Winsorized Modified One Step M-estimator in Alexander-Govern Test

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 (<em>AG</em>) test uses mean as a measure of its central tendency. It is a better alternative to the Welch test, James test and the <em>ANOVA</em>, 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 <em>MOM</em> 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 <em>MOM</em> estimator was applied in <em>AG</em> test as a measure of its central tendency. 5,000 data sets were simulated and analysed using Statistical Analysis Software (<em>SAS</em>). 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 <em>AGWMOM</em> test has the best control of Type I error rates, across the distributions and across the groups, compared to the <em>AG</em> test, the <em>AGMOM</em> test and the <em>ANOVA</em>.