Statistics Definitions > Levene Test
What is the Levene Test?
Levene’s test is used to check that variances are equal for all samples when your data comes from a non normal distribution. You can use Levene’s test to check the assumption of equal variances before running a test like One-Way ANOVA.
The null hypothesis for Levene’s is that the variances are equal across all samples. In more formal terms, that’s written as:
H0: σ12 = σ22 = … = σk2.
The alternate hypothesis (the one you’re testing), is that the variances are not equal for at least one pair:
H0: σ12 ≠ σ22 ≠… ≠ σk2.
The test statistic is a little ugly:
Zi,j can take on three meanings, depending on if you use the mean, median, or trimmed mean of any subgroup. The three choices actually determine the robustness and power of the test.
- Robustness, is a measure of how well the test does not falsely report unequal variances (when the variances are actually equal).
- Power is a measure of how well the test correctly reports unequal variances.
According to Brown and Forsythe:
- Trimmed means work best with heavy-tailed distributions like the Cauchy distribution.
- For skewed distributions, or if you aren’t sure about the underlying shape of the distribution, the median may be your best choice.
- For symmetric and moderately tailed distributions, use the mean.
Levene’s test is built into most statistical software. For example, the Independent Samples T Test in SPSS generates a “Levene’s Test for Equality of Variances” column as part of the output. The result from the test is reported as a p-value, which you can compare to your alpha level for the test. If the p-value is larger than the alpha level, then you can say that the null hypothesis stands — that the variances are equal; if the p-value is smaller than the alpha level, then the implication is that the variances are unequal.
Brown, M. B. and Forsythe, Robust Tests for the Equality of Variances. A. B. (1974), Journal of the American Statistical Association, 69, pp. 364-367. Available here.
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