Roy's largest root in MANOVA refers to which of the following?

Roy's largest root in MANOVA refers to which of the following?

• A. The mean of the discriminant function scores.
• B. An eigenvalue for the first discriminant function variate in MANOVA.
• C. The determinant of the covariance matrix.
• D. The Hotelling T-squared statistic.

Answer: (B)

Roy's largest root captures the strongest multivariate separation among the groups by using the eigenvalues that come from the discriminant analysis. In MANOVA you form the within-group and between-group scatter—often denoted E and H—and look at the matrix E^{-1}H. The eigenvalues of this matrix tell you how much of the separation between group means can be explained along each discriminant function. The largest of these eigenvalues—the Roy's largest root—belongs to the first discriminant function variate, the linear combination of the dependent variables that yields the greatest separation among the groups. So this statistic is specifically an eigenvalue associated with the first discriminant function variate. It’s not a mean of discriminant scores, not the determinant of a covariance matrix, and not Hotelling’s T-squared.

Roy's largest root captures the strongest multivariate separation among the groups by using the eigenvalues that come from the discriminant analysis. In MANOVA you form the within-group and between-group scatter—often denoted E and H—and look at the matrix E^{-1}H. The eigenvalues of this matrix tell you how much of the separation between group means can be explained along each discriminant function. The largest of these eigenvalues—the Roy's largest root—belongs to the first discriminant function variate, the linear combination of the dependent variables that yields the greatest separation among the groups. So this statistic is specifically an eigenvalue associated with the first discriminant function variate. It’s not a mean of discriminant scores, not the determinant of a covariance matrix, and not Hotelling’s T-squared.