The basic function of discriminant analysis is to determine the variable(s) that serve as the best predictor of a subject's membership in a group or classification. For example, an education researcher could use discriminant function analysis to determine which predictor variables best discriminate whether students successfully complete high school, or which variables predict whether high school graduates go on to college.
As with any regression analysis, discriminant analysis involves two types of variables: dependent and independent. The dependent variable is the measure of group membership or classification, such as high school graduate or not. The independent variables are those that a researcher believes may discriminate between categories to which a subject belongs (e.g., graduate or not) and may subsequently predict, from new cases, to which category a given case will belong.
In discriminant analysis, the dependent variable is categorical in nature. Categorical variables distinguish subjects by classifying them in a limited number of categories, meaning the dependent variable has only a limited range of values. Often, the dependent variable is dichotomous, taking the value of zero or one. In the graduation example, students who graduate high school may be coded as "1" for graduate, while those who do not graduate are coded "0."
Discriminant analysis strives to predict group membership based on one or more independent or predictor variables. Unlike the dependent variable measure of group membership, which is generally coded 1 or zero (group member or not), the predictor variables are continuous, measured on an interval scale. This means that the predictor variables can assume a large range of values. Height, weight and test scores are examples of continuous variables. A student, for example, can have a test score of 88, 89, 90, etc.
Identifying the key predictors from discriminant analysis can provide insight into how each variable--whether individually or interacting with other independent variables--influences group membership.