One-Way Random Effects Model For Asymmetric Trimmed Means - Chin, Ee Laine (2019)
There are two very important concerns for the random effects model. The first concern being the assumption of equal variances of groups and the second concern is assuming normality. Violations of these result in unsatisfactory Type I errors and considerable loss of power. Jeyaratnam-Othman (1985) addresses the first concern in dealing with unequal variances while assuming normality. Wilcox in 1994 continued the study by suggesting a generalization on Jeyaratnam-Othman’s procedure based on symmetric trimmed means. The procedure resulted in significant gain in power but was unsatisfactory for skewed distributions with unequal group sizes. This research replaces Wilcox’s symmetric trimmed means with asymmetric ones aiming to obtain good, if not, better Type I errors. Two hinge estimators by Reed and Stark (1996), Q1 and Q2, were employed to obtain the asymmetric trimmed means for this research. Simulations were carried out for Jeyaratnam-Othman (1985), Wilcox (1994) and the two proposed procedures for a four-group design subjected to different data distributions. Good control of Type I errors was evident for both proposed procedures for balanced designs with values ranging from 0.026 to 0.082. Good power averaging 0.782 was also obtained. However, power and Type I errors for the unbalanced design were very unsatisfactory.