Researchers often have expectations about the research outcomes in regard to inequality constraints between, e.g., group means. Consider the example of researchers who investigated the effects of inducing a negative emotional state in aggressive boys. It was expected that highly aggressive boys would, on average, score higher on aggressive responses toward other peers than moderately aggressive boys, who would in turn score higher than nonaggressive boys. In most cases, null hypothesis testing is used to evaluate such hypotheses. We show, however, that hypotheses formulated using inequality constraints between the group means are generally not evaluated properly. The wrong hypotheses are tested, i.e.. the null hypothesis that group means are equal. In this article, we propose an innovative solution to these above-mentioned issues using Bayesian model selection, which we illustrate using a case study. (Contains 5 tables and 1 figure.)