Robust Statistical Procedures For Testing The Equality Of Central Tendency Parameters Under Skewed Distributions

This study examined the effect of Type I error and power on two types of robust methods. The first method is known as the S1 statistic, which was first studied by Babu et al. (1999). This statistic uses median as the central tendency measure. An interesting characteristic of the S1 statistic is that the data needs no trimming when skewed. The second method, proposed by Othman et al. (2004) is known as the MOM-H statistic. In contrast to the S1 method, the MOM-H statistic will trim any extreme values, and unlike trimmed means, this statistic empirically det ermines the amount of trimming needed thus avoiding unnecessary trimming. The central tendency measure for this statistic is the modified one-step M-estimator (MOM) proposed by Wilcox and Keselman (2003). In this study, we modified the two statistical methods by incorporating some of the more robust scale estimators to these statistics. We identified four robust scale estimators with highest breakdown point and bounded influence functions as ascertained by Rouesseuw and Croux (1993) i.e. MADn, Qn, Sn, and Tn. These scale estimators functioned differently in each of the two statistical methods. For the S 1 statistic, the estimators replaced the default scale estimator to form modified S 1 procedures, and for the MOM-H statistic, these scale estimators were used as the trimming criterion used to determine the sample values for modified one-step M-estimator (MOM). To identify the sturdiness or robustness of each procedure, some variables were manipulated to create conditions which are known to highlight the strengths and weaknesses of tests designed to determine the central tendency measures equality