Evaluating Test Statistics for Covariance Matrix Equality in Multivariate Repeated-Measures Data: A Comprehensive Simulation Study

Abstract

This study evaluates the performance of the Likelihood Ratio Test (LRT), Box’s M test, Nagao’s Trace test, and Ahmad’s Tau statistics for testing the equality of covariance matrices in multivariate repeated-measures data. Using extensive Monte Carlo simulations that vary the number of variables, groups, and sample sizes, the study compares the tests in terms of Type I error control and statistical power. Results show that while LRT provides high power, it exhibits inflated Type I error rates in small samples and higher dimensions. Box’s M test consistently maintains appropriate Type I error rates and demonstrates robust power across diverse scenarios, making it a reliable choice for moderate-dimensional data. Nagao’s Trace test tends to be conservative with lower power in smaller samples, and Ahmad’s Tau statistics are overly conservative, limiting their practical utility. These findings offer guidance for researchers in biomedical, psychological, and social sciences in selecting suitable methods for covariance matrix equality testing, emphasizing a balance between Type I error control and statistical power.