Abstract
<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>
Highlights
The independent group tests in statistics are about comparing the equality of independent groups via parametric or non-parametric approach
Their method produced a remarkable control of Type I error rates and high power efficiency under normality condition. It is considered as a better alternative to the analysis of variance (ANOVA), due to its easy of computation. These robust methods give a better solution to the classical test statistics, that is the ANOVA when the assumptions of homogeneity of the variance is violated, but these tests have failed to handle the problem of non-normality in a data distribution
Investigation under empirical test reveals that the Alexander-Govern test did remarkably well compared to the ANOVA in the control of Type I error rates and produces high power efficiency for a normal data under variance heterogeneity (Alexander-Govern, 1994)
Summary
The independent group tests in statistics are about comparing the equality of independent groups via parametric or non-parametric approach. Past researchers have shown that the original James tests and the Welch tests are commonly robust when there is heterogeneity of the variance and at the same time, it has a good performance when there is a big difference in the sample sizes (Kohr & Games, 1974; Krishnamoorthy, Lu & Matthew, 2007). Another alternative technique to handle the problem of variance heterogeneity is proposed by Alexander-Govern (1994). These robust methods give a better solution to the classical test statistics, that is the ANOVA when the assumptions of homogeneity of the variance is violated, but these tests have failed to handle the problem of non-normality in a data distribution
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