APPLIED MULTIVARIATE STATISTICS: WITH SAS® SOFTWARE

3.4. ANOVA Partitioning

In the multivariate context, the role of the total sum of squares is played by the p by p positive definite matrix of (corrected) total sums of squares and crossproducts (SS&CP) defined as

Apart from the dividing factor, a typical element of the matrix in Equation 3.6, say the one corresponding to the i^th row and j^th column, is the same as the sample covariance between the i^th and j^th dependent variables. Consequently, the diagonal elements of T are the (corrected) total sums of squares for the respective dependent variables.

Assuming that Rank(X) = k + 1, this matrix can be partitioned as the sum of the two p by p positive ...