Table 10.5a we note that the estimates of b1, b2, and b3 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 associated with the various exposure cells. That this variation is significant is borne out by Table 10.5b.

At this point, it is of interest to inquire into the amount of variation in the birthweights accounted for by variation in the individual regressions after removing the portion associated with the common regression (see Sec. 6.3). From the data in Table 10.5, we form the mean 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 perspective only if we know the amount of variation in birthweight accounted for by the common regression. The latter we obtain from the mean square ratio

At this point, it is of interest to inquire into the amount of variation in the birthweights accounted for by variation in the individual regressions after removing the portion associated with the common regression (see Sec. 6.3). From the data in Table 10.5, we form the mean

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

MS

F

Variation removed by regression

761,262.72

3

253,754.240

145.246**

Residual within cells (pool)

28,264,084.66

16,178

1,747.069

(b) Test of the homogeneity of the regressions (all exposure cells considered)

Source

SS

DF

MS

F

Differences in regressions

116,630.11

45

2,591.780

1.485*

Residual within cells (sum)

28,147,454.55

16,133

1,744.713

(c) Test of the homogeneity of the regressions (only those cells in which both parents were exposed are considered)

Source

SS

DF

MS

F

Difference in regressions

38,429.76

24

1,601.240

1.124

Residual within cells (sum)

3,473,234.85

1,929

1,800.536

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 account for 0.14 per cent of the variation in birthweight not accounted for by the common regression. This value obviously attains perspective only if we know the amount of variation in birthweight accounted for by the common regression. The latter we obtain from the mean square ratio

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 effects anticipated from irradiation, variation, accountable 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 which one would obtain if each exposure cell had the same maternal age and parity distribution. 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 birth weight 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 exposure 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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