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This article provides a Bayes factor approach to multiway analysis of variance (ANOVA) that allows researchers to state graded evidence for effects or invariances as determined by the data. ANOVA is conceptualized as a hierarchical model where levels are clustered within factors. The development is comprehensive in that it includes Bayes factors for fixed and random effects and for within-subjects, between-subjects, and mixed designs. Different model construction and comparison strategies are discussed, and an example is provided. We show how Bayes factors may be computed with BayesFactor package in R and with the JASP statistical package.