In this paper, a new test statistic based on the weighted Frobenius norm of covariance matrices is proposed to homogeneity multi-group population matrices. The asymptotic distributions under null and alternative hypotheses are derived, respectively. Simulation results show that procedure tends outperform some existing procedures.

The usual practice for testing homogeneity of several populations in terms of means and variances is first to test for the equality of variances and once this assumption is found to be tenable then to test the equality of means. Singh (1986) proposes a very interesting procedure based on two likelihood ratio statistics for testing homogeneity of several normal (μ, σ) populations. Singh uses a m...