title: Living with p values: resurrecting a Bayesian perspective on frequentist statistics.
abstract: 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.
authors.affiliation: Department of Epidemiology, University of California, Los Angeles, CA, USA. lesdomes@ucla.edu
authors.forename: Sander
authors.initials: S
authors.lastname: Greenland
authors.forename: Charles
authors.initials: C
authors.lastname: Poole
mesh_terms: D001499:Bayes Theorem; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D016013:Likelihood Functions; D015233:Models, Statistical