Modifying and Evaluating the Alexander-Govern Test Using Real Data

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.

The Implementation of the Alexander-Govern Test in Factorial Design Analysis

“…On the other hand, the AG test is used as the alternative to the ANOVA to deal with unequal variance (Abdullah et al, 2011;Jamaluddin, 2015;Ochuko et al, 2015cOchuko et al, , 2015a. The AG test provides excellent control of Type I error rates for variance heterogeneity in normal data.…”

“…For variance heterogeneity in normal data, the AG test provides excellent control of Type I error rates (Schneider & Penfield, 1997). This test, however, is not robust to non-normal data because it cannot handle noisy data or outliers when sample sizes are unequal (Ochuko et al, 2015a).…”

“…According to Ochuko et al (2015b), non-normality and variance heterogeneity are obstacles to ANOVA. This increases the likelihood of Type I errors while decreasing power (Ochuko et al, 2015a).…”