Null hypothesis testing (NHT) is the most commonly used tool in empirical psychological research even though it has several known limitations. It is argued that since the hypotheses evaluated with NHT do not reflect the research-question or theory of the researchers, conclusions from NHT must be formulated with great modesty, that is, they cannot be stated in a confirmative way. Since confirmation or theory evaluation is, however, what researchers often aim for, we present an alternative approach that is based on the specification of explicit, informative statistical hypotheses. The statistical approach for the evaluation of these hypotheses is a Bayesian model-selection procedure. A non-technical explanation of the Bayesian approach is provided and it will be shown that results obtained with this method give more direct answers to the questions asked and are easier to interpret. An additional advantage of the offered possibility to formulate and evaluate informative hypotheses is that it stimulates researchers to more carefully think through and specify their expectations. (Contains 2 tables and 3 figures.)