A Modified Mantel Test for the Compound Symmetry Covariance Structure

• Activity Number: 286
• Type: Contributed
• Date/Time: Tuesday, August 4, 2009 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Megan Duke*+ and Tracy Morris and Mark E. Payton
• Companies: University of Central Oklahoma and University of Central Oklahoma and Oklahoma State University
• Keywords: permutation test ; covariance matrix ; compound symmetry ; Mantel test ; correlation ; likelihood ratio test

Abstract

The parametric method of testing for compound symmetry involves the use of a LRT. These tests require large samples from multivariate normal populations and are undefined for cases in which the sample size, n, is not greater than the number of variables, p. In a previous study, a permutation test for compound symmetry was developed. While this permutation test performed better than the LRT in some situations, the type I error rates were much too high when p>n. In this study, we have developed a new permutation test that is a modification of the Mantel Test for the relationship between two distance matrices. Samples with various values of n and p were simulated from three families of distributions. The new permutation test performed well with regard to the simulated type I error rates if p was not considerably larger than n, and performed consistently regardless of the distribution.