<Dl> <Dd> F = S X 2 S Y 2 (\ displaystyle F = (\ frac (S_ (X) ^ (2)) (S_ (Y) ^ (2)))) </Dd> </Dl> <Dd> F = S X 2 S Y 2 (\ displaystyle F = (\ frac (S_ (X) ^ (2)) (S_ (Y) ^ (2)))) </Dd> <P> has an F - distribution with n − 1 and m − 1 degrees of freedom if the null hypothesis of equality of variances is true . Otherwise it follows an F - distribution scaled by the ratio of true variances . The null hypothesis is rejected if F is either too large or too small . </P> <P> This F - test is known to be extremely sensitive to non-normality, so Levene's test, Bartlett's test, or the Brown--Forsythe test are better tests for testing the equality of two variances . (However, all of these tests create experiment-wise type I error inflations when conducted as a test of the assumption of homoscedasticity prior to a test of effects .) F - tests for the equality of variances can be used in practice, with care, particularly where a quick check is required, and subject to associated diagnostic checking: practical text - books suggest both graphical and formal checks of the assumption . </P>

F-procedures for comparing variances of populations are robust