Levene's test

In statistics, Levene's test is an inferential statistic used to assess the equality of variance in different samples. Some common statistical procedures assume that variances of the populations from which different samples are drawn are equal. Levene's test assesses this assumption. It tests the null hypothesis that the population variances are equal. If the resulting p-value of Levene's test is less than some critical value (typically .05), the obtained differences in sample variances are unlikely to have occurred based on random sampling. Thus, the null hypothesis of equal variances is rejected and it is concluded that there is a difference between the variances in the population.

Procedures which typically assume homogeneity of variance 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. The instructions for performing the test are extensive, complete with sample problem, but the theoretical reasons for performing it are largely absent.

Levene's test may also test a meaningful question in its own right if a researcher is interested in knowing whether population group variances are different.