C~ o _ V) . ~ ~ o :^ _ : 8 o . o . ~ ~ o o =d 4- ~ V) ~4 C) ~ tJ O . O C~ ~ _ ~ B ~ _ C~ ._ ._ >~ oo U~ o ~ U~ o = - V~ U~ * oo ~ ~ 1 C) ~ o :: o - ~4 ~ ~^ ~ _4 _ _ '` _4 =0 00 ~ m_ O ~0_O ~d4^ - ^ ~ ~ `= U~ ~O _ ~ :: m~ 0C 0 a-~ Q, s~t X : au :: ~ ~4 . . O . . :~ . . ~ . . . . . O .~ ~ .O _ C) C) ~ ~O O .~ ~ - 4 ~J ~ ~ _ ~ ~ ~- C) C~ _ ~ -1 1 1 1 1 1 1 1 1 1 1 1 1 Q ~ 0 ~ ~ I I 1 1 1 * ~ ~ ~ ws c~ ~1 1 ~ - . 1 .5: ~ c~ ~4 _4 c, ~ ~ ~>~ L7 ~1 1 1 1 ~ =. ~ ~ U~ ~c ~tm ~\ O ~ ~ O ~ ~ ~ ~ -4 ~4 N 1 1 1 1 0 ~ ~ ~ ~_ - GN O ~I C~1 ~O C ~ - ~= Z ~ ~ ~ ~6._ ~4 ~O O ~ 0 - O 1- ~Cs N N ~ W ~V~ ~ X 00 0 V ~C' \O _I \0 00 =. ~ W - - ~ o ~ 0 ~ ,_ V) V~ 00 ~ ~ ~ ~ ~ ~ ~i O ~04 ~ O O O 1- 00 - = ~0 ~ oo a' oo [L7 ~r~ ~ ~ ~ v~ ~ v~ r . ~ ~ oo C~ ~ ~ ~ V~ cn W 1 ~ ~ ~ ~ oo 0 ~ ~ ~ C~ X W . . C O ~ ._ _ V, ~ .C (~) .C ~ C ~ C O ~ ~r c' ~ ~ ~ ~ V~ ~ ~ _ _ - _ ed ~d G~ ~ =~ - ~ C V~ ~ ~ =xr - = 11 11 ~3 N 1-~N~ ~ 00 ~ ~ 0 - N 00 ~ 00~ ~4oo ~ -~ ~ ~CN-~ -~ ~J -~ ~\ ~- ~^ ^~ ^ ^ ~ rAl O ~ ~ ~ ~ ~ ~ _ ~ ~ ~ ~r c~ ~ oo u~ a: ~ oo ~ r` - ~ ~- ~ - X V~ ~ ~CN 5 ~C) ~ ~V~ ~(X) CC ~ Co t W ~ ~ ~ ~ ~ ,_ ^ CJ) =4 ~ ~`,t~ t-~ ,r, ~_ ~ ~ 3 .` _ ~ t~, _ ~ ~oo o Cx ,_ _ NC0 _,_. _, 1~. 00 ~ 00 CO D 5^ - - - _ - - _ = ~ ~ ~ O C~ ~ ~ ~ V~ Cx ~ CN O Cx ~ X _ _ _ - _ 00 ~ O O _ - - _ - U~ V~ 1 ~ _I _4 _I . . . . . V~ O - . . C C =~ tV '- + ~ a:> >~>

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146 Genetic Effects of Atomic Bombs Chapter X TABLE 10.22 THE ADJUSTED BIRTHWEIGHT MEANS: FEMALES, NAGASAKI Y Y x w z Ax low Liz unadjusted adjusted a Father's exposure 1 2.820 10.848 28.093 -.191 -1.689 -.480 303.391 303.858 2 3.664 18.379 30.200 +.653 +5.842 +1.627 304.339 302.774 3 3.475 15.960 29.842 +.464 +3.423 +1.269 307.781 306.317 4 + 5 3.305 14.790 29.311 +.294 +2.253 +.738 305.168 304.266 Mean 3.011 12.537 28.573 - 303.690 303.690 Mother's exposure 1 2.916 11.547 28.579 -.095 - .990 +.006 303.384 303.608 2 3.110 13.574 28.606 +.099 +1.037 +.033 303.677 303.457 3 3.229 14.472 28.542 +.218 +1.935 -.031 307.910 307.212 4 + 5 3.011 12.756 27.875 0 +.219 -.698 304.023 303.936 Mean 3.011 12.537 28.573 - - 303.690 303.690 a y adjusted = y unadjusted-box-blow-buzz. b1 = 7.846 b2 =-0.528 be =-0.291 Ax- (I-x ) Aw _ (w,-w) Liz = (zig-z3 TABLE 10.23 THE RESIDUAL MEAN SQUARES FROM THE INDIVIDUAL CELL REGRESSIONS: FEMALES, NAGASAKI (The degrees of freedom are given in parentheses.) Mothers c~ ~. . - 1 2 3 4-5 r1,685.03 1,688.20 1,364.31 1,246.83 11 (6,757) (4,309) (363) (263) 2 r1,675.37 1,7S7.11 1,639.73 1,974.58 ~ (1,007) (1,937) (134) (53) l r1,878.25 1,303.64 2,294.75 2,872.48 31 (106) (125) (38) (14) 4_5 il,691.59 1,821.47 1,506.31 1,867.23 ~ (59) (66) (17) (9) Bartlett's test for between-cell heterogeneity of mean squares: x2 = 29.99* DF= 15 Bartlett's test for between-cell heterogeneity of mean squares when category 1 parents are excluded: %2=9-40 DF = 8 x = parity w = parity squared z = maternal age

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148 city cell for three of the four sex-city cells. But, from this same table (10.24b), we note that when exposure category 1 parents are eliminated both the heterogeneity in regressions and in residual mean squares largely disappears. Before we consider the implications of this, let us first consider what might account for the differences observed when all exposure cells are utilized. Table 10.24a, then, provides evidence, albeit inconclusive at this stage, that birthweight may be associated with parental exposure. Two points are involved, namely: 1. In two of the four sex-city cells, the relation of birthweight to parity and maternal age varies in a minor but significant fashion among father- mother cells. 