# Nonparametric equal variance tests

I have two large, non-normal samples as evidenced by the Kolmogorov-Smirnov test. I now wish to test for equality of variance nonparametrically. I'm confused as to which nonparametric test is appropriate when comparing variances across two samples that are both non-normal. I have seen Fligner-Killeen and Brown-Forsythe, though I'm not positive which option is best. The samples are not paired, and neither is normal. I'll be performing the test in R.

• Sample sizes are around 50,000 observations. The results of K-S aren't really that critical here, however, as it has been shown that the type of data I'm dealing with is non- normal. My question really pertains to the differences between nonparametric equality of variance tests. What makes Brown-Forsythe different from Fligner-Killeen? In which scenarios are certain tests more appropriate? – logan_stats Jul 21 '15 at 4:44
• Neither of the tests you mention are really nonparametric (though it may arguably depend on just how you define the term); though Fligner-Killeen would tend to come closer to it, I think. They are both pretty robust against non-normality, however (at the expense of some power at the normal, naturally). What would constitute the "best" one may depend on circumstances (and what things you want to do "best" at). However, with 50K observations, (is that in each group, or in total?) ... let me put my money down: you're going to reject the null with either test. – Glen_b Jul 21 '15 at 5:02
• @Glen_b meant with 50K observations, unless your two samples are exactly identical, your test will have enough power to reject almost anything, even some small deviation. – SmallChess Jul 21 '15 at 9:45
• Okay. That makes sense. I'm dealing with specific financial data that are known to be non-normal, so I'd be very shocked if I didn't reject. I'm most concerned with the results of the homogeneity of variance tests – logan_stats Jul 21 '15 at 10:37
• My comments apply to pretty much any test you might use (at least among tests with reasonable power properties), including tests for homogeneity of variance. You will reject with either test. – Glen_b Jul 21 '15 at 11:02