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Research has shown that independent groups often differ not only in their means, but also in their variances. Comparing and testing variances is therefore of crucial importance to understand the effect of a grouping variable on an outcome variable. Researchers may have specific expectations concerning the relations between the variances of multiple groups. Such expectations can be translated into hypotheses with inequality and/or equality constraints on the group variances. Currently, however, no methods are available for testing (in)equality constrained hypotheses on variances. This article proposes a novel Bayesian approach to this challenging testing problem. Our approach has the following useful properties: First, it can be used to simultaneously test multiple (non)nested hypotheses with equality as well as inequality constraints on the variances. Second, our approach is fully automatic in the sense that no subjective prior specification is needed. Only the hypotheses need to be provided. Third, a user-friendly software application is included that can be used to perform this Bayesian test in an easy manner.