Let X be binomial (n, p), with n known. Suppose we wish to test H: (Equation presented) against K: (Equation presented). We consider the problem of choosing a prior distribution for p. Using a theory which introduces certain ideas of the Neyman-Pearson approach to Bayesian testing, it is shown that one need not specify a prior exactly, but only an equivalence class of priors. The equivalence class of the uniform prior over K allows us to specify certain situations involving only partial knowledge about the parameter in which one can use the uniform as the appropriate prior. © 1974, Taylor & Francis Group, LLC.