Abstract
This study examines the use of independent group test of comparing two or more means by using parametric method, such as the Alexander-Govern (<em>AG</em>) 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 <em>ANOVA</em>. 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 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 <em>MOM</em> 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 <em>AGWMOM </em>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 <em>AGWMOM</em> test has a smaller p-value of 0.0000002869 that is less than 0.05, compared to the <em>AG</em> test that produced a p-value of 0.06982, that is greater than 0.05. Therefore, the <em>AGWMOM</em> test is considered to be significant, compared to the <em>AG</em> test.
Highlights
In comparing independent group means, the analysis of variance is applicable in different aspects of life, such as in sociology, agriculture, economics and in medicine, as explained by Pardo, Pardo, Vincente and Esteban (1997)
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
Summary
In comparing independent group means, the analysis of variance is applicable in different aspects of life, such as in sociology, agriculture, economics and in medicine, as explained by Pardo, Pardo, Vincente and Esteban (1997). For a skewed data distribution, the trimming process is not done on the tails of the data distribution Another weakness in using the trimmed mean is that it could not give a good control of Type I error rates, when the number of groups is more than two, especially when it was applied in Alexander-Govern test (Lix & Keselman, 1995). Another technique in handling the influence of outliers in a data distribution is with the use of Winsorization approach. The results from the Test statistic, shows that the AGWMOM test is very significant compared to the AG test
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