Testing for Hardy-Weinberg Equilibrium in Small Samples

An investigation is made of the validity of several statistics to test whether a small sample comes from a population having the binomial proportions p2AA, 2pqAa, q2aa, where q = I p. In particular the significance levels (P-values) indicated by these tests are compared to those of a well-known exact test (Haldane 1954). It is found that, for sample sizes of 20 or greater and significance level 0.15 or less for the exact test, a useful approximation to the significance level is obtained when the X2-statistic, with Yates' correction, is averaged with a similar statistic that used conditional expectations, and the result referred to the x2-distribution. For other situations, or for greater accuracy, a recursive relation is given that reduces the amount of computation necessary to determine the exact significance level.