Levene and Brown-Forsythe Test for Equality of Variances
Also known as: Levene test, Brown-Forsythe test, homogeneity of variance test, Levene ve Brown-Forsythe Varyans Testi
The Levene and Brown-Forsythe test checks whether two or more groups share the same variance (homogeneity of variance). Levene (1960) built the test on absolute deviations from each group mean, and Brown and Forsythe (1974) made it robust to non-normal data by centring on the group median instead.
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When to use it
Use it before an ANOVA, t-test, or any procedure that assumes equal variances across two or more independent groups of continuous data, with at least about 20 observations overall. Because it does not require the data to be normally distributed, the median-centred Brown-Forsythe form is the safer default when the distributions are skewed or have heavy tails. The groups must be independent and the response measured on a continuous scale.
Strengths & limitations
- Does not require the data to be normally distributed, unlike Bartlett's test.
- The Brown-Forsythe (median-centred) variant is robust to skew and outliers, staying accurate on non-normal distributions.
- Conceptually simple: it is just a one-way ANOVA applied to absolute deviations from the group centre.
- Statistical power is low in very small samples; with fewer than 10 observations a permutation test is preferable.
- With fewer than 5 observations the homogeneity-of-variance test is essentially meaningless.
- Assumes independent groups and a continuous response; it does not handle repeated-measures or paired structures.
Frequently asked
What is the difference between the Levene and Brown-Forsythe versions?
Both run an ANOVA on absolute deviations from a group centre. The original Levene test uses the group mean as the centre, while the Brown-Forsythe variant uses the group median, which makes it much more robust to skewed distributions and outliers.
Do my data need to be normally distributed?
No. A key advantage of this test is that it does not assume normality. The median-centred Brown-Forsythe form in particular stays reliable on non-normal data, which is why it is often preferred over Bartlett's test.
What does a significant result mean?
A small p-value rejects the hypothesis that all groups have equal variance, indicating heterogeneity of variance. It says nothing about whether the group means differ — it only concerns the spread of the data.
What if my samples are very small?
With fewer than about 10 observations the test has low power, so a permutation test is preferable; with fewer than 5 observations a variance-homogeneity test is essentially uninformative and bootstrap-based inference is more appropriate.
Sources
- Levene, H. (1960). Robust Tests for Equality of Variances. In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling. Stanford University Press. link ↗
- Brown, M. B. & Forsythe, A. B. (1974). Robust Tests for the Equality of Variances. Journal of the American Statistical Association, 69(346), 364-367. DOI: 10.1080/01621459.1974.10482955 ↗
How to cite this page
ScholarGate. (2026, June 1). Levene and Brown-Forsythe Test for Equality of Variances. ScholarGate. https://scholargate.app/en/statistics/levene-brown-forsythe
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