2. In three of the four sex-city cells, the residual mean squares vary substantially (and signih- cantly) among the father-mother cells. Let us consider these points. In point (2), under the assumption that within a sex-city cell the observations within a father-mother cell have homogeneous variance, common mean, and normal distributions, we should conclude that the variance differs between the exposure cells, and that this obtains for most sex-city cells. Normality may be safely assumed, but there exists the possibility that the other assumptions are invalid here. Accordingly, two alternative or supplementary explanations of the Endings in point (2) must be entertained, namely: (a) The variances are different between ex- posure cells, and presumably due to irradiation. (b) The variances are different between ex- posure cells due to unaccounted-for concomitant variation. For example, if there were year-of- birth effects, or a socio-economic status effect, then differences in the residual mean squares might reflect unequal representations with re- spect to year of birth, or social background. Similarly, for point (1) we must entertain more than one explanation, namely: (a) The relation of birthweight to parity and age of mother is different among exposure cells and presumably due to irradiation. (b) Factors partially correlated with age and parity may differ between exposure cells and thus give rise to an apparent variation in the relation of birthweight to parity and mother's age. Genetic Effects of Atomic Bombs Chapter X What evidence is available which might permit a choice among these alternatives? In addition to data covering maternal age and parity, information is available on two other concomitant variables which are relevant to the questions raised in the preceding paragraph. These variables are year of birth (for all in- fants) and the parental socio-economic status (for a random 10 per cent of infants). Let us consider first the effect of year of birth on the residual mean squares. Two alternatives which might be entertained here are the following: Firstly, we could assume that the relationship of mother's age and parity to birthweight is constant over the years within a given exposure cell, but that the intercept (mean) of the regression may vary from year to year. This would lead us to fit a model asserting that E (`)ijrk`) = miJr + bi (XiJrk-Xtj) + b2 (`W,~jrk-Wq,j`) + iO3 (`Z',jrk-Z,,j`) That is to say, the expected value of the kth observation on birthweight in the rth year of the ij~h exposure cell (sex and city are fixed) is a function of the mean of the rt7t year in the ij~h cell, of parity, of parity-squared, and of ma- ternal age. Secondly, we might prefer not to assume that the relationship of mother's age and parity to birthweight is constant over years within a given exposure cell, and hence to fit a model of the form E (irk) = m,,jr + tar (XiJric-X~jr) + /2r (`W1,jrk-Wi~jr`J + bar (~ZzJrk-Z7,jr`) The latter approach is, of course, equivalent to fitting a regression in each of the 112 year- exposure combinations within a given sex-city cell. It is questionable whether the increase in precision of the latter approach over the former is sufficient to justify the not insignificant addi- tional labor in computing some 448 regressions. As a first approximation, then, we have elected to proceed using the simpler (the first) model. To determine whether year of birth contrib- utes significantly to the variation in birth- weights, within exposure cells, following the removal of maternal age and parity effects, we may employ the mean square ratio test. The latter test consists of forming the likelihood ratio, say L, of the "mean square following re- moval of age and parity" to the "mean square following removal of age, parity, and year."

