Bayesian methods are increasingly used in psychology for analyzing experimental data and for identifying mechanisms that mediate the experimental treatments. This article provides a tutorial on a Bayesian approach to the analysis of variance (BANOVA), which provides a comprehensive and coherent framework for those analyses. BANOVA encompasses the analysis of data from between, within, and mixed experimental designs with normal and non-normal dependent variables and accommodates unobserved individual differences in participants' response to the experimental manipulations. An accompanying R package allows specification of a wide range of models with a simple syntax, and can calculate planned comparisons, simple effects, floodlight ranges, indirect effects in mediation, moderated mediation, and effect sizes of direct and indirect effects. The methodology and package are illustrated with applications to three data sets from previously published studies in psychology. (PsycInfo Database Record (c) 2022 APA, all rights reserved).