In response to the widespread abuse and misinterpretation of significance tests of null hypotheses, some editors and authors have strongly discouraged P values. However, null P values still thrive in most journals and are routinely misinterpreted as probabilities of a “chance finding” or of the null, when they are no such thing. This misuse may be lessened by recognizing correct Bayesian interpretations. For example, under weak priors, 95% confidence intervals approximate 95% posterior probability intervals, one-sided P values approximate directional posterior probabilities, and point estimates approximate posterior medians. Furthermore, under certain conditions, a one-sided P value for a prior median provides an approximate lower bound on the posterior probability that the point estimate is on the wrong side of that median. More generally, P values can be incorporated into a modern analysis framework that emphasizes measurement of fit, distance, and posterior probability in place of “statistical significance” and accept/reject decisions.
From the aDepartment of Epidemiology and bDepartment of Statistics, University of California, Los Angeles, CA; and the cDepartment of Epidemiology, University of North Carolina, Chapel Hill, NC.The authors report no conflicts of interest.
Submitted 2 May 2012; accepted 9 October 2012.
Editors’ note: Related articles appear on pages 69 and 73.
Correspondence: Sander Greenland, 22333 Swenson Drive, Topanga, CA. E-mail: email@example.com.