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

<p class="zhengwen"><span lang="EN-GB">This study centres on the comparison of independent group tests in terms of power, by using parametric method, such</span><span lang="EN-GB"> as the Alexander-Govern test. The Alexander-Govern (<em>AG</em>) test uses mean as its central tendency measure. It is a better alternative compared to the Welch test, the James test and the <em>ANOVA</em>, 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 <em>MOM</em> 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 <em>MOM</em> estimator was applied in the <em>AG</em> test, as its central tendency measure. A simulation of 5,000 data sets were generated and analysed on the test, using the <em>SAS</em> 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 (<em>f</em> = 0.8), the <em>AGWMOM </em>test only produced a high power value of 0.9562 and 0.8336 compared to the <em>AG </em>test, the <em>AGMOM </em>test and the <em>ANOVA </em>respectively and the test is considered to be sufficient.</span></p>