The Study of Efficiency of Nonparametric Multivariate Analysis of Variance using the Median Test, the Rank Sum Test, the Normal Scores Test and the Pillai – Bartlett Trace Test

Abstract

The purpose of this research was to study the efficiency of nonparametric multivariate analysis of variance using the median test (MMT), the rank sum test (MRST), the normal scores test (MNST) and the Pillai – Bartlett trace test (MPBT) with Monte Carlo simulation technique. The findings could be summarized as follows: 

1. In case of multivariate normal distribution and heterogeneity variance - covariance matrix at .05 significant level when,  (1.1) for small sample size (n<50), the MRST, MMT and MNST could control rate of the type I error and have higher power, (1.2) for medium sample size (n=50), the MRST, MMT and MNST could control the rate of type I error and have higher power for the data set 2, 3 and 5 dependent variables however, the MPBT could control the rate of type I error and have higher power with 2 dependent variables, and (1.3) for large sample size (n ≥ 100), the MRST, MMT and MNST could control rate of the type I error and have higher power for data set with 2, 3 and 5 dependent variables, however, the MPBT could control the rate of type I error and have higher power with 2 and 3 dependent variables, Furthermore, at .01 significant level, the MPBT could control the rate of type I error and has higher power with large sample size and 5 dependent variables.


2. In case of non-multivariate normal distribution and homogeneity variance - covariance matrix and the case of non-multivariate normal distribution and heterogeneity variance - covariance matrix at .05 and .01 significant level, no statistical tests could control the rate of type I error and have higher powers.