Statistical power when testing for genetic differentiation

A variety of statistical procedures are commonly employed when testing for genetic differentiation. In a typical situation two or more samples of indi viduals have been genotyped at several gene loci by molecular or biochemica l means, and in a first step a statistical test for allele frequency homoge neity is performed at each locus separately, using, e.g. the contingency ch i-square test, Fisher's exact test, or some modification thereof. In a seco nd step the results from the separate tests are combined for evaluation of the joint null hypothesis that there is no allele frequency difference at a ny locus, corresponding to the important case where the samples would be re garded as drawn from the same statistical and, hence, biological population . Presently, there are two conceptually different strategies in use for tes ting the joint null hypothesis of no difference at any locus. One approach is based on the summation of chi-square statistics over loci. Another metho d is employed by investigators applying the Bonferroni technique (adjusting the P-value required for rejection to account for the elevated alpha error s when performing multiple tests simultaneously) to test if the heterogenei ty observed at any particular locus can be regarded significant when consid ered separately. Under this approach the joint null hypothesis is rejected if one or more of the component single locus tests is considered significan t under the Bonferroni criterion. We used computer simulations to evaluate the statistical power and realized alpha errors of these strategies when ev aluating the joint hypothesis after scoring multiple loci. We find that the 'extended' Bonferroni approach generally is associated with low statistica l power and should not be applied in the current setting. Further, and cont rary to what might be expected, we find that 'exact' tests typically behave poorly when combined in existing procedures for joint hypothesis testing. Thus, while exact tests are generally to be preferred over approximate ones when testing each particular locus, approximate tests such as the traditio nal chi-square seem preferable when addressing the joint hypothesis.