Default Bayes Factors for Testing the (In)equality of Several Population Variances
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Testing the (in)equality of variances is an important problem in many statistical applications. We develop default Bayes factor tests to assess the (in)equality of two or more population variances, as well as a test for whether the population variance equals a specific value. The resulting test can be used to check assumptions for commonly used procedures such as the t-test or ANOVA, or test substantive hypotheses concerning variances directly. We further extend the Bayes factor to allow H_0 to have a null-region. Researchers may have directed hypotheses such as σ_1^2 > σ_2^2, or want to combine hypotheses about equality with hypotheses about inequality, for example σ_1^2 = σ_2^2 > (σ_3^2, σ_4^2). We generalize our Bayes factor to accommodate such hypotheses for K > 2 groups. We show that our Bayes factor fulfills a number of desiderata, provide practical examples illustrating the method, and compare it to a recently proposed fractional Bayes factor procedure by Böing-Messing Mulder (2018). Our procedure is implemented in the R package bfvartest.
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