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It is conventionally believed that a permutation test should ideally use allpermutations. If this is computationally unaffordable, it is believed oneshould use the largest affordable Monte Carlo sample or (algebraic) subgroup ofpermutations. We challenge this belief by showing we can sometimes obtaindramatically more power by using a tiny subgroup. As the subgroup is tiny, thissimultaneously comes at a much lower computational cost. We exploit this toimprove the popular permutation-based Westfall & Young MaxT multiple testingmethod. We study the relative efficiency in a Gaussian location model, and findthe largest gain in high dimensions.

More Power by using Fewer Permutations