Null-hypothesis significance testing remains the standard inferential tool in cognitive science despite its serious disadvantages. Primary among these is the fact that the resulting probability value does not tell the researcher what he or she usually wants to know: How probable is a hypothesis, given the obtained data? Inspired by developments presented by Wagenmakers ( Psychonomic Bulletin & Review, 14 , 779–804, 2007 ), I provide a tutorial on a Bayesian model selection approach that requires only a simple transformation of sum-of-squares values generated by the standard analysis of variance. This approach generates a graded level of evidence regarding which model (e.g., effect absent null hypothesis vs. effect present alternative hypothesis) is more strongly supported by the data. This method also obviates admonitions never to speak of accepting the null hypothesis. An Excel worksheet for computing the Bayesian analysis is provided as supplemental material .