Which statistical test evaluates equality of variances across groups?

Which statistical test evaluates equality of variances across groups?

• A. Bartlett's test
• B. Shapiro-Wilk test
• C. ANOVA test
• D. Levene's test

Answer: (D)

Equal variances across groups is about homogeneity of variances, an assumption for many parametric tests. Levene's test checks whether the variability in each group is similar by looking at how far observations deviate from their group mean (or median, in a robust version) and then using an ANOVA on those deviations. If the deviations differ a lot across groups, you infer that variances are not equal. This test is preferred in many situations because it is more robust to departures from normality than Bartlett's test, which also assesses equality of variances but relies on normal data. Shapiro-Wilk, on the other hand, assesses whether a single sample is normally distributed, not whether variances are equal across groups. ANOVA analyzes whether group means differ and assumes equal variances as part of its conditions, but it does not directly test variance equality itself.

Equal variances across groups is about homogeneity of variances, an assumption for many parametric tests. Levene's test checks whether the variability in each group is similar by looking at how far observations deviate from their group mean (or median, in a robust version) and then using an ANOVA on those deviations. If the deviations differ a lot across groups, you infer that variances are not equal.

This test is preferred in many situations because it is more robust to departures from normality than Bartlett's test, which also assesses equality of variances but relies on normal data. Shapiro-Wilk, on the other hand, assesses whether a single sample is normally distributed, not whether variances are equal across groups. ANOVA analyzes whether group means differ and assumes equal variances as part of its conditions, but it does not directly test variance equality itself.