Discriminant Function Analysis

Discriminant function analysis involves the predicting of a categorical dependent variable by one or more continuous or binary independent variables. It is statistically the opposite of MANOVA. It is useful in determining whether a set of variables is effective in predicting category membership. It is also a useful follow-up procedure to a MANOVA. Instead of doing a series of one-way ANOVAs, for ascertaining how the groups differ on the composite of dependent variables.
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Discriminant function analysis is used to determine which variables discriminate between two or more naturally occurring groups (it is used as either a hypothesis testing or exploratory method). For example, an educational researcher may want to investigate which variables discriminate between high school graduates who decide (1) to go to college, (2) to attend a trade or professional school, or (3) to seek no further training or education. For that purpose the researcher could collect data on numerous variables prior to students' graduation. After graduation, most students will naturally fall into one of the three categories. Discriminant Analysis could then be used to determine which variable(s) are the best predictors of students' subsequent educational choice (e.g., IQ, GPA, SAT).
For more information, see the Discriminant Function Analysis chapter; see also the Classification Trees chapter.