Discriminant Analysis

Discriminant analysis assigns subjects to groups or categories. Using formal terminology, discriminant analysis is a statistical technique predicting group membership from a set of predictors. Let us consider a simple example. Suppose we examine the voting record of a group of senators on several issues. Scores on the variable X were obtained by counting the votes of each senator on a series of ballots. Scores on the variable Y were obtained by coding the senators as conservative (0) or liberal (1).

The graphic plot of the above data is shown below

In the diagram, the cluster of conservative senators is marked by the red band, the cluster of the liberal senators by the yellow band. Analyze the above data by using a computer program for discriminant analysis. The coefficients of the discriminant function can be obtained and the discriminant score for each subject is computed as

Discriminant Score = (.632)Number of Votes +(-2.846)

The discriminant scores for two groups can be plotted as shown below

Note that about 53% of the variance in the discriminant scores is accounted for by group membership.

Next, use the discriminant scores to classify cases into groups. For our example of two groups, a case is classified into the conservative group (mean = -.949) if its discriminant score is below zero, and into the liberal group (mean = .949) if the discriminant score is above zero. The original and predicted group memberships are presented below.

In the conservative group, 4 out of 5 cases (80%) are classified correctly. 1 out of 4 cases (20%) is misclassified as the liberal group. In the liberal group, 4 out of 5 cases (80%) are classified correctly. 1 out of 4 cases (20%) is misclassified as the conservative group. The overall percentage of cases classified correctly can be computed as 8/10 = .8 = 80%