The Modification and Evaluation of the Alexander-Govern Test in Terms of Power

Abstract

This study centres on the comparison of independent group tests in terms of power, by using parametric method, such as the Alexander-Govern test. The Alexander-Govern ( AG) test uses mean as its central tendency measure. It is a better alternative compared to the Welch test, the James test and the ANOVA, because it produces high power and gives good control of Type I error rates for a normal data under variance heterogeneity. But this test is not robust for a non-normal data. When trimmed mean was applied on the test as its central tendency measure under non-normality, the test was only robust for two group condition, but as the number of groups increased more than two groups, the test was no more robust. As a result, a highly robust estimator known as the MOM estimator was applied on the test, as its central tendency measure. This test is not affected by the number of groups, but could not control Type I error rates under skewed heavy tailed distribution. In this study, the Winsorized MOM estimator was applied in the AG test, as its central tendency measure. A simulation of 5,000 data sets were generated and analysed on the test, using the SAS package. The result of the analysis, shows that with the pairing of unbalanced sample size of (15:15:20:30) with equal variance of (1:1:1:1) and the pairing of unbalanced sample size of (15:15:20:30) with unequal variance of (1:1:1:36) with effect size index ( f = 0.8), the AGWMOM test only produced a high power value of 0.9562 and 0.8336 compared to the AG test, the AGMOM test and the ANOVA respectively and the test is considered to be sufficient.