Comparing measures of the 'typical' score across treatment groups

Researchers can adopt one of many different measures of central tendency to examine the effect of a treatment variable across groups. These include least squares means, trimmed means, M-estimators and medians. In addition, some methods begin with a preliminary test to determine the shapes of distributions before adopting a particular estimator of the typical score. We compared a number of recently developed adaptive robust methods with respect to their ability to control Type I error and their sensitivity to detect differences between the groups when data were non-normal and heterogeneous, and the design was unbalanced. In particular, two new approaches to comparing the typical score across treatment groups, due to Babu, Padmanabhan, and Puri, were compared to two new methods presented by Wilcox and by Keselman, Wilcox, Othman, and Fradette. The procedures examined generally resulted in good Type I error control and therefore, on the basis of this critetion, it would be difficult to recommend one method over the other. However, the power results clearly favour one of the methods presented by Wilcox and Keselman; indeed, in the vast majority of the cases investigated, this most favoured approach had substantially larger power values than the other procedures, particularly when there were more than two treatment groups.