Robust Statistical Procedures For Testing The Equality Of Central Tendency Parameters Under Skewed Distributions
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Date
2005-05
Authors
Sharipah Soaad Syed Yahaya.
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
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.
Description
Keywords
Robust statistical procedures , testing the equality of central tendency