Tests Concerning Equicorrelation Matrices with Grouped Normal Data

ABSTRACT

This article considers three practical hypotheses involving the equicorrelation matrix for grouped normal data. We obtain statistics and computing formulae for common test procedures such as the score test and the likelihood ratio test. In addition, statistics and computing formulae are obtained for various small sample procedures as proposed in Skovgaard (2001). The properties of the tests for each of the three hypotheses are compared using Monte Carlo simulations.

Key Words:

• Intraclass correlation
• Likelihood ratio test
• Maximum likelihood estimation
• Score test
• Small-sample inference

Mathematics Subject Classification:

• Primary 62H15
• Secondary 62F05, 62H20

Acknowledgments

The authors P. S. Gill and T. B. Swartz were partially supported by grants from the Natural Sciences and Engineering Research Council of Canada. The work was initiated during S. G. Banneheka's sabbatical visit to Simon Fraser University in 2003. The authors thank a referee for valuable comments.