# Using F-tests for variance in non-normal populations

I'm fairly new to stats, so please excuse me if this problem is hopelessly elementary or misinformed. Basically, I'm wondering if you can help me understand whether I'm using the F-Test for variance correctly.

I have two fairly small populations (n=15), and I'd like to employ a statistical test to determine their respective variances differ significantly. Group A is relatively normally distributed, and group B is skewed left. Originally, I used an F-Test for variance to test for a difference in variance, but then I learned that the F-test can yield false positives if a population isn't normally distributed (as is the case with group B). To remedy this, I created a distribution of sample means for each of the two groups and then performed the F-Test to compare the variance of those distributions. Those distributions of sample means are obviously normal. However, is it appropriate to do an F-Test for variance on those distributions? And how exactly should I interpret the test results?

Just in case it's important, the software I'm using is R and the F-test in R is accessed through var.test()

• Presumably you have two small samples of much larger populations or processes, for otherwise applying a statistical test makes no sense. If one of those samples looks strongly skewed, and you believe that implies the population it represents must be skewed, too, then please pause to ponder why you are comparing variances in the first place. You already believe the population distributions differ (in shape) and the variance has a different interpretation for a skewed population than it does for a symmetrical one. What, then, would the point of testing the variances be?
– whuber
Jul 9, 2014 at 19:22
• How exactly did you create "a distribution of sample means for each of the two groups"? Jul 9, 2014 at 19:37