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Statistical evidence and surprise unified under possibility theory

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  • David R. Bickel

Abstract

Sander Greenland argues that reported results of hypothesis tests should include the surprisal, the base‐2 logarithm of the reciprocal of a p‐value. The surprisal measures how many bits of evidence in the data warrant rejecting the null hypothesis. A generalization of surprisal also can measure how much the evidence justifies rejecting a composite hypothesis such as the complement of a confidence interval. That extended surprisal, called surprise, quantifies how many bits of astonishment an agent believing a hypothesis would experience upon observing the data. While surprisal is a function of a point in hypothesis space, surprise is a function of a subset of hypothesis space. Satisfying the conditions of conditional min‐plus probability, surprise inherits a wealth of tools from possibility theory. The equivalent compatibility function has been recently applied to the replication crisis, to adjusting p‐values for prior information, and to comparing scientific theories.

Suggested Citation

  • David R. Bickel, 2023. "Statistical evidence and surprise unified under possibility theory," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 923-928, September.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:923-928
    DOI: 10.1111/sjos.12648
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    References listed on IDEAS

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    1. David R. Bickel, 2022. "Confidence distributions and empirical Bayes posterior distributions unified as distributions of evidential support," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(10), pages 3142-3163, May.
    2. David R. Bickel, 2021. "Null Hypothesis Significance Testing Defended and Calibrated by Bayesian Model Checking," The American Statistician, Taylor & Francis Journals, vol. 75(3), pages 249-255, July.
    3. David R. Bickel, 2021. "The sufficiency of the evidence, the relevancy of the evidence, and quantifying both with a single number," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1157-1174, October.
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