Use of Discriminant Analysis in Counseling Psychology Research
Discriminant analysis is a technique for the multivariate study of group differences. More specifically, it provides a method of examining the extent to which multiple predictor variables are related to a categorical criterion, that is, group membership. Situations in which the technique is particularly useful include those in which the researcher wishes to assess which of a number of continuous variables best differentiates groups of individuals or in which he or she wishes to predict group membership on the basis of the discriminant function (analogous to a multiple regression equation) yielded by the analysis. The method is also useful as a follow-up to a significant analysis of variance. In this article, I describe the method of discriminant analysis, including the concept of discriminant function, discriminant score, group centroid, and discriminant weights and Ioadings. I discuss methods for testing the statistical significance of a function, methods of using the function in classification, and the concept of rotating functions. The use of discriminant analysis in both the two-group case and the multigroup case is illustrated. Finally, I provide a number of illustrative examples of use of the method in the counseling literature. I conclude with cautions regarding the use of the method and with the provision of resources for further study. The technique ofdiscriminant analysis, developed by R. A. Fisher (1936), is one method for the multivariate study of group differences. When used for explanatory purposes, discriminant analysis is particularly appropriate when one wishes (a) to describe, summarize, and understand the differences between or among groups, (b) to determine which of a set of continuous variables best captures or characterizes group differences, (c) to describe the dimensionality of group differences (much like factor analysis describes the dimensionality of a set of continuous variables), (d) to test theories that use stage concepts or taxonomies, and (e) to examine the nature of group differences following a multivariate analysis of variance (MANOVA; Borgen & Seling, 1978). Probably the most frequent applications of discriminant analysis are for predictive purposes, that is, for situations in which it is necessary or desirable to classify subjects into groups or categories. The results of a discriminant analysis allow the prediction of group membership based on the best linear composite or combination of predictor scores. Discriminant analysis is analogous to multiple regression in that both involve prediction from a set of continuous predictor variables (sometimes designated independent variables) to a criterion. The major difference between them is that multiple regression predicts to a continuous criterion variable (sometimes designated the dependent variable), whereas discriminant analysis predicts to a categorical criterion, that is, group membership. Thus, given multiple predictor variables, multiple regression would be the appropriate method of analysis if the dependent variable were continuous, and discriminant analysis would be appropriate if the dependent variable were categorical, with two or more levels.