Direct Inference Requiring Only a Touch of Bayes

• Activity Number: 246
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Consulting
• Author(s): Ralph G. O'Brien*+
• Companies: Case Western Reserve University
• Keywords: sequential testing ; meta analysis ; equivalence testing ; non-inferiority testing ; false discovery rate

Abstract

For some parameter, tau, define a null interval, {0} = {tau0.lo <= tau <= tau0.hi}, with tau0.lo = tau0.hi = tau0 defining a point null value. Non-null regions are {-} = {tau < tau0.lo} and {+} = {tau > tau0.hi}. Let Pr{-}, Pr{0}, Pr{+} be prior probabilities, a "touch of Bayes." Let S be a frequentist statistic for testing hypotheses on tau. A proposed likelihood-based method yields posteriors: Pr[{-}|S], Pr[{+}|S], Pr[{0}|S]; thus providing "direct" inference, as opposed to the "circumstantial" inference obtained using ordinary p-values. This presentation outlines the theory and gives several examples, beginning with a traditional-like, two-sided test of Ho: tau = tau0. Other examples show how the scheme handles tests with an interval null region (e.g., equivalence and non-inferiority tests), and sequential and meta analyses. A related statistical interval for tau is also proposed.