  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 $\sigma_{1}^{2} > \sigma_{2}^{2}$, they may want to
extend $\mathcal{H}_{0}$ to have a null-region, or wish to combine hypotheses
about equality with hypotheses about inequality, for example $\sigma_{1}^{2} =
\sigma_{2}^{2} > (\sigma_{3}^{2}, \sigma_{4}^{2})$. 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 $bfvartest$.
