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 and select Matrices (hypothesis, error, partial correlations) under Display of Results.

Use 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.

## Interpretation

For these results, the univariate sums of squares for usability and quality for
method are 29.07 and 9.22. 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 Rating | 29.0738 | 16.3722 |
---|

Quality Rating | 16.3722 | 9.2196 |
---|

## SSCP Matrix (adjusted) for Error

Usability Rating | 49.7543 | 29.4504 |
---|

Quality Rating | 29.4504 | 68.5900 |
---|

## Partial Correlations for the Error SSCP Matrix

Usability Rating | 1.00000 | 0.50413 |
---|

Quality Rating | 0.50413 | 1.00000 |
---|