P Values and Statistical Practice

Like many Bayesians, I have often represented classical confidence intervals as posterior probability intervals and interpreted one-sided P values as the posterior probability of a positive effect. These are valid conditional on the assumed noninformative prior but typically do not make sense as unconditional probability statements. As Sander Greenland has discussed in much of his work over the years, epidemiologists and applied scientists in general have knowledge of the sizes of plausible effects and biases. I believe that a direct interpretation of P values as posterior probabilities can be a useful start-if we recognize that such summaries systematically overestimate the strength of claims from any particular dataset. In this way, I am in agreement with Greenland and Poole's interpretation of the one-sided P value as a lower bound of a posterior probability, although I am less convinced of the practical utility of this bound, given that the closeness of the bound depends on a combination of sample size and prior distribution.The default conclusion from a noninformative prior analysis will almost invariably put too much probability on extreme values. A vague prior distribution assigns much of its probability on values that are never going to be plausible, and this disturbs the posterior probabilities more than we tend to expect-something that we probably do not think about enough in our routine applications of standard statistical methods. Greenland and Poole1 perform a valuable service by opening up these calculations and placing them in an applied context. © 2012 by Lippincott William & Wilkins.