A corrected χ2 test has previously been proposed to correct for inflated false positive rates for association tests in the context of known relationships [Bourgain et al., 2003]. We begin by outlining this test for the diallelic case. Suppose we have Nc sampled individuals in a case group and Nt sampled individuals in a control group. Let Y = (Y1, …Yi, …YN)T where Yi = 0.5 × (the number of alleles of type 1 in individual i) and N = Nc + Nt. Let p be the frequency of allele 1, 0 < p < 1. Under the null hypothesis of no association between a given marker and disease and HWE for the given marker, E0(Y) = p1N and Var0(Y)=12p(1−p)Φ, where
