In MANOVA, the Hotelling-Lawley trace can be interpreted as the sum of eigenvalues across discriminant variates. What does this imply about the statistic?

• A. It is the product of eigenvalues across all discriminant functions
• B. It is the average of eigenvalues
• C. It is the sum of eigenvalues for each discriminant function
• D. It is the difference between largest and smallest eigenvalues

Answer: (C)

In MANOVA, the Hotelling-Lawley trace captures how much group separation there is across all discriminant functions by adding up the contributions from each function. Each discriminant function has an eigenvalue that measures how strongly that particular linear combination separates the groups. By summing these eigenvalues across all discriminant functions, the statistic provides a single overall measure of multivariate separation. Therefore, this implies the statistic is the sum of eigenvalues for each discriminant function. It’s not a product, an average, or a difference of eigenvalues—the trace inherently adds the contributions from all canonical variates to reflect total discriminant strength.