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In this paper, we show that the conditional frequentist method of testing a precise hypothesis can be made virtually equiva- lent to Bayesian testing. The conditioning strategy proposed by Berger, Brown and Wolpert in 1994, for the simple versus simple case, is gener- alized to testing a precise null hypothesis versus a composite alternative hypothesis. Using this strategy, both the conditional frequentist and the Bayesian will report the same error probabilities upon rejecting or ac- cepting. This is of considerable interest because it is often perceived that Bayesian and frequentist testing are incompatible in this situation. That they are compatible, when conditional frequentist testing is allowed, is a strong indication that the \wrong" frequentist tests are currently be- ing used for postexperimental assessment of accuracy. The new unied testing procedure is discussed and illustrated in several common testing situations.

Unified frequentist and Bayesian testing of a precise hypothesis