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Classical p-values and the Bayesian posterior probability that the hypothesis is approximately true

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  • Kline, Brendan

Abstract

This paper relates p-values for the hypothesis that θ=c to the Bayesian posterior probability that the hypothesis is approximately true, in the sense that θ∈[c−ϵ,c+ϵ] for a selected ϵ>0. In a setup with a continuous prior for θ, the results show that a larger (respectively, smaller) p-value does not necessarily correspond to a higher (respectively, lower) probability that θ is close to c. Therefore, the results suggest caution about common ways of using p-values, specifically the use of small p-values as a key standard in empirical research.

Suggested Citation

  • Kline, Brendan, 2024. "Classical p-values and the Bayesian posterior probability that the hypothesis is approximately true," Journal of Econometrics, Elsevier, vol. 240(1).
    • Handle: RePEc:eee:econom:v:240:y:2024:i:1:s030440762400023x
    DOI: 10.1016/j.jeconom.2024.105677
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    References listed on IDEAS

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    More about this item

    Keywords

    Frequentist; Hypothesis; Posterior; Testing;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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