Type I error and power rates of robust methods with variable trimmed mean
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Date
2010
Authors
Md Yusof, Zahayu
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Abstract
The effects of nonnormality and heteroscedasticity on the T1 and trimmed F (Ft) test
statistics were investigated using two methods of trimming namely the proposed
automatic trimmed mean and the typical fixed amount of trimming. These are typical
problems in any test of equality of central tendency measure. For each test statistic,
three automatic trimming procedures using different scale estimators MADn, Tn, and
LMSn, and a fixed trimmed mean procedure were examined for their robustness via Type
I error and power rates. To identify the robustness of each procedure, several variables
were manipulated such as number of groups, balanced and unbalanced sample sizes,
variance heterogeneity, pairing of group variances and group sample sizes, and types of
distributions. The fmdings show that when automatic trimming using LMSn was applied
on F1 statistic under the condition of extremely skewed distribution with homogeneous
variance cases, the performance of Type I error is very convincing. For normal-tailed
distributions and heterogeneous variances, the T1 statistic with automatic trimming using
Tn performed reasonably well. With regard to power, the automatic trimming is able to
produce high power rates especially for the conditions of unequal sample sizes and
homogeneous variances. By means of automatic trimming, the performance of Ft
statistic is better than the T1 statistic simultaneously in terms of Type I error and power
rates for homogeneous variances and unequal sample sizes. For other conditions, fixed
trimmed mean is still favorable.
Keywords: Robust statistics, Type I error, power, robust scale estimators, skewed
distributions
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Keywords
Power rates , Variable trimmed