This study examines the use of independent group test of comparing two or more means by using parametric method, such as the Alexander-Govern (AG) test. The Alexander-Govern test is used for comparing two or more groups and is a better alternative compared to the James test, the Welch test and the ANOVA. This test has a good control of Type I error rates and gives a high power under variance heterogeneity for a normal data, but it is not robust for non-normal data. As a result, trimmed mean was

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... applied on the test under non-normal data for two group condition. But this test could not control the Type I error rates, when the number of groups exceed two groups. As a result, the MOM estimator was introduced on the test, as its central tendency measure and is not influenced by the number of groups. But this estimator fails to give a good control of Type I error rates, under skewed heavy tailed distribution. In this study, the AGWMOM test was applied in Alexander-Govern test as its central tendency measure. To evaluate the capacity of the test, a real life data was used. Descriptive statistics, Tests of Normality and boxplots were used to determine the normality and non-normality of the independent groups. The results show that only the group middle is not normally distributed due extreme value in the data distribution. The results from the test statistic show that the AGWMOM test has a smaller p-value of 0.0000002869 that is less than 0.05, compared to the AG test that produced a p-value of 0.06982, that is greater than 0.05. Therefore, the AGWMOM test is considered to be significant, compared to the AG test.