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For the one-sided hypothesis testing problem it is shown that it is possible to reconcile Bayesian evidence against H0, expressed in terms of the posterior probability that Ho is true, with frequentist evidence against H0, expressed in terms of the p value. In fact, for many classes of prior distributions it is shown that the infimum of the Bayesian posterior probability of Ho is equal to the p value; in other cases the infimum is less than the p value. The results are in contrast to recentdoi:10.2307/2289130 fatcat:4j7r6wj77nb43ntry2jie7vr54