Minitab can display three sums of squares and cross products (SSCP) matrices to examine variability, error, and partial correlations. To display the SSCP matrix, go to Matrices (hypothesis, error, partial correlations) under Display of Results.

and selectUse the SSCP matrix to assess the partitioning of variability in the same way you do for univariate sums of squares. The matrix labeled as SSCP Matrix for model term is the hypothesis SSCP matrix for the responses with the specified model term. The diagonal elements are the univariate ANOVA sums of squares for the model term for each response. The off-diagonal elements of this matrix are the cross products.

The matrix labeled as SSCP Matrix for Error is the error sums of squares and cross products matrix. The diagonal elements of this matrix are the univariate ANOVA error sums of squares for the response variables. The off-diagonal elements of this matrix are the cross products. This matrix is displayed one time, after the SSCP matrix for the first model term.

Use the matrix of partial correlations, labeled as Partial Correlations for the Error SSCP Matrix, to assess how the response variables are related. The off-diagonal elements are the correlations among the residuals or, equivalently, the correlations among the responses conditioned on the model. If the correlation between the responses is low, you may want to perform univariate ANOVA tests for the individual responses. This matrix is displayed one time, after the SSCP matrix for error.

For these results, the univariate sums of squares for usability and quality for method are 29.07 and 9,220. The univariate error sums of squares for usability and quality are 49.75 and 68.59. The partial correlation between usability and quality is 0.50413, indicating that the response variables are moderately correlated.

SSCP Matrix (adjusted) for Method
Usability Quality
Rating Rating
Usability Rating 29.07 16.372
Quality Rating 16.37 9.220

SSCP Matrix (adjusted) for Error
Usability Quality
Rating Rating
Usability Rating 49.75 29.45
Quality Rating 29.45 68.59

Partial Correlations for the Error SSCP Matrix
Usability Quality
Rating Rating
Usability Rating 1.00000 0.50413
Quality Rating 0.50413 1.00000