This article is motivated by an interest in comparing inferences made when using a Bayesian or frequentist statistical approach. The article addresses the study of one-sided superiority and noninferiority Bayesian tests. These tests are stated in terms of the posterior probability that the null hypothesis is true for the binomial distribution and in terms of one-sided credible limits. We restrict our considerations to conjugate beta priors with integer parameters. Under this assumption, the posterior probabilities of tested hypotheses can be transformed into the frequentist probabilities of Bernoulli trials with an adjusted number of events and population sizes. The method resembles a standard frequentist problem formulation. By using an appropriate choice of prior parameters, the posterior probabilities of the null hypothesis can be made smaller or larger than the p-values of frequentist tests.