Levene's test

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In statistics, Levene's test compares the variances of samples. Some common statistical procedures assume that variances across samples are equal and Levene's test is used to examine this assumption. These procedures include analysis of variance and t-tests.

Levene's test is often used before a comparison of means. When Levene's test is significant, modified procedures are used that do not assume equality of variance.

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},

where

Z_{ij} = |Y_{ij} - \bar{Y}_{i\cdot}|.

See Jason Crowther's document regarding Levene's test at [1]. The instructions for performing the test are extensive, complete with sample problem, but the theoretical reasons for performing it are largely absent.

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