(Received March 27, 1995; revised April 3, 1996)
Abstract. In the usual frequentist formulation of testing and interval estimation there is a strong relationship between alpha-level tests and 1 - alpha confidence intervals. Such strong relationships do not always persist for post-data, or Bayesian, measures of accuracy of these procedures. We explore the relationship between post-data measures of accuracy of both tests and interval estimates, measures that are derived under a decision-theoretic structure. We find that, in general, there are strong post-data relationships in the one-sided case, and some relationships in the two-sided case.
Key words and phrases: Posterior probability, coverage probability, null hypothesis, Bayes, p-value.