A Robust Combination Test Using the Normal Distribution, with Application to Phylogenetic Inference

Combination tests are used to combine P-values from individual studies to test a global null hypothesis. These types of tests can also be applied to combine P-values from testing separate null hypotheses within the same study in cases for which the procedure for testing a global null hypothesis is unavailable. One such application of a combination test is to detect the presence of hybrid species within a set of species. Although many combination tests have been proposed in the literature, there is no uniformly most powerful test applicable for all conditions. For instance, in the hybrid detection application, it is expected that only a few of the species within a set species might have truly arisen via hybridization, and thus when tested, only a few of the individual P-values are expected to be significant. Thus, a desirable property of a combination test for this situation is to be able to reject the global null hypothesis even if only a small fraction of the individual P-values are significant. In this paper, we propose a new combination test based on the normal distribution that assigns weight to each test adaptively, thereby providing powerful results even when only a small fraction of the individual null hypotheses are false. A comprehensive simulation study, as well as real data applications, demonstrate that the proposed test is powerful in detecting false global null hypotheses under several situations for which existing tests have low power.