2020/03/13 by Fabian Dablander, Don van den Bergh, Dablander, Fabian +5
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods in Clinical Trials
paper · doi:10.48550/arxiv.2003.06278
openalex publication_date 2020/03/13 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
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 variances equal 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 show that our Bayes factor fulfills a number of desiderata. Researchers may have directed hypotheses such as σ12 > σ22, they may want to extend H0 to have a null-region, or wish to combine hypotheses about equality with hypotheses about inequality, for example σ12 = σ22 > (σ32, σ42). We extend our Bayes factor test to allow for these deviations from our proposed default and illustrate it on a number of practical examples. Our procedure is implemented in the R package bfvartest.