Heteroscedasticity in One Way Multivariate Analysis of Variance

Adeleke Bl,Adebayo Po,Oyeyemi Gm

doi:10.4172/2090-0902.1000270

Abstract

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. The alternative procedure was developed by adopting SatterthwaiteA¢Â€Â™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 by using simulated data when it is Multivariate normal, Multivariate Gamma and real life data. The new procedure performed better in terms of power of the test and type I error rate when compared with Johanson procedure.

Highlights

Multivariate Analysis of Variance (MANOVA) can be viewed as a direct extension of the univariate (ANOVA) general linear model that is most appropriate for examining differences between groups of means on several variables simultaneously [1,2]
In ANOVA, differences among various group means on a single-response variable are studied
MANOVA has three basic assumptions that are fundamental to the statistical theory: (i) independent, (ii) multivariate normality and (iii) equality of variance-covariance matrices

Summary

Introduction

Multivariate Analysis of Variance (MANOVA) can be viewed as a direct extension of the univariate (ANOVA) general linear model that is most appropriate for examining differences between groups of means on several variables simultaneously [1,2]. When the assumption of equality of variance-covariance matrix failed or violated it means that none of the aforementioned test statistic is appropriate for the analysis otherwise the result will be prejudiced. This predicament is known as the multivariate Behrens - Fisher problem which deal with testing the equality of normal mean vector under heteroscedasticity of dispersion matrices. An approximate degree of freedom used [16] for comparing k normal mean vectors when the population variance - covariance matrices are unknown is proposed and compared with an existing procedure (by Johanson) when the groups (k) and random variables (p) are three respectively

Methodology

Proposed Method

Result