Descriptive Discriminant Analysis

Discriminant analysis comprises two approaches to analyzing group data: descriptive discriminant analysis (DDA) and predictive discriminant analysis (PDA). Both use continuous (or intervally scaled) data to analyze the characteristics of group membership. However, PDA uses this continuous data to predict group membership (i.e., How accurately can a classification rule classify the current sample into groups?), while DDA attempts to discover what continuous variables contribute to the separation of groups (i.e., Which of these variables contribute to group differences and by how much?). In addition to the primary goal of discriminating among groups, DDA can examine the most parsimonious way to discriminate between groups, investigate the amount of variance accounted for by the discriminant variables, and evaluate the relative contribution of each discriminant (continuous) variable in classifying the groups.

For example, a psychologist may be interested in which psychological variables are most responsible for men's and women's progress in therapy. [Page 349]For this purpose, the psychologist could collect data on therapeutic alliance, resistance, transference, and cognitive distortion in a group of 50 men and 50 women who report progressing well in therapy. DDA can be useful in understanding which variables of the four (therapeutic alliance, resistance, transference, and cognitive distortion) contribute to the differentiation of the two groups (men and women). For instance, men may be low on therapeutic alliance and high on resistance. On the other hand, women may be high on therapeutic alliance and low on transference. In this example, the other variable of cognitive distortion may not be shown to be relevant to group differentiation at all because it does not capture much difference among the groups. In other words, cognitive distortion is unrelated to how men and women progress in therapy. This is just a brief example of the utility of DDA in differentiating among groups.

DDA is a multivariate technique with goals similar to those of multivariate analysis of variance (MANOVA) and computationally identical to MANOVA. As such, all assumptions of MANOVA apply to the procedure of DDA. However, MANOVA can determine only whether groups are different, not how they are different. In order to determine how groups differ using MANOVA, researchers typically follow the MANOVA procedure with a series of analyses of variance (ANOVAs). This is problematic because ANOVAs are univariate tests. As such, several ANOVAs may need to be conducted, increasing the researcher's likelihood of committing Type I error (likelihood of finding a statistically significant result that is not really there). What's more, what makes multivariate statistics more desirable in social science research is the inherent assumption that human behavior has multiple causes and effects that exist simultaneously. Conducting a series of univariate ANOVAs strips away the richness that multivariate analysis reveals because ANOVA analyzes data as if differences among groups occur in a vacuum, with no interaction among variables. Consider the earlier example. A series of ANOVAs would assume that as men and women progress through therapy, there is no potential shared variance between the variables therapeutic alliance, resistance, transference, and cognitive distortion. And while MANOVA does account for this shared variance, it cannot tell the researcher how or where the differences come from.

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