Discriminant Analysis

General Overview

Discriminant function analysis has long been used in the social sciences to predict membership to particular groups. The earliest use is documented by British statistician Karl Pearson who proposed the coefficient of racial likeness, which was an intergroup distance index. Simultaneously in India, Prasanta Chandra Mahalanobis worked on his own conceptualization of an intergroup distance index. This work by both scholars was translated into a linear equation in the 1930s [Page 395]by Ronald Alymer Fisher, which serves as the foundation of how discriminant function analysis is used today.

Most of the initial applications of discriminant analysis were in biology and medicine, but social science also took interest, particularly those in business, education, and psychology. Some of the earliest work based on Fisher’s discriminant function equation appeared in sex role research, where psychologists sought to identify behaviors that would explain the separate social fit and behaviors of boys and girls. Other early uses included placement testing for personnel, economic differences as varied by geographical regions, and voting behavior.

For almost 40 years, discriminant analysis was referred to as predictive discriminant analysis because it was used solely to predict belonging to a group. Despite Fisher’s mathematical foundation, which likens the discriminant function analysis to other statistical analyses, it was not considered a potential supplement in explanation of multivariate analysis of variance (MANOVA) until the 1960s. When used to explain such results, discriminant analysis has often been labeled descriptive discriminant analysis. The descriptive discriminant analysis makes a useful follow-up analysis to running a MANOVA because where the MANOVA focuses on identifying differences, the discriminant analysis emphasizes classification of those differences to place subjects or cases into groups.

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