Abstract
Currently used tests of Hardy-Weinberg proportions do not take into account the nature of the alternative hypothesis, which is generally a heterozygote deficiency. Different exact tests, appropriate for small sample size and large number of alleles, are proposed in this perspective, and their properties are evaluated by power comparisons. Some tests are found to be close to optimal for the detection of inbreeding or heterozygote excess, one of which is a score test closely related to Robertson and Hill's estimator of the inbreeding coefficient. This test is also easily applied to multiple samples. Such tests are not always the most appropriate if alternative hypotheses differ from those considered here.