Title: An omnibus test for the global null hypothesis,
Abstract: Global hypothesis tests are a useful tool in the context of, e.g, clinical
trials, genetic studies or meta analyses, when researchers are not interested
in testing individual hypotheses, but in testing whether none of the hypotheses
is false. There are several possibilities how to test the global null
hypothesis when the individual null hypotheses are independent. If it is
assumed that many of the individual null hypotheses are false, combinations
tests have been recommended to maximise power. If, however, it is assumed that
only one or a few null hypotheses are false, global tests based on individual
test statistics are more powerful (e.g., Bonferroni or Simes test). However,
usually there is no a-priori knowledge on the number of false individual null
hypotheses. We therefore propose an omnibus test based on the combination of
p-values. We show that this test yields an impressive overall performance. The
proposed method is implemented in the R-package omnibus.