Three Insights from a Bayesian Interpretation of the One-Sided P Value. (June 2017)

• Record Type: Journal Article
• Authors: Marsman, Maarten; Wagenmakers, Eric-Jan
• Is Part Of: Educational and psychological measurement. Volume 77:Number 3(2017:Jun.)
• Page Start: 529
• Page End: 539
• Publication Date: 2017-06
• Subjects: hypothesis testing -- Bayesian inference -- null hypothesis -- estimation; Educational tests and measurements -- Periodicals; Psychological tests -- Periodicals; 151.205
• DOI: 10.1177/0013164416669201
• Languages: English
• ISSNs: 0013-1644

Abstract

P values have been critiqued on several grounds but remain entrenched as the dominant inferential method in the empirical sciences. In this article, we elaborate on the fact that in many statistical models, the one-sided P value has a direct Bayesian interpretation as the approximate posterior mass for values lower than zero. The connection between the one-sided P value and posterior probability mass reveals three insights: (1) P values can be interpreted as Bayesian tests of direction, to be used only when the null hypothesis is known from the outset to be false; (2) as a measure of evidence, P values are biased against a point null hypothesis; and (3) with N fixed and effect size variable, there is an approximately linear relation between P values and Bayesian point null hypothesis tests.