Which test assesses the equality of covariance matrices across groups?

Which test assesses the equality of covariance matrices across groups?

• A. Mauchly's test
• B. Levene's test
• C. Box's test
• D. Bartlett's test

Answer: (C)

Box's M test is used to assess whether the covariance matrices of multiple dependent variables are the same across groups. In MANOVA, this equality of covariance structures across groups is an important assumption, and Box's test directly tests it by comparing each group's covariance matrix to a pooled estimate. The null hypothesis is that all groups share a common covariance matrix. A significant result suggests that the covariance patterns differ between groups, which can impact the validity of MANOVA results and may lead you to consider robustness checks or alternative analyses. Mauchly's test, by contrast, checks sphericity in repeated-measures designs, not equality of covariance matrices across groups. Levene's test assesses whether variances are equal across groups for a single variable, and Bartlett's test focuses on equality of variances under normality for a single variable. None of these examine the equality of covariance matrices among several dependent variables across groups.

Box's M test is used to assess whether the covariance matrices of multiple dependent variables are the same across groups. In MANOVA, this equality of covariance structures across groups is an important assumption, and Box's test directly tests it by comparing each group's covariance matrix to a pooled estimate. The null hypothesis is that all groups share a common covariance matrix. A significant result suggests that the covariance patterns differ between groups, which can impact the validity of MANOVA results and may lead you to consider robustness checks or alternative analyses.

Mauchly's test, by contrast, checks sphericity in repeated-measures designs, not equality of covariance matrices across groups. Levene's test assesses whether variances are equal across groups for a single variable, and Bartlett's test focuses on equality of variances under normality for a single variable. None of these examine the equality of covariance matrices among several dependent variables across groups.