Open Access
2023 Default Bayes Factors for Testing the (In)equality of Several Population Variances
Fabian Dablander, Don van den Bergh, Eric-Jan Wagenmakers, Alexander Ly
Author Affiliations +
Bayesian Anal. Advance Publication 1-25 (2023). DOI: 10.1214/23-BA1369


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 a 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 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.

Funding Statement

FD, DvB, EJW, and AL were supported by a Vici grant no. C.2523.0278.01.


The authors would like to thank Victor Peña for inspiring discussions on across-sample consistency and the editor Michele Guindani and two anonymous reviewers for their remarks on a previous version of the manuscript.


Download Citation

Fabian Dablander. Don van den Bergh. Eric-Jan Wagenmakers. Alexander Ly. "Default Bayes Factors for Testing the (In)equality of Several Population Variances." Bayesian Anal. Advance Publication 1 - 25, 2023.


Published: 2023
First available in Project Euclid: 3 February 2023

arXiv: 2003.06278
Digital Object Identifier: 10.1214/23-BA1369

Primary: 62F03 , 62F15

Keywords: Bayes factors , Comparing variances , Model selection

Advance Publication
Back to Top