A new method of testing for Hardy-Weinberg equilibrium and ordering populations

The assumption of Hardy-Weinberg equilibrium (HWE) among alleles in a nonevolving population is of fundamental importance in genetic studies. Deviation from HWE in a population usually indicates inbreeding, stratification and sometimes problems in genotyping. In populations of affected individuals, these deviations can also provide evidence for association. In this paper, we introduce a measure based on the Kullback-Leibler discrimination information function that quantifies the deviation from HWE in a population. We use this measure to order populations. We also propose a test for HWE based on an estimate of this measure. The test is a statistically consistent test of the null hypothesis for all alternatives and is very easy to implement. Our proposed test statistic is compared with an earlier, widely used, test. Finally, the use of the proposed new test is shown in an illustrative example.