Frequentist asymptotic χ2 and exact tests provide the most common approaches to the testing of HWE (Weir, 1996). The exact test is recommended (Balding, 2006) because it does not depend on large sample sizes, and the χ2 test can have inaccurate type I errors as documented by Wigginton et al. (2005). We concentrate on the exact test. For two alleles, one proceeds by considering the distribution of the counts conditional on the observed numbers of A1 alleles, n1 = 2n11 + n12, to give, under the null Pr(n12∣n1)=n![(n1−n12)∕2]!n12![(n−n1−n12)∕2]!×2n12n1!(n−n1)!(2n)!. The null of HWE is rejected if the observed data fall into the tails of this distribution, with the tail defined by the specified significance level. In the multiallelic case the enumeration of the counts in the tails may be computationally expensive and a number of Monte Carlo algorithms have been proposed (Guo and Thompson, 1992; Huber et al., 2006). In general the distribution of the p-value under the null is not uniform due to the discreteness of n12 and so enumeration of all possible tables consistent with n1 is advised to obtain the empirical p-value distribution (Rohlfs and Weir, 2008).
