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How the Maximal Evidence of -Values Against Point Null Hypotheses Depends on Sample Size

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  • Leonhard Held
  • Manuela Ott

Abstract

Minimum Bayes factors are commonly used to transform two-sided p-values to lower bounds on the posterior probability of the null hypothesis. Several proposals exist in the literature, but none of them depends on the sample size. However, the evidence of a p-value against a point null hypothesis is known to depend on the sample size. In this article, we consider p-values in the linear model and propose new minimum Bayes factors that depend on sample size and converge to existing bounds as the sample size goes to infinity. It turns out that the maximal evidence of an exact two-sided p-value increases with decreasing sample size. The effect of adjusting minimum Bayes factors for sample size is shown in two applications.

Suggested Citation

  • Leonhard Held & Manuela Ott, 2016. "How the Maximal Evidence of -Values Against Point Null Hypotheses Depends on Sample Size," The American Statistician, Taylor & Francis Journals, vol. 70(4), pages 335-341, October.
    • Handle: RePEc:taf:amstat:v:70:y:2016:i:4:p:335-341
    DOI: 10.1080/00031305.2016.1209128
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    Cited by:

    1. Pathairat Pastpipatkul & Petchaluck Boonyakunakorn & Kanyaphon Phetsakda, 2020. "The Impact of Thailand’s Openness on Bilateral Trade between Thailand and Japan: Copula-Based Markov Switching Seemingly Unrelated Regression Model," Economies, MDPI, vol. 8(1), pages 1-13, January.
    2. Kelter, Riko, 2022. "Power analysis and type I and type II error rates of Bayesian nonparametric two-sample tests for location-shifts based on the Bayes factor under Cauchy priors," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    3. Kline, Brendan, 2024. "Classical p-values and the Bayesian posterior probability that the hypothesis is approximately true," Journal of Econometrics, Elsevier, vol. 240(1).

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