The testing of Hardy–Weinberg equilibrium (HWE) is an important step in many analyses of genetic data. Frequentist methods are popular for testing HWE, with χ2 and exact tests providing the usual implementations. There are a number of important complications that require consideration when such approaches are used. A first problem is that the discreteness of the sample space leads to nonuniformity of p-values under the null (Rohlfs and Weir, 2008). An additional major problem with frequentist tests is how to decide upon a threshold for significance, in particular as a function of the sample size. When the exact test is used, computation is an issue when the number of alleles at the locus is not small (Guo and Thompson, 1992; Huber et al., 2006). Recently, there has been great interest in testing for HWE in genome-wide association studies (GWAS) in which departure from HWE may indicate problems with quality control for the SNP in question (Wigginton, Cutler, and Abecasis, 2005).
