Journal of Basic and Applied Research International
 

Journal of Basic and Applied Research International, ISSN No. : 2395-3438 (Print), 2395-3446 (Online), Vol.: 22, Issue.: 4

Original Research Article

COMPARATIVE STUDY ON SIZE AND POWER LEVELS OF FOUR SOLUTIONS TO MULTIVARIATE BEHRENS-FISHER PROBLEM USING MULTIVARIATE NORMAL AND LOG-NORMAL DISTRIBUTIONS

 

U. USMAN1*, F. MANU1 AND U. DAUDA2

1Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria.

2Department of Mathematics and Computer, Umaru Musa Yar’adua University, Katsina, Nigeria.

Abstracts

The comparison of the means of two independent samples with unequal variance-covariance matrices is one of the most popular problems in real-world data analysis. In the multivariate context, Hotelling’s T2 test is the standard tool for inference about the mean of a multivariate normal population assuming homogeneity of variance-covariance matrix between the samples. However, when this assumption is violated, the test cannot be distributed as T2 and this problem is known as Multivariate Behrens-Fisher problem. But also in practice, not all data satisfy the multivariate normality assumption, therefore, this research study the performance of four approximate solutions tests under normal and log-normal multivariate distributions with variance heteroscedasticity between the samples. Simulation study has been conducted using different sample sizes and variance-covariance imbalances. The result of the simulation study for the normally distributed data show that Nel and Van Der Mere’s test satisfactorily control type I error in all sample size combination in simulation with two variables In the evaluation of the power Yao’s test tend to be more powerful in all the sample size combination and effect size setting. In simulation with multivariate log- normal data, only Nel and Van Der Mere’s  and Yao’s tests satisfactorily control type I error when  n1=35, n2 =20 and  n1 =10, n2 =15 in simulation with six and three variables., all other tests have their size above the nominal level. In terms of power evaluation, Yao’s test tend to be more powerful.

Keywords :

Hotelling T2; hypothesis testing; size; power; Heteroscedasticity; effect size.