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Testing the equality of correlation matrices |
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| Authors: | Reza Modarres Robert W. Jernigan |
| Affiliation: | 1. Department of Statistics/Computer and Information Systems , The George Washington University , Washington, D.C, 20052, U.S.A;2. Department of Mathematics and Statistics , The American University , Washington, D.C, 20016, U.S.A |
| Abstract: | We present results that extend an existing test of equality of correlation matrices. A new test statistic is proposed and is shown to be asymptotically distributed as a linear combination of independent x 2 random variables. This new formulation allows us to find the power of the existing test and our extensions by deriving the distribution under the alternative using a linear combination of independent non-central x 2 random variables. We also investigate the null and the alternative distribution of two related statistics. The first one is a quadratic form in deviations from a control group with which the remaining k-1 groups are to be compared. The second test is designed for comparing adjacent groups. Several approximations for the null and the alternative distribution are considered and two illustrative examples are provided. |
| Keywords: | correlation matrices quadratic forms covariance matrices power function |