Robustness of trimmed F statistic when handling non-normal data - Md Yusof, Zahayu; Othman, Abdul Rahman; Syed Yahaya, Sharipah Soaad (University of Malaya, 2013)
When the assumptions of normality and homoscedasticity are met, researchers should have no doubt in using classical test such as t-test, to test for the equality of central tendency measures for two groups.However, in real life this perfect situation is rarely encountered.When the problem of non-normality 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.The effect of non-normality on the trimmed F statistic was demonstrated in this study.We propose the modifications of the trimmed F statistic mentioned by using (1) a priori determined 15% symmetric trimming and (2) empirically determined trimming using robust scale estimators such as MAD n , T n and LMS n .The later trimming method will trim extreme values without prior trimming percentage. Based on the rates of Type I error, the procedures were then compared. Data from g-and h-distributions were considered in this study.We found the trimmed F statistic using robust scale estimator LMS n as trimming criterion provided good control of Type I error compared to the other methods.