Some cautions about Levene’s test: You need to assume that the absolute values of the residuals satisfy the assumptions of ANOVA. Another choice may be better based on knowledge of the underlying distribution of the data. Using the mean provided the best power for symmetric, moderate-tailed, distributions.Īlthough 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 power. They performed Monte Carlo studies that indicated that using the trimmed mean performed best when the underlying data had a heavy-tailed distribution and the median performed best when the underlying data had a skewed distribution. Brown and Forsythe extended Levene’s test to use either the median or the trimmed mean. Levene’s original paper only proposed using the mean. By power, we mean the ability of the test to detect unequal variances when the variances are in fact unequal. By robustness, we mean the ability of the test to not falsely detect unequal variances when the underlying data are not normally distributed and the variables are in fact equal. The three choices determine the robustness and power of Levene’s test.
Use of mean (as in the explanation above).There are three versions of the Levene’s test: 05 = α (Figure 1), we cannot reject the null hypothesis, and conclude there is no significant difference between the 4 group means, and so the ANOVA test conducted previously for Example 2 of Basic Concepts for ANOVA satisfies the homogeneity of variances assumption.
If the group variances are equal, then the average size of the residual should be the same across all groups.Įxample 1: Use Levene’s test to determine whether the 4 samples in Example 2 of Basic Concepts for ANOVA have significantly different population variances. For Levene’s test of the homogeneity of group variances, the residuals e ijof the group means from the cell means are calculated as follows:Īn ANOVA is then conducted on the absolute value of the residuals.
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