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Levene's and Brown-Forsythe's tests
for homogeneity of varianceLevene's test Brown-Forsythe's tests
Levene'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 F-ratio calculated as below:
The F-ratio is tested against the upper critical value of the F distribution with k-1 and N-k 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 Brown-Forsythe versions of the test are preferred.
Levene'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.