7. Tests on Covariance Matrices
Published Online: 27 MAR 2003
Copyright © 2002 John Wiley & Sons, Inc.
Methods of Multivariate Analysis, Second Edition
How to Cite
Rencher, A. C. (2002) Tests on Covariance Matrices, in Methods of Multivariate Analysis, Second Edition, John Wiley & Sons, Inc., New York, NY, USA. doi: 10.1002/0471271357.ch7
- Published Online: 27 MAR 2003
- Published Print: 22 FEB 2002
Print ISBN: 9780471418894
Online ISBN: 9780471271352
- chi-square approximation;
- compound symmetry;
- intraclass correlation;
- Box's M-test;
- F approximation;
- Wilks' test statistic;
- canonical correlations
In this chapter, we consider the pattern of the variances and covariances. Tests on covariance matrices may be carried out to check assumptions pertaining to other tests and procedures. The tests, most of which are based on the likelihood ratio, can be summarized in three basic types: (1) tests on the structure of the covariance matrix or correlation matrix, (2) tests comparing two or more covariance matrices, and (3) testing the hypothesis that two or more of the random variables are independent. The first of these, tests on the structure, include an arbitrary pattern, independent variables with a common variance, and a common variance and a common covariance.
Most techniques in this chapter are illustrated with examples using real data. The problems at the end of the chapter call for derivations of some of the techniques and provide further illustrations with real data.