{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/combining-p-values-via-averaging","title":"Combining p-values via averaging","arxiv_id":"1212.4966","date":"2012-12-20","proceeding":null,"authors":["Vladimir Vovk","Ruodu Wang"],"abstract":"This 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. An old result by R\\\"uschendorf and, independently, Meng 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 about the geometric mean (Mattner) 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 $\\ln K$ (asymptotically as $K\\to\\infty$). 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.","url_abs":"https://arxiv.org/abs/1212.4966v5","url_pdf":"https://arxiv.org/pdf/1212.4966v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"combining-p-values-via-averaging","repo_url":"https://github.com/statmlben/dnn-inference","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1212.4966","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}