Which statistic is the multivariate equivalent of the total sum of squares?

• A. Total sum of squares
• B. Trimmed mean
• C. Total SSCP (T)
• D. Transformation

Answer: (C)

In multivariate analysis, overall dispersion across several dependent variables is captured by a matrix that sums up the squared deviations and their cross-products. This total SSCP matrix summarizes variances for each variable on the diagonal and covariances between variable pairs off the diagonal, providing a single multivariate measure of total variability. It’s the direct generalization of the univariate total sum of squares, just in matrix form, often denoted T.

The other terms don’t express dispersion across multiple variables: the univariate total sum of squares is a single scalar for one variable, a trimmed mean relates to a robust measure of central tendency, and a transformation is just a data processing step.