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Testing by betting: A strategy for statistical and scientific communication

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  • Glenn Shafer

Abstract

The most widely used concept of statistical inference—the p‐value—is too complicated for effective communication to a wide audience. This paper introduces a simpler way of reporting statistical evidence: report the outcome of a bet against the null hypothesis. This leads to a new role for likelihood, to alternatives to power and confidence, and to a framework for meta‐analysis that accommodates both planned and opportunistic testing of statistical hypotheses and probabilistic forecasts. This framework builds on the foundation for mathematical probability developed in previous work by Vladimir Vovk and myself.

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  • Glenn Shafer, 2021. "Testing by betting: A strategy for statistical and scientific communication," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(2), pages 407-431, April.
    • Handle: RePEc:bla:jorssa:v:184:y:2021:i:2:p:407-431
    DOI: 10.1111/rssa.12647
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    References listed on IDEAS

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    1. Ronald L. Wasserstein & Allen L. Schirm & Nicole A. Lazar, 2019. "Moving to a World Beyond “p," The American Statistician, Taylor & Francis Journals, vol. 73(S1), pages 1-19, March.
    2. Blakeley B. McShane & David Gal, 2017. "Rejoinder: Statistical Significance and the Dichotomization of Evidence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 904-908, July.
    3. Min-ge Xie & Kesar Singh, 2013. "Confidence Distribution, the Frequentist Distribution Estimator of a Parameter: A Review," International Statistical Review, International Statistical Institute, vol. 81(1), pages 3-39, April.
    4. Stephen Senn, 2011. "You May Believe You Are a Bayesian But You Are Probably Wrong," Rationality, Markets and Morals, Frankfurt School Verlag, Frankfurt School of Finance & Management, vol. 2(42), September.
    5. Campbell R. Harvey, 2017. "Presidential Address: The Scientific Outlook in Financial Economics," Journal of Finance, American Finance Association, vol. 72(4), pages 1399-1440, August.
    6. David Colquhoun, 2019. "The False Positive Risk: A Proposal Concerning What to Do About p-Values," The American Statistician, Taylor & Francis Journals, vol. 73(S1), pages 192-201, March.
    7. Blakeley B. McShane & David Gal, 2017. "Statistical Significance and the Dichotomization of Evidence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 885-895, July.
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    Cited by:

    1. Thomas Cook & Patrick Flaherty, 2024. "Hedging in Sequential Experiments," Papers 2406.15867, arXiv.org.
    2. Alexander Henzi & Johanna F Ziegel, 2022. "Valid sequential inference on probability forecast performance [A comparison of the ECMWF, MSC, and NCEP global ensemble prediction systems]," Biometrika, Biometrika Trust, vol. 109(3), pages 647-663.
    3. Turner, Rosanne J. & Grünwald, Peter D., 2023. "Exact anytime-valid confidence intervals for contingency tables and beyond," Statistics & Probability Letters, Elsevier, vol. 198(C).
    4. Ruodu Wang & Aaditya Ramdas, 2022. "False discovery rate control with e‐values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 822-852, July.
    5. Sander Greenland, 2023. "Divergence versus decision P‐values: A distinction worth making in theory and keeping in practice: Or, how divergence P‐values measure evidence even when decision P‐values do not," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 54-88, March.

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