Sub-uniformity of harmonic mean p-values
Abstract
We obtain several inequalities on the generalized means of dependent p-values. In particular, the weighted harmonic mean of p-values is strictly sub-uniform under several dependence assumptions of p-values, including independence, negative upper orthant dependence, the class of extremal mixture copulas, and some Clayton copulas. Sub-uniformity of the harmonic mean of p-values has an important implication in multiple hypothesis testing: It is statistically invalid (anti-conservative) to merge p-values using the harmonic mean unless a proper threshold or multiplier adjustment is used, and this applies across all significance levels. The required multiplier adjustment on the harmonic mean p-value grows sub-linearly to infinity as the number of p-values increases, and hence there does not exist a constant multiplier that works for any number of p-values, even under independence.
Cite
@article{arxiv.2405.01368,
title = {Sub-uniformity of harmonic mean p-values},
author = {Yuyu Chen and Ruodu Wang and Yuming Wang and Wenhao Zhu},
journal= {arXiv preprint arXiv:2405.01368},
year = {2025}
}