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The Analysis of the Bir~hweight Data 149 We assert that year of birth contributes signifi- cantly if L>Lo where the critical value, Lo' is given by L-f+ (J-f)Fo o- f, and where f and ft are, respectively, the degrees of freedom associated with the lesser and the greater mean square, and To is the critical F TABLE 10.25 THE DISTRIBUTION BY PARENTAL EX POSURE OF THE RESIDUAL MEAN SQUARES AFTER REMOVAL OF VARIATION DUE TO YEAR OF BIRTH OF THE INFANT: MALES, HIROSHIMA (Degrees of freedom are given in parentheses.) Fathers v, at) ~ , it. o TABLE 10.26 THE DISTRIBUTION BY PARENTAL EX POSURE OF THE RESIDUAL MEAN SQUARES AFTER REMOVAT OF VARIATION DUE TO YEAR OF BIRTH OF THE INFANT: FEMALES, HIROSHIMA (Degrees of freedom are given in parentheses.) Fathers In Tables 10.25 to 10.28 are given the distri- butions by parental exposure of the residual mean squares following removal of the "year- of-birth effect" for the four sex-city cells. In three of the four sex-city cells the residual mean squares do not, now, differ significantly one from another (two of these three previously revealed significant heterogeneity among the mean squares). TABLE 10.27 THE DISTRIBUTION BY PARENTAL EX POSURE OF THE RESIDUAL MEAN SQUARES AFTER REMOVAL OF VARIATION DUE TO YEAR OF BIRTH OF THE INFANT: MALES, NAGASAKI (Degrees of freedom are given in parentheses.) Fathers , ~ 1 2 3 =5 1 2 3 =5 1 (1,709.60 1,793.66 1,835.06 2,347.31 1 r1,805.73 1,712.89 2,359.97 1,465.77 W(8,662) (735) (286) (190) ~ (7,278) (1,059) (112) (63) 2~1,639.79 1,786.50 1,982.83 1,982.08 2 r1,782-86 1,854.71 2,133.38 2,051.48 W(2,707) (889) (182) (105) ~ (4,644) (2,015) (126) (94) 3 [1,790.77 1,747.22 1,764.08 1,647.70 O r1,771-84 2,166.44 2,544.20 1,542.99 W(1,056) (210) (247) (68) ~31 (330) (121) (41) (5) 4 5r1,597.92 1,914.44 1,811.33 1,745.37 (5 {1,643.25 1,824.87 3,360.16 1,002.24 - ~ (532) (99) (39) (46) ~ (263) (45) (9) (6) %2 = 21.147 DF = 15 %2 = 20.442 DF 15 TABLE 10.28 THE DISTRIBUTION BY PARENTAL EX POSURE OF THE RESIDUAL MEAN SQUARES AFTER REMOVAL OF VARIATION DUE TO YEAR OF BIRTH OF THE INFANT: FEMALES, NAGASAKI (Degrees of freedom are given in parentheses.) Fathers _ . ~, 1 2 3 (5 1 2 3 =5 r 1 rl,611.26 1,646.48 1,773.60 1,941.68 rl,680~50 1,753.30 1,892.83 1,591.88 :(7,990) (691) (257) (166) 1) (6,752) (1,003) (101) (54) 2~1,559.88 1,786.51 1,309.50 1,163.41 2 rl,688.58 1,753.37 1,344.54 1,865.09 A ~1(2,419) (865) (172) (109) ~)(4,305) (1,932) (120) (61) JO 3;l,682.01 2,224~61 2,181.14 2,219.93 0 3 rl,675.05 1,662.10 2,280.34 1,752.83 :(1,023) (189) (237) (66) ~ (358) (129) (33) (13) =5 il,603 27 1,80~2~62 1,445.23 1,321.28 4 rl,505~33 2,050.00 4,305.18 2,363.29 ~ (517) (80) (46) (49) 5l (259) (49) (7) (5) %2 = 45.110* * DF = 15 %2 _ 22.003 DF = 15 (here Fo5 ) at (f'-f ) and f degrees of freedom. In all sex-city cells, year of birth can be shown to exert an effect; this effect is, however, signifi- cant in only two instances, namely, Hiroshima- females and Nagasaki-males. Under the circum- stances, then, to prevent ambiguity it seems appropriate to remove the year-of-birth effects in all cells. view of the fact that the variances were heterogeneous in only one sex-city cell (Hiro- shima-females) when year of birth was taken into account, no attempt was made to exploit the data with regard to socio-economic status. The latter decision stemmed primarily from the fact that analysis of the socio-economic data would, since such data are available on only 10

