Sub-uniformity of harmonic mean p-values

Yuyu Chen; Ruodu Wang; Yuming Wang; Wenhao Zhu

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arXiv · 2405.01368

Sub-uniformity of harmonic mean p-values

Yuyu Chen·Ruodu Wang·Yuming Wang·Wenhao Zhu

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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.

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Yuyu Chen, Ruodu Wang, Yuming Wang, Wenhao Zhu. 2024-05-02. Sub-uniformity of harmonic mean p-values. https://arxiv.org/abs/2405.01368

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