# Discriminant Visualizations

The following tables and options are available for Discriminant visualizations.

Analysis Case Processing Summary table

Displays the total and valid numbers of unweighted cases or records in the data set, along with the numbers excluded due to missing data or other data issues.

Group Statistics table

Displays means and standard deviations for predictor fields, as well as unweighted and weighted sample sizes, within each group and the overall data set.

Tests of Equality of Group Means table

Shows tests of equality of group means on each of the predictor fields, based on one-way univariate analyses of variance. Assuming reasonable sample sizes, predictors that do not show significant mean differences over groups are unlikely to be very helpful in classifying observations.

Pooled Within Groups Matrices

Shows covariance and correlation matrices for predictor fields computed by averaging over the within-groups matrices with weights based on group sizes.

Covariance Matrices

Shows covariance matrices of predictor fields within each group and for the entire data set. Examining the matrices for the individual groups can help you to assess whether the assumption of equal population covariance matrices is reasonable, or whether you should specify using separate group covariance matrices for classification.

Eigenvalues table

Displays the eigenvalues, percentages of variance, cumulative percentages of variance, and canonical correlations associated with each of the canonical discriminant functions. The variance percentages are relative to the total variance accounted for by all of the discriminant functions and will thus the cumulative percentage for the final function listed will always be 100%. The percentages of variance of the functions will always be in decreasing order. In problems with three or more discriminant functions, the values in this table can be used to assess how well the first two functions approximate the results for the entire set, which is useful to know when looking at plots in first two dimensions of the discriminant function space.

Wilks' Lambda table

Displays tests of significance for the canonical discriminant functions. With reasonable sample sizes, these can be used as a sanity check on the model. The significance value for the first line, which shows a test for the entire set of functions, should be very small, allowing you to reject the null hypothesis that all functions are simply picking up random variation among the groups.

Standardized Canonical Discriminant Function Coefficients table

Displays the standardized canonical discriminant function coefficients for each of the functions. The standardized metric allows easier comparison of the relative sizes of the loadings of each predictor on each function than is possible with the raw function coefficients. These values are similar to standardized regression coefficients in a linear regression model.

Structure Matrix

Displays pooled within-groups correlations of predictor fields and standardized discriminant functions. These values are particularly helpful in characterizing the discriminant functions in terms of the original predictors.

Canonical Discriminant Function Coefficients table

Displays the raw or unstandardized canonical discriminant function coefficients, which include a constant term for each function and are the functions used in classification. Score computation for each function is similar to that in a linear regression problem, where a linear combination of predictors times coefficients plus the constant is calculated.

Functions at Group Centroids table

Displays the values of the raw or unstandardized canonical discriminant functions evaluated at the group means on each of the predictor fields. These are the points in the discriminant function space to which scored instances are compared in classification.

All Groups Scatter Plot

Plots the data points in the space of the first two canonical discriminant functions, with markers showing actual group values. Also shows the location of each group centroid. If equal prior probabilities of group membership are assumed, observations would be classified into the group with the closest centroid in the full space of the canonical discriminant functions.