This work consider the problem of comparing two multivariate normal mean vectors under the heteroscedasticity of dispersion matrices. We develop a new procedure using approximate degree of freedom method by Satterthwaite [23] and broaden it to Multivariate Behrens Fisher. The New procedure is compared with existing ones via R package simulation and Data used by James [8] and Yao [31]. And we ascertain that, new procedure is better in terms of power of the test and type I error rate than all existing procedure mull over when the sample sizes are not equal, but the propose procedure perform the same with the selected procedure when sample sizes are equal.
Keywords: Heteroscedasticity, Multivariate Behrens-Fisher Problem, Null Hypothesis, Power The Test, R Statistical Package., Type I Error Rate
