Improvement of the trimmed mean procedure using bootstrap method

When the assumptions of normality and homoscedasticity are met, researchers should have no doubt in using classical test such as t-test and ANOVA, to test for the equality of central tendency measures for two and more than two groups, respectively. However, in real life this perfect situation is rarely encountered. When the problem of nonnormality and variance heterogeneity simultaneously arise, rates of Type I error are usually inflated resulting in spurious rejection of null hypotheses. In addition, the classical least squares estimators can be highly inefficient when assumptions of normality are not fulfilled. Thus, by substituting robust measures of location and scale such as trimmed means and Winsorized variances in place of the usual means and variances respectively, tests that are insensitive to the combined effects of nonnormality and variance heterogeneity can be obtained. In this study, we compared the performance of TI statistic using bootstrap methods with the approximate trimmed F statistic (F,). Both statistics used 15% symmetric trimming. The procedures examined generally resulted in good Type I error controlled. The F, statistic shown good controlled of Type I error for balanced design. In contrast the TI statistic gave better controlled of Type I error for the unbalanced design