Wilks's lambda in MANOVA represents what?

• A. The ratio of explained variance to total variance for each dependent variable.
• B. The sum of squared residuals across all dependent variables.
• C. The eigenvalue associated with the first discriminant function.
• D. The product of the unexplained variance on each discriminant variate, i.e., the ratio of error variance to total variance for each variate.

Answer: (D)

Wilks's lambda measures how much of the variance in the dependent variables remains unexplained by the group differences, across the set of dependent variables. It’s computed as a determinant ratio that effectively captures the unexplained spread after accounting for the grouping, across all discriminant functions. In practice, you can think of it as the product, across the canonical discriminant variates, of the proportion of variance not explained by the model. A smaller lambda means the groups differ more on the combined dependent variables, because more variance has been explained by group membership. This aligns with the option describing it as the product of the unexplained variance on each discriminant variate, i.e., the ratio of error variance to total variance for each variate.