Type I Error Rates of Ft Statistic with Different Trimming Strategies for Two Groups Case

摘要

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 we do not often encounter with this ideal situation. A robust method known as F t statistic has been identified as an alternative to the above methods in handling the problem of nonnormality. Motivated by the good performance of the method, in this study we proposed to use F t statistic with three different trimming strategies, namely, i) fixed symmetric trimming (10%, 15% and 20%), ii) fixed asymmetric trimming (10%, 15% and 20%) and iii) empirically determined trimming, to simultaneously handle the problem of nonnormality and heteroscedasticity. To test for the robustness of the procedures towards the violation of the assumptions, several variables were manipulated. The variables are types of distributions and heterogeneity of variances. Type I error for each procedures were then be calculated. This study will be based on simulated data with each procedure been simulated 5000 times. Based on the Type I error rates, we were able to identify which procedures ( F t with different trimming strategies) are robust and have good control of Type I error. The best procedure that should be taken into consideration is the F t with MOM - T n for normal distribution, 15% fixed trimming for skewed normal-tailed distribution and MOM - MAD n for skewed leptokurtic distribution. This is because, all of the procedures produced the nearest Type I error rates to the nominal level.