# One-sided test of equal variances with small (but equal) sample size and non-normal data

I have two groups, each with 6 observations. One group was generated by an old test method. The other group was generated by a new test method. I would like to test if the new method produces more consistent results.

My first instinct is a test for equal variances, with an alternative hypothesis that the new test has a lower variance. I'd like to do this one sided test at the .05 level.

Because my data doesn't look normal (looked at Q-Q plots for each group, for what that is worth with 6 points), I don't want to use the F-Test for unequal variances.

I've read that the Levene and Brown-Forsythe tests are more robust. But the test statistics are derived from absolute values of differences with the mean (Levene) or median (Brown-Forsythe). With an F test the test statistic will be greater (than 1) when the variance in the numerator is higher and between 1 and 0 when the variance in the numerator is lower. So a one-sided interpretation seems intuitive here. The Levene and BF tests will just give a higher test statistic when the variances are further apart and a lower test statistic when they are similar. So I don't understand how to test my one-sided hypothesis with these tests.

• – Peter Ellis Jan 24 '18 at 0:04