In MANOVA, which assumption ensures that the covariance matrices of the dependent variables are equal across groups?

• A. Homogeneity of variance
• B. Homogeneity of regression slopes
• C. Homogeneity of covariance matrices
• D. Normality

Answer: (C)

In MANOVA, the key assumption is that the covariance matrices describing how the dependent variables co-vary are the same across all groups. This equal-covariance condition lets the multivariate test statistics (like Wilks’ Lambda) behave as expected under the null, so differences in group means can be detected accurately without being distorted by different patterns of inter-variable relationships in each group. Box’s M test is commonly used to check this assumption, though it can be sensitive to nonnormal data. If the covariance matrices differ across groups, the results of the multivariate tests can be biased. Other assumptions—such as equal variances for each dependent variable across groups (univariate homogeneity), the same relationship between covariates and dependent variables across groups (homogeneity of regression slopes), and multivariate normality within groups—address different aspects and do not specify the equality of the entire covariance structure.