P-value and Bayes factor: Criticism and reconciliation perspectives

The p-value, namely a tool put forth by Sir Ronald Fisher to make statistical inference, is currently used in the applications. Some statisticians argue that the alternative to the p-value is the Bayes factor, i.e., a tool proposed by Sir Harold Jeffreys. The contrast between the p-value and the Bayes factor is still a matter of discussion, even though almost 100 years have passed since the origin of the dispute. As to the debate on the p-value, position papers have been written and conferences have been organized to identify possible alternative procedures. The Bayes factor is kept in shadow even if it has become more used in the literature, especially in the psychological field. Some authors tried to reconcile the p-value with the Bayes factor. It has been proposed to view the Bayes factor as a function of the p-value or, following the proposals of Matthews and Held, to assess the credibility of the p-value itself through the use of Bayesian tools. In this paper, we review these two positions with particular regard to the analysis credibility, for which a measure is put forward.