 Combining p-values via averagingVladimir Vovk and Ruodu Wang Biometrika, vol. 107, issue 4, 791-808 Abstract: SummaryThis paper proposes general methods for the problem of multiple testing of a single hypothesis, with a standard goal of combining a number of $p$-values without making any assumptions about their dependence structure. A result by Rüschendorf (1982) and, independently, Meng (1993) implies that the $p$-values can be combined by scaling up their arithmetic mean by a factor of 2, and no smaller factor is sufficient in general. A similar result by Mattner about the geometric mean replaces 2 by e. Based on more recent developments in mathematical finance, specifically, robust risk aggregation techniques, we extend these results to generalized means; in particular, we show that $K$ $p$-values can be combined by scaling up their harmonic mean by a factor of $\log K$ asymptotically as $K$ tends to infinity. This leads to a generalized version of the Bonferroni–Holm procedure. We also explore methods using weighted averages of $p$-values. Finally, we discuss the efficiency of various methods of combining $p$-values and how to choose a suitable method in light of data and prior information. Keywords: Hypothesis testing; Multiple hypothesis testing; Multiple testing of a single hypothesis; Robust risk aggregation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:107:y::i:4:p:791-808. Ordering information: This journal article can be ordered from Access Statistics for this article Biometrika is currently edited by Paul Fearnhead More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK. |
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