<P> Levene's test is often used before a comparison of means . When Levene's test shows significance, one should switch to more generalized tests that is free from homoscedasticity assumptions (sometimes even non-parametric tests). </P> <P> Levene's test may also be used as a main test for answering a stand - alone question of whether two sub-samples in a given population have equal or different variances . </P> <P> The test statistic, W (\ displaystyle W), is defined as follows: </P> <Dl> <Dd> W = (N − k) (k − 1) ∑ i = 1 k N i (Z i ⋅ − Z ⋅ ⋅) 2 ∑ i = 1 k ∑ j = 1 N i (Z i j − Z i ⋅) 2, (\ displaystyle W = (\ frac ((N-k)) ((k - 1))) (\ frac (\ sum _ (i = 1) ^ (k) N_ (i) (Z_ (i \ cdot) - Z_ (\ cdot \ cdot)) ^ (2)) (\ sum _ (i = 1) ^ (k) \ sum _ (j = 1) ^ (N_ (i)) (Z_ (ij) - Z_ (i \ cdot)) ^ (2))),) </Dd> </Dl>

Levene's test of equality of error variances significant anova