STATISTICS Subcommand (DISCRIMINANT command)

By default, DISCRIMINANT produces the following statistics for each analysis: analysis case processing summary, valid numbers of cases in group statistics, variables failing tolerance test, a summary of canonical discriminant functions, standardized canonical discriminant function coefficients, a structure matrix showing pooled within-groups correlations between the discriminant functions and the predictor variables, and functions at group centroids.

  • Group statistics. Only valid number of cases is reported.
  • Summary of canonical discriminant functions. Displayed in two tables: an eigenvalues table with percentage of variance, cumulative percentage of variance, and canonical correlations and a Wilks’ lambda table with Wilks’ lambda, chi-square, degrees of freedom, and significance.
  • Stepwise statistics. Wilks’ lambda, equivalent F, degrees of freedom, significance of F and number of variables are reported for each step. Tolerance, F-to-remove, and the value of the statistic used for variable selection are reported for each variable in the equation. Tolerance, minimum tolerance, F-to-enter, and the value of the statistic used for variable selection are reported for each variable not in the equation. (These statistics can be suppressed with HISTORY=NONE.)
  • Final statistics. Standardized canonical discriminant function coefficients, the structure matrix of discriminant functions and all variables named in the analysis (whether they were entered into the equation or not), and functions evaluated at group means are reported following the last step.

In addition, you can request optional statistics on the STATISTICS subcommand. STATISTICS can be specified by itself or with one or more keywords.

  • STATISTICS without keywords displays MEAN, STDDEV, and UNIVF. If you include a keyword or keywords on STATISTICS, only the statistics you request are displayed.

MEAN. Means. Total and group means for all variables named on the ANALYSIS subcommand are displayed.

STDDEV. Standard deviations. Total and group standard deviations for all variables named on the ANALYSIS subcommand are displayed.

UNIVF. Univariate F ratios. The analysis-of-variance F statistic for equality of group means for each predictor variable is displayed. This is a one-way analysis-of-variance test for equality of group means on a single discriminating variable.

COV. Pooled within-groups covariance matrix.

CORR. Pooled within-groups correlation matrix.

FPAIR. Matrix of pairwise F ratios. The F ratio for each pair of groups is displayed. This F is the significance test for the Mahalanobis distance between groups. This statistic is available only with stepwise methods.

BOXM. Box’s M test. This is a test for equality of group covariance matrices.

GCOV. Group covariance matrices.

TCOV. Total covariance matrix.

RAW. Unstandardized canonical discriminant functions.

COEFF. Classification function coefficients. Although DISCRIMINANT does not directly use these coefficients to classify cases, you can use them to classify other samples (see the CLASSIFY subcommand).

TABLE. Classification results. If both selected and unselected cases are classified, the results are reported separately. To obtain cross-validated results for selected cases, specify CROSSVALID.

CROSSVALID. Cross-validated classification results. The cross-validation is done by treating n–1 out of n observations as the training dataset to determine the discrimination rule and using the rule to classify the one observation left out. The results are displayed only for selected cases.

ALL. All optional statistics.