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We show that two procedures for false discovery rate (FDR) control -- theBenjamini-Yekutieli procedure for dependent p-values, and thee-Benjamini-Hochberg procedure for dependent e-values -- can both be made morepowerful by a simple randomization involving one independent uniform randomvariable. As a corollary, the Hommel test under arbitrary dependence is alsoimproved. Importantly, our randomized improvements are never worse than theoriginals, and they are typically strictly more powerful, with markedimprovements in simulations. The same technique also improves essentially everyother multiple testing procedure based on e-values.

More powerful multiple testing under dependence via randomization