Fligner-Killeen Test for Homogeneity of Variances
Also known as: Fligner-Killeen test of variance homogeneity, rank-based variance homogeneity test, Fligner-Killeen Varyans Homojenliği Testi
The Fligner-Killeen test is a rank-based test that checks whether several independent groups share the same variance (scale). Introduced by Fligner and Killeen in 1976, it does not require the data to be normally distributed, making it a robust nonparametric alternative to the Levene and Bartlett tests.
Key highlights
- Does not require normality, so it stays valid for skewed and heavy-tailed data.
- Highly robust against outliers and departures from the normal distribution, often outperforming Levene and Bartlett.
- Simple to apply to two or more independent groups and easy to interpret as a yes/no answer on equal variances.
Intuition
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How it works
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When to use it
Use Fligner-Killeen when you have continuous data in two or more independent groups and want to test the equal-variance (homoscedasticity) assumption without assuming normality. It needs only continuous measurements, independent groups, and a reasonable sample (about 20 or more observations); it does not require the data to be normal. It is the preferred choice over Levene or Bartlett when the data are skewed or heavy-tailed. Below roughly 10 observations its power drops and a permutation test is better, and with fewer than 5 observations a rank-based scale test is not meaningful.
Strengths & limitations
- Does not require normality, so it stays valid for skewed and heavy-tailed data.
- Highly robust against outliers and departures from the normal distribution, often outperforming Levene and Bartlett.
- Simple to apply to two or more independent groups and easy to interpret as a yes/no answer on equal variances.
- Loses statistical power in very small samples (n < 10); a permutation test is preferable there.
- With fewer than 5 observations the rank-based scale comparison becomes meaningless.
- Assumes the groups are independent, so it does not apply to paired or repeated-measures designs.
Common pitfalls
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Applications
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Frequently asked
How is Fligner-Killeen different from Levene's test?
Both test equality of variances, but Levene works on absolute deviations directly while Fligner-Killeen converts ranked absolute deviations into normal scores. This rank transformation makes Fligner-Killeen more robust to non-normal and heavy-tailed data.
When should I prefer Fligner-Killeen over Bartlett's test?
Bartlett's test is sensitive to departures from normality and can give misleading results on skewed data. When normality is doubtful, Fligner-Killeen is the safer, distribution-free choice.
Does it tell me which group has a different variance?
No. Like other omnibus variance tests, it only signals whether the variances differ overall. A significant result means at least one group differs in spread, but not which one.
What if my sample is very small?
Below about 10 observations the test loses power, so a permutation test is preferable, and with fewer than 5 observations a rank-based scale test is not meaningful at all.
Sources
- 1.Fligner, M. A., & Killeen, T. J. (1976). Distribution-Free Two-Sample Tests for Scale. Journal of the American Statistical Association, 71(353), 210-213.
- 2.Conover, W. J., Johnson, M. E., & Johnson, M. M. (1981). A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data. Technometrics, 23(4), 351-361.
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ScholarGate. (2026, June 1). Fligner-Killeen Test. ScholarGate. https://scholargate.app/statistics/fligner-killeen-test