Testing the Equality of Location Parameters using Ft statisticbased on Trimming Criteria with High Breakdown Robust ScaleEstimators for Skewed Distributions

Abstract

Non-normality and heteroscedasticity are two common problems encountered when dealing with testing for location measures. When these two problems occur at the same time, rates of Type I error are usually inflated and reduced the power of test statistic. By substituting robust measures of location and scale such as trimmed means and Winsorized variances respectively in place of the usual means and variances, tests that are insensitive to the combined effects of non-normality and variance heterogeneity can be obtained. In this study, Ft statistic was modified using trimming strategies with indeterminate percentage (trimming criteria) and also trimming strategy with 15% symmetric trimming, o| . The trimming criteria percentages were based upon robust scale estimators, MADn and Tn. Type I error and power rates of these methods on J = 4 groups in unbalanced designs having unequal variances were compared. Normal and skewed data from g- and h- distributions were considered in this study. For skewed distribution with positive pairings, all trimming strategies showed good control of Type I error rates. The findings on power showed that trimming criteria MADn and Tn has higher power value than o| for both distributions. It is also shown that the negative pairings have higher power than the positive pairings.