Beyond p <.05: a critical review of new Bayesian proposals for assessing the p-value

This paper reviews recent contributions from a Bayesian-oriented perspective, after the ASA statement on p-values (2016). We classify proposals that (i) supplement the p-value; (ii) modify the p-value itself. In the first group, we review the Bayes factor, the False Positive risk, the rejection odds and the analysis of credibility from both Matthews’ and Held’s point of view. We also put forth and discuss a new index of credibility, about which we conduct a delimited simulation study. In the second group, we discuss Gannon’s modification of the p-value based on the Bayes factor and the second-generation p-value. The theory is illustrated with two case studies on pharmacotherapy in infectious diseases. Contemporary authors still refer to the p-value as a statistical indicator but have abandoned the perspective of evaluating p-values with fixed thresholds. Statistical societies worldwide should target new strategies to disseminate the debate on p-values in all applied fields of knowledge, as well as they may promote the use of different statistical procedures to supplement p-values.