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150 Genetic Ejects of Atomic Bombs Chapter X per cent of the observations, be applicable only heterogeneous among exposure cells (all ex- inferentially to the problem of whether residual posure cells considered) in three of the four concomitant variation could account for the heterogeneity of the variance estimates within the Hiroshima-females cell. What, now, may we conclude with regard to the effect of parental exposure on birthweights ? Three points are involved, namely, 1. Does parental exposure affect birthweight means ? 2. Does parental exposure affect the relation- ship between birthweight and concomitant vari- ables, notably maternal age and parity? 3. Does parental exposure affect birthweight variances ? With regard to birthweight means, we cannot demonstrate a significant effect of parental ex- posure in any one of the four sex-city cells. With regard to the regressions of birthweight on parity and maternal age, significant differ- ences obtain among exposure cells in two sex- city cells. In one of these instances, significance does not obtain if attention is limited to only those infants born to parents both of whom were exposed. In view of the known somatic effects of irradiation, it would seem most likely that the regression differences, if real, reflect either a "disaster" effect or a direct (non- genetic) effect of irradiation. Lastly, with regard to the effect of parental exposure on birthweight variances, we note that, when maternal age and parity are removed, the variance estimates are sex-city cells. If, however, year of birth is also removed, only one sex-city cell continues to exhibit significant heterogeneity in the variance estimates among exposure cells. Moreover, we note that if attention is limited to those termina- tions to parents both of whom were exposed, the variance estimates among the exposure cells are significantly heterogeneous in only one sex- city cell even if year of birth is not removed. These facts raise some doubt as to the reality of the differences in mean squares as an irradiation effect, especially if one assumes that a consistent pattern is the sine qua rzon of a radiation- induced change. Whether consistency is a valid assumption is difficult to appraise. One can postulate certain parental interactions or rela- tionships between fetal resorption and degree of radiation damage, both admissible hypotheses, from which it would not necessarily follow that the variance would be similarly affected in all sex-city cells. The conservative interpretation of the data with regard to the birthweight vari- ances would be one which asserts no clearly demonstrable effect of parental irradiation on the spread of birthweights. 10.5 Summary. There exist no consistent findings suggestive of an effect of parental ex- posure on (a) birthweight means, (b) the rela- tionship of maternal age and parity to birth- weight, or (c) birthweight variances.