Hypothesis Test for Unequal Variance When Populations are not Normally Distributed

#1
Hello,

I have a situation where I would like to test the hypothesis that the variance of population one is great than the variance of population two. The two samples taken are known to come from populations that are not normally distributed. Also, there doesn't appear to be any symmetry in the distributions of the samples. I've looked into both the Brown Forsythe test and Levene's test, but these test seem to only allow you to test for the variances being unequal(you can't make an assertion about which is greater). Essentially, I would like something like the standard F-test for comparing var1>var2, but that isn't extremely sensitive to the underlying populations for each sample being normally distributed. Any ideas or suggestions would be appreciated.