In MANOVA, which statistic is the sum of eigenvalues for each discriminant function variate and is conceptually the same as the F-statistic in ANOVA?

In MANOVA, which statistic is the sum of eigenvalues for each discriminant function variate and is conceptually the same as the F-statistic in ANOVA?

• A. Hotelling-Lawley trace (T2)
• B. Wilks' lambda
• C. Pillai's trace
• D. Roy's largest root

Answer: (A)

Hotelling's trace sums the eigenvalues that come from the E⁻¹H decomposition in MANOVA. Those eigenvalues arise from the discriminant functions that best separate the groups, and adding them up gives an overall measure of how different the groups are on the combined dependent variables. Because it aggregates information across all discriminant functions, this statistic functions much like the F-statistic in ANOVA: a larger value signals stronger multivariate group differences and is used to assess significance. The other options summarize multivariate effects in different ways—Wilks' lambda uses a determinant ratio, Pillai's trace combines eigenvalues differently, and Roy's largest root relies on a single largest eigenvalue—so they don’t provide the same overall sum across all discriminant variates.

Hotelling's trace sums the eigenvalues that come from the E⁻¹H decomposition in MANOVA. Those eigenvalues arise from the discriminant functions that best separate the groups, and adding them up gives an overall measure of how different the groups are on the combined dependent variables. Because it aggregates information across all discriminant functions, this statistic functions much like the F-statistic in ANOVA: a larger value signals stronger multivariate group differences and is used to assess significance. The other options summarize multivariate effects in different ways—Wilks' lambda uses a determinant ratio, Pillai's trace combines eigenvalues differently, and Roy's largest root relies on a single largest eigenvalue—so they don’t provide the same overall sum across all discriminant variates.