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

Brendan Kline

Journal of Econometrics, 2024, vol. 240, issue 1

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.

Keywords: Frequentist; Hypothesis; Posterior; Testing (search for similar items in EconPapers)
JEL-codes: C11 C12 C18 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:240:y:2024:i:1:s030440762400023x

DOI: 10.1016/j.jeconom.2024.105677

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