Canonical Analysis - Advanced Tab

Select the Advanced tab of the Canonical Analysis dialog box to access the options described here. Use these options to review complete summary results from the canonical analysis. Canonical variate spreadsheets are unlimited/user-limited as defined by the Max. number of cases in a single results spreadsheet box on the Discriminant Function Analysis Results dialog box - Classification tab.

Summary: Chi square tests of successive roots

Click this button to produce a spreadsheet with a step-down test for canonical roots (and discriminant functions). The first row in that spreadsheet contains the test of significance for all roots combined. The second row contains the significance of the remaining roots, after removing the first root, and so on. Thus, this spreadsheet allows you to evaluate how many significant roots to interpret.

Coefficients for canonical variables

Click this button to produce a spreadsheet with the raw discriminant (canonical) function coefficients. These are the coefficients that can be used to compute the raw canonical scores for each case for each discriminant function. Also included in this spreadsheet will be the eigenvalues for each discriminant function and the cumulative proportion of (common) variance extracted by each discriminant function.

Note: standardized discriminant function weights. A second spreadsheet will be produced that reports the standardized discriminant function coefficients. These coefficients are computed by multiplying the raw coefficients by the square root of the pooled within-group covariances for the respective variables (use option Pooled within-groups covariances & correlations from the Within tab of the Review Descriptive Statistics dialog box to display the within-group covariances). These coefficients thus apply to the standardized variables (with unit variance), in the sense that these coefficients reflect the change in the canonical scores per unit change in the (standardized) independent (continuous or Y) variables (if you rescale the Y variables, the raw coefficients will change but the standardized coefficients remain the same). Therefore, these coefficients may be compared in order to determine the magnitudes and directions of the (unique) contributions of the variables to each canonical function.

Factor structure

Click the Factor structure button to produce a spreadsheet with the pooled within-groups correlations of variables with the respective discriminant (canonical) functions. If you are familiar with factor analysis (see Factor Analysis), you may think of these correlations as the factor loadings of the respective variables on the discriminant functions.

Some authors have argued that to interpret the "meaning" of the discriminant functions, one should use these structure coefficients rather than the standardized discriminant function coefficients. Refer to the Introductory Overview of Discriminant Function Analysis for a discussion of this argument. The most important thing to remember is that the discriminant function weights denote the unique (partial) contribution of each variable to the discriminant functions, while the structure coefficients denote the simple correlations between the variables and the functions; therefore, the structure coefficients are usually more appropriate for substantive interpretations of functions.

Means of canonical variables

Click this button to produce a spreadsheet containing the means for the discriminant functions. These means make it possible for you to determine the groups that are best identified (discriminated) by each discriminant function.