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Comparing Modeling interaction in variance between 4 groups by two independent variables

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Comparing variance between 4 groups by two independent variables

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!