This paper considers the problem of choosing the sample size for testing hypotheses on the parameters of a model using Bayes factors. Extending the evidential approach outlined in Royall (Statistical Evidence: a Likelihood paradigm. Chapman & Hall, London (1997), J. Amer. Statist. Assoc. 95 (2000) 760) to the Bayesian framework, the predictive criterion proposed for determining the sample size is maximizing the probability of obtaining substantial evidence in favor of the true hypotheses, i.e. minimizing the probabilities of having either misleading or weak evidence. The method is developed for the normal model in several testing problems that arise, for instance, when comparing treatments in clinical trials. © 2003 Elsevier B.V. All rights reserved.