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I run an experiment on both men and women participants, where I manipulate an independent variable. I know that the manipulation causes greater variance in the outcomes of the experimental group (a Levene's test comes back highly significant). Now I wonder whether the increase in variance when being exposed to the manipulation is greater for men participants than it is for women participants, but am not sure how to do this two-way comparison. Or, in other words, I'm interested in an interaction effect, but where the dependent variable is variance. What test should I use? Thanks!

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Answering my own question: Turns out this reply to another post was really helpful. Levene's test is just an ANOVA where the dependent variable is the residual to the mean (or median, in the case of Brown-Forsythe). And so, you can actually run a two-way Levene's and voila, problem solved.

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