A consideration of the chi-square test of Hardy--Weinberg equilibrium in a non-multinomial situation

The multinomial Dirichlet distribution was used to study the effect of correlation between observations in a sample on the frequency of rejection of the Hardy--Weinberg Law when in fact it was true in the population being sampled. It was shown that the usual X2 goodness-of-fit test of Hardy--Weinberg is very sensitive to non-multinomial sampling. In view of the lack of statistical power of the test to detect deviations due to in breeding, it is likely that whenever H--W is rejected using samples of size 100 or less, the underlying causation is sample correlation rather than failure of the H--W law to be true. Related to these findings is, of course, the effect of pooling heterogeneous frequencies or, in the case of contingency tables, Simpson's paradox (see Simpson, 1951).