A note on exact conditional and unconditional tests for Hardy-Weinberg equilibrium.

The exact conditional approach is frequently used for testing Hardy-Weinberg equilibrium in population genetics. This approach respects the test size as compared to the traditionally used asymptotic approaches. It is a full-enumeration method and very computational. Many efficient algorithms have been successfully developed to implement this exact approach. An alternative to the conditional approach is the unconditional approach, which relaxes the restriction of the fixed number of allelic counts as in the conditional approach. The first unconditional test considered in this study is the one based on maximization, which has been shown to be more powerful than the conditional test to loci with two alleles for small sample sizes. By using the p value of the conditional approach as a test statistic in the following maximization step, the second unconditional test is uniformly more powerful than the conditional approach. We compared these exact tests based on three commonly used test statistics with regards to type I error rate and power. It is recommended to use the second unconditional approach in practice due to the power gain in the case with two alleles.