It makes sense to attribute a definite percentage of variation in some measure of behavior to variation in heredity only if the effects of heredity and environment are truly additive. Additivity is often tested by examining the interaction effect in a two-way analysis of variance (ANOVA) or its equivalent multiple regression model. If this effect is not statistically significant at the α = 0.05 level, it is common practice in certain fields (e.g., human behavior genetics) to conclude that the two factors really are additive and then to use linear models, which assume additivity. Comparing several simple models of nonadditive, interactive relationships between heredity and environment, however, reveals that ANOVA often fails to detect nonadditivity because it has much less power in tests of interaction than in tests of main effects. Likewise, the sample sizes needed to detect real interactions are substantially greater than those needed to detect main effects. Data transformations that reduce interaction effects also change drastically the properties ofthe causal model and may conceal theoretically interesting and practically useful relationships. If the goal ofpartitioning variance among mutually exclusive causes and calculating “heritability” coefficients is abandoned, interactive relationships can be examined more seriously and can enhance our understanding of the ways living things develop.

The Lévy distance, L(F,G), between two distribution functions F and G has the important property that convergence of L(Fn,F) is equivalent to convergence in distribution. The fact that L(F,G) is not invariant under a change of scale has been thought to be a disadvantage. However, simple bounds on the Lévy distance between the transformed distribution functions can be found.