What Is Discriminant Analysis?
Discriminant analysis identifies the combination of variables that best discriminates between two or more predefined groups. It is similar in purpose to logistic regression but is better suited when the normality assumption is met and when the dependent variable has more than two categories. Applications include clinical diagnosis classification, customer segmentation, and species identification.
Assumptions
- Predictors are multivariate normally distributed within each group.
- Homogeneity of within-group covariance matrices (tested by Box's M test).
- No severe multicollinearity among predictors.
- Adequate sample size per group (at least 20 per group recommended).
Running Discriminant Analysis in SPSS
Go to Analyze → Classify → Discriminant.
- Move the grouping variable to Grouping Variable and define the range of group codes.
- Move predictor variables to Independents.
- Statistics: Means, ANOVA table, Box's M, Within-groups correlation.
- Classify: Check Leave-one-out classification for cross-validated accuracy estimates.
Interpreting the Output
Wilks' Lambda: Ranges from 0 (perfect discrimination) to 1 (no discrimination). Associated p-value tests significance. Standardized Canonical Discriminant Function Coefficients: Higher absolute values indicate stronger contribution to group separation — analogous to standardized beta in regression. Classification Results: The percentage of original cases correctly classified. Values above 70% are generally acceptable; cross-validated accuracy is a less optimistic and more realistic estimate.
Practical Example
In a clinical study distinguishing three disease groups using five biomarkers, discriminant analysis identified two significant discriminant functions. The model correctly classified 84% of participants, substantially exceeding the 33% chance level for three groups.
APA Reporting
Report Wilks' Lambda, χ², df, p-value, canonical correlation, and the classification accuracy table. Boss Statistics supports advanced analysis interpretation and manuscript-ready reporting.