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Valid P-Values Behave Exactly as They Should: Some Misleading Criticisms of P-Values and Their Resolution With S-Values

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  • Sander Greenland

Abstract

The present note explores sources of misplaced criticisms of P-values, such as conflicting definitions of “significance levels” and “P-values” in authoritative sources, and the consequent misinterpretation of P-values as error probabilities. It then discusses several properties of P-values that have been presented as fatal flaws: That P-values exhibit extreme variation across samples (and thus are “unreliable”), confound effect size with sample size, are sensitive to sample size, and depend on investigator sampling intentions. These properties are often criticized from a likelihood or Bayesian framework, yet they are exactly the properties P-values should exhibit when they are constructed and interpreted correctly within their originating framework. Other common criticisms are that P-values force users to focus on irrelevant hypotheses and overstate evidence against those hypotheses. These problems are not however properties of P-values but are faults of researchers who focus on null hypotheses and overstate evidence based on misperceptions that p = 0.05 represents enough evidence to reject hypotheses. Those problems are easily seen without use of Bayesian concepts by translating the observed P-value p into the Shannon information (S-value or surprisal) –log2(p).

Suggested Citation

  • Sander Greenland, 2019. "Valid P-Values Behave Exactly as They Should: Some Misleading Criticisms of P-Values and Their Resolution With S-Values," The American Statistician, Taylor & Francis Journals, vol. 73(S1), pages 106-114, March.
  • Handle: RePEc:taf:amstat:v:73:y:2019:i:s1:p:106-114
    DOI: 10.1080/00031305.2018.1529625
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    Cited by:

    1. Keith R Lohse & Kristin L Sainani & J Andrew Taylor & Michael L Butson & Emma J Knight & Andrew J Vickers, 2020. "Systematic review of the use of “magnitude-based inference” in sports science and medicine," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-22, June.
    2. Pütz, Peter & Kramer-Sunderbrink, Arne & Dreher, Robin Tim & Hoffmann, Leona & Werner, Robin, 2022. "A Proposed Hybrid Effect Size Plus p-Value Criterion. A Comment on Goodman et al. (The American Statistician, 2019)," Journal of Comments and Replications in Economics (JCRE), ZBW - Leibniz Information Centre for Economics, vol. 1(2022-4), pages 1-15.
    3. Eleni Verykouki & Christos T. Nakas, 2023. "Adaptations on the Use of p -Values for Statistical Inference: An Interpretation of Messages from Recent Public Discussions," Stats, MDPI, vol. 6(2), pages 1-13, April.
    4. Gunter, Ulrich & Önder, Irem & Smeral, Egon, 2019. "Scientific value of econometric tourism demand studies," Annals of Tourism Research, Elsevier, vol. 78(C), pages 1-1.
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    6. Heckelei, Thomas & Huettel, Silke & Odening, Martin & Rommel, Jens, 2021. "The replicability crisis and the p-value debate – what are the consequences for the agricultural and food economics community?," Discussion Papers 316369, University of Bonn, Institute for Food and Resource Economics.
    7. Markku Maula & Wouter Stam, 2020. "Enhancing Rigor in Quantitative Entrepreneurship Research," Entrepreneurship Theory and Practice, , vol. 44(6), pages 1059-1090, November.
    8. Jae H. Kim, 2022. "Moving to a world beyond p-value," Review of Managerial Science, Springer, vol. 16(8), pages 2467-2493, November.
    9. Michal Lehnert & Mark De Ste Croix & Amr Zaatar & Patrycja Lipinska & Petr Stastny, 2020. "Effect of a Simulated Match on Lower Limb Neuromuscular Performance in Youth Footballers—A Two Year Longitudinal Study," IJERPH, MDPI, vol. 17(22), pages 1-17, November.
    10. Smriti Kumar & Elizabeth G. Miller & Martin Mende & Maura L. Scott, 2022. "Language matters: humanizing service robots through the use of language during the COVID-19 pandemic," Marketing Letters, Springer, vol. 33(4), pages 607-623, December.
    11. Arjen Witteloostuijn, 2020. "New-day statistical thinking: A bold proposal for a radical change in practices," Journal of International Business Studies, Palgrave Macmillan;Academy of International Business, vol. 51(2), pages 274-278, March.
    12. Cheng, Yuanyuan, 2023. "A method of 3R to evaluate the correlation and predictive value of variables," OSF Preprints c79tu, Center for Open Science.

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