# 8. Discriminant Analysis: Description of Group Separation

1. Alvin C. Rencher

Published Online: 27 MAR 2003

DOI: 10.1002/0471271357.ch8

## Methods of Multivariate Analysis, Second Edition

#### How to Cite

Rencher, A. C. (2002) Discriminant Analysis: Description of Group Separation, in Methods of Multivariate Analysis, Second Edition, John Wiley & Sons, Inc., New York, NY, USA. doi: 10.1002/0471271357.ch8

#### Author Information

1. Brigham Young University, USA

#### Publication History

1. Published Online: 27 MAR 2003
2. Published Print: 22 FEB 2002

#### Book Series:

1. Wiley Series in Probability and Statistics

#### ISBN Information

Print ISBN: 9780471418894

Online ISBN: 9780471271352

## SEARCH

### Keywords:

• discriminant functions;
• standardized discriminant functions;
• eigenvalues;
• stepwise discriminant analysis;
• ranking the variables;
• orthogonality;
• measures of association;
• T2 test;
• Wilks' Λ test;
• chi-square approximation;
• F approximation;
• partial Λ-statistic;
• partial F-statistic;
• structure coefficients;
• rotation

### Summary

In this chapter, the term discriminant analysis refers to descriptive group separation using (linear) discriminant functions to characterize the differences between two or more groups. The goals of descriptive discriminant analysis include identifying the relative contribution of the p variables to separation of the groups and finding the optimal plane on which the points can be projected to best illustrate the configuration of the groups.

Prediction or allocation of observations to groups (predictive discriminant analysis) is referred to in this book as classification analysis and is discussed in Chapter 9.

For two groups, the discriminant function can be calculated using matrix manipulation or by multiple regression with dummy grouping variables. For the several-group case, the discriminant function coefficient vectors are obtained using eigenvectors. In either case, the coefficients can be standardized to better show the relative contribution of the variables to separation of the groups. The discriminant functions can be tested for significance. Various approaches are given to interpreting the discriminant functions or determining the contribution of each variable.

The techniques in the chapter are well illustrated by examples using real data. The problems at the end of the chapter provide derivations and further numerical illustrations.