Abstract

This research centres on independent group test of comparing two or more means by using the parametric method, namely the Alexander-Govern test. The Alexander-Govern (AG) test uses mean as a measure of its central tendency. It is a better alternative to the Welch test, James test and the ANOVA, because it has a good control of Type I error rates and produces a high power efficient for a normal data under variance heterogeneity, but not for non-normal data. As a result, trimmed mean was applied on the test under non-normal data for two group condition, but as the number of groups increased above two, the test fails to be robust. Due to this, when the MOM estimator was applied on the test, it was not influenced by the number of groups, but failed to give a good control of Type I error rates under skewed heavy tailed distribution. In this research, the Winsorized MOM estimator was applied in AG test as a measure of its central tendency. 5,000 data sets were simulated and analysed using Statistical Analysis Software (SAS). The result shows that with the pairing of unbalanced sample size with unequal variance of (1:36) and the combination of both balanced and unbalanced sample sizes with both equal and unequal variances, under six group condition, for g = 0.5 and h = 0.5, for both positive and negative pairing condition, the test gives a remarkable control of Type I error rates. In overall, the AGWMOM test has the best control of Type I error rates, across the distributions and across the groups, compared to the AG test, the AGMOM test and the ANOVA.

This work is licensed under a Creative Commons Attribution 4.0 License.