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Levene's and BrownForsythe's testsfor homogeneity of varianceLevene's test BrownForsythe's testsLevene's testLevene's test is one of the more widely used tests of homogeneity of variances carried out prior to performing an analysis of variance. It tests the null hypothesis that the population variances are equal by carrying out an analysis of variance on the absolute deviations of observations from the group mean. The test statistic is an Fratio calculated as below:
The Fratio is tested against the upper critical value of the F distribution with k1 and Nk degrees of freedom. The (original) Levene's test (detailed above) gives the best power for symmetric, moderate tailed distributions. However, such distributions tend to be rather rare for biological data  so generally the BrownForsythe versions of the test are preferred.
BrownForsythe's testsLevene's test was extended by
Brown and Forsythe
These modifications make the test more robust to nonnormality. The use of deviations from the median is recommended for skewed distributions.
