The Power of the Test for the Winsorized Modified Alexander-Govern Test

Abstract

This research examined the usage of the parametric method in comparing two or more means as independent group test, for instance, the Alexander-Govern (AG) test. The utilization of mean as the determinant for the center of distribution of variance diversity takes place in testing, and the test provides excellence in maintaining the amount of Type I error and giving immense sensitivity for a regular data. Unfortunately, it is ineffective on irregular data, leading to the application of trimmed mean upon testing as the determinant for the center of distribution under irregular data for two group condition. However, as the group quantity is more than two, the estimator unsuccessfully provides excellence in maintaining the amount of Type I error. Therefore, an estimator high in effectiveness called the MOM estimator was introduced for the testing as the determinant for the center of distribution. Group quantity in a test does not affect the estimator, but it unsuccessfully provides excellence in maintaining the amount of Type I error under intense asymmetry and unevenness. The application of Winsorized modified one-step M-estimator (WMOM) upon the Alexander-Govern testing takes place so that it can prevail against its drawbacks under irregular data in the presence of variance diversity, can eliminate the presence of the outside observation and can provide effectiveness for the testing on irregular data. Statistical Analysis Software (SAS) was used for the analysis of the tests. The results show that the AGWMOM test gave the most intense sensitivity under g = 0,5 and h = 0,5, for four group case and g = 0 and h = 0, under six group case, differing from three remaining tests and the sensitivity of the AG testing is said suffices and intense enough.