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.

*If you’re fairly certain your data comes from a normal or nearly normal distribution, use Bartlett’s Test instead. *

The null hypothesis for Levene’s is that the variances are equal across all samples. In more formal terms, that’s written as:

H_{0}: σ_{1}^{2} = σ_{2}^{2} = … = σ_{k}^{2}.

The alternate hypothesis (the one you’re testing), is that the variances are **not equal** for at least one pair:

H_{0}: σ_{1}^{2} ≠ σ_{2}^{2} ≠… ≠ σ_{k}^{2}.

The test statistic is a little ugly:

Z_{i,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* un*equal.

**Reference**:

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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*Statistical concepts explained visually* - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.

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