{"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/the-most-difference-in-means-a-statistic-for","title":"The Most Difference in Means: A Statistic for the Strength of Null and Near-Zero Results","arxiv_id":"2201.01239","date":"2022-01-04","proceeding":null,"authors":["Bruce A. Corliss","Taylor R. Brown","Tingting Zhang","Kevin A. Janes","Heman Shakeri","Philip E. Bourne"],"abstract":"Statistical insignificance does not suggest the absence of effect, yet scientists must often use null results as evidence of negligible (near-zero) effect size to falsify scientific hypotheses. Doing so must assess a result's null strength, defined as the evidence for a negligible effect size. Such an assessment would differentiate strong null results that suggest a negligible effect size from weak null results that suggest a broad range of potential effect sizes. We propose the most difference in means ($\\delta_M$) as a two-sample statistic that can both quantify null strength and perform a hypothesis test for negligible effect size. To facilitate consensus when interpreting results, our statistic allows scientists to conclude that a result has negligible effect size using different thresholds with no recalculation required. To assist with selecting a threshold, $\\delta_M$ can also compare null strength between related results. Both $\\delta_M$ and the relative form of $\\delta_M$ outperform other candidate statistics in comparing null strength. We compile broadly related results and use the relative $\\delta_M$ to compare null strength across different treatments, measurement methods, and experiment models. Reporting the relative $\\delta_M$ may provide a technical solution to the file drawer problem by encouraging the publication of null and near-zero results.","url_abs":"https://arxiv.org/abs/2201.01239v4","url_pdf":"https://arxiv.org/pdf/2201.01239v4.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":"the-most-difference-in-means-a-statistic-for","repo_url":"https://github.com/bac7wj/ACES","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"the-most-difference-in-means-a-statistic-for","repo_url":"https://github.com/bacorliss/ace","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"the-most-difference-in-means-a-statistic-for","repo_url":"https://github.com/bac7wj/contra","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}