Living with p values: resurrecting a Bayesian perspective on frequentist statistics

Epidemiology. 2013 Jan;24(1):62-8. doi: 10.1097/EDE.0b013e3182785741.


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.

MeSH terms

  • Bayes Theorem*
  • Confidence Intervals
  • Data Interpretation, Statistical*
  • Likelihood Functions
  • Models, Statistical