On Modification of Multivariate Behrens-Fisher Problem

Adebayo OP, Ogunjimi OA, Ahmed I and Shehu B

Published on: 2024-09-12

Abstract

Based on a critical examination of existing procedures and solutions by [1], it was observed that there were no generally accepted testing procedures. This prompted the development of a new procedure for the multivariate Behrens-Fisher test that is less sensitive to violation of the homogeneity of the dispersion matrix compared to existing procedures. The new multivariate procedure was created by modifying the procedure of [1] using the Welch Univariate procedure. This modified procedure was then compared with three existing procedures: [1-3], using the R package for simulation. During the simulation, it was discovered that Krishnamoorthy's procedure performed better than the other procedures for two random variables (P=2) when the sample size was small and equal. However, as the number of random variables increased to three (P=3), there was tough competition between the Krishnamoorthy and Modified procedures. Finally, when the number of random variables increased to four (P=4), Adebayo's procedure performed better. The simulation covered various scenarios, including sample size (small, medium, and large), random variables (P=2, 3, 4), equal mean, unequal variance-covariance matrix, and a significant level of 0.05. Despite the different scenarios, the modified procedure outperformed the three selected procedures in terms of test power.