This work aimed at developing an alternative procedure to MANOVA test when there is problem of heteroscedasticity of dispersion matrices and compared the procedure with an existing multivariate test for vector of means (by Johanson). The alternative procedure was developed by adopting Satterthwaite’s approach of univariate test for unequal variances. The approach made use of approximate degree of freedom method in one way MANOVA when the dispersion matrices are not equal and unknown but positive definite. The new procedure was compared with Johanson (1980) procedure using simulated data when it is Multivariate normal, Multivariate Gamma and real life data by Krishnamoorthy (2010). The new procedure performed better in terms of power of the test and type I error rate when compared with Johanson procedure.
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  and broaden it to Multivariate Behrens Fisher. The New procedure is compared with existing ones via R package simulation and Data used by James  and Yao . 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.