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Error statistics, Bayes-factor Tests and the Fallacy of Non-exhaustive Alternatives

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  • Mayo, Deborah

Abstract

In this paper I discuss a fundamental contrast between two types of statistical tests now in use: those where the post-data inferential assessment is sensitive to the method’s error probabilities—error statistical methods (e.g., statistical significance tests), and those where it is insensitive (e.g., Bayes factors). It might be thought that if a method is insensitive to error probabilities that it escapes the inferential consequences of inflated error rates due to biasing selection effects. I will argue that this is not the case. I discuss a recent paper advocating subjective Bayes factors (BFs) by van Dongen, Sprenger, and Wagenmakers (VSW 2022). VSW claim that the comparatively more likely hypothesis H passes a stringent test, despite insensitivity to the error statistical properties of that test. I argue that the BF test rule they advocate can accord strong evidence to a claim H, even though little has been done to rule out H’s flaws. There are two reasons the BF test fails to satisfy the minimal requirement for stringency: its insensitivity to biasing selection effects, and the fact that H and its competitor need not exhaust the space of possibilities. Data can be much more probable under hypothesis H than under a chosen non-exhaustive competitor H’, even though H is poorly warranted. I will recommend VSW supplement their BF tests with a report of how severely H has passed, in the frequentist error statistical sense. I begin by responding to the criticisms VSW raise for a severe testing reformulation of statistical significance tests. A post-data severity concept can supply a transparent way for skeptical consumers, who are not steeped in technical machinery, to check if errors and biases are avoided in specific inferences that affect them.

Suggested Citation

  • Mayo, Deborah, 2024. "Error statistics, Bayes-factor Tests and the Fallacy of Non-exhaustive Alternatives," OSF Preprints tmgqd, Center for Open Science.
  • Handle: RePEc:osf:osfxxx:tmgqd
    DOI: 10.31219/osf.io/tmgqd
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    References listed on IDEAS

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    1. Andrew Gelman & Christian Hennig, 2017. "Beyond subjective and objective in statistics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 967-1033, October.
    2. Neyman, Jerzy, 1952. "Lectures and Conferences on Mathematical Statistics and Probability," USDA Miscellaneous 327287, United States Department of Agriculture.
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