Kaedah Alexander-Govern Menggunakan Penganggar Teguh Dengan Pendekatan Pangkasan Data: Kajian Simulasi

Alexander-Govern method enables equality test of central tendency measures when the problem of heterogeneous variances arises. However, this method distorts under non-normal data. This shortcoming is caused by the use of mean as the central tendency measure, which is non robust to the non-normal data. Under this condition, substituting the usual mean with robust estimators, namely adaptive trimmed mean and modified one step M estimator (MOM) apparently contribute to good control of Type I Error rates and improve the power of Alexander-Govern test. Both of these robust estimators used the technique of data trimming, yet with different approaches. Adaptive trimmed mean removes data based on a predetermined percentage of trimming and the trimming is done after the distributional shape of the data has been identified. The percentages of trimming used in this study encompassed the 10%, 15%, 20% and 25%. In contrast, the MOM estimator uses the technique of trimming data empirically. Empirical data trimming in this study emphasized on the trimming mechanism using three scale estimators, namely MADn, Sn and Tn. The new Alexander-Govern method is categorized as AH (Alexander-Govern method with adaptive trimmed mean) and AM (Alexander-Govern method with MOM estimator). AH method consists of AH10, AH15, AH20 and AH25 which are AH with trimming percentage of 10%, 15%, 20% and 25% respectively. While AM method comprises of AMM, AMS and AMT which denotes the integration of each of the scale estimators, MADn, Sn and Tn respectively in Alexander-Govern method. These new methods were assessed at certain conditions ranging from ideal to extreme. Evidently, the method of AH with 15% trimming is robust for all the conditions, with most of them are robust under liberal criterion. However, this method has low power in regards to heavy-tailed distribution. The performances of all the AM methods are however comparable to each other based on their ability to control Type I Error rates and the power of the tests which are almost the same for all the scale estimators used. Even though AM methods failed to control Type I error rates under heavy tailed distribution, nonetheless, the AM methods are very robust under skewed distribution where in most cases these methods meet the stringent robust criteria and high in power. All the new Alexander-Govern methods also show comparable performances with the original Alexander-Govern and the classical method under ideal conditions.