The Brown–Forsythe test is a statistical test for the equality of group variances based on performing an Analysis of Variance (ANOVA) on a transformation of the response variable.
When a one-way ANOVA is performed, samples are assumed to have been drawn from distributions with equal variance.
If this assumption is not valid, the resulting F-test is invalid.
The Brown–Forsythe test statistic is the F statistic resulting from an ordinary one-way analysis of variance on the absolute deviations of the groups or treatments data from their individual medians.
[1] The transformed response variable is constructed to measure the spread in each group.
Although the optimal choice depends on the underlying distribution, the definition based on the median is recommended as the choice that provides good robustness against many types of non-normal data while retaining good statistical power.
Using the mean provided the best power for symmetric, moderate-tailed, distributions.
O'Brien tested several ways of using the traditional analysis of variance to test heterogeneity of spread in factorial designs with equal or unequal sample sizes.
The jackknife pseudovalues of s2 and the absolute deviations from the cell median are shown to be robust and relatively powerful.
[5] This article incorporates public domain material from the National Institute of Standards and Technology