We begin by discussing the false positive test results that arise because of cryptic relatedness and population substructure when testing a disease susceptibility locus. We extend and evaluate the Hardy-Weinberg disequilibrium (HWD) method, allowing for an inbreeding coefficient (F) in a similar way that Devlin and Roeder (1999) allowed for inbreeding in a case-control study. Then we compare the HWD measure and the common direct measure of linkage disequilibrium, both when there is no population substructure (F = 0) and when there is population substructure (F not = 0), for a single marker. The HWD test statistic gives rise to false positives caused by population stratification. These false positives can be controlled by adjusting the test statistic for the amount of variance inflation caused by the inbreeding coefficient (F). The power loss for the HWD test that arises when controlling for population structure is much less than that which arises for the common direct measure of linkage disequilibrium. However, in the multiplicative model, the HWD test has virtually no power even when allowing for non-zero F.