Robust Testing 1 Comparing Measures of the “Typical ” Score Across Treatment Groups by

Researchers can adopt one of many different measures of central tendency and test statistics to examine the effect of a treatment variable across groups. That is, methods for examining the effect of a treatment variable can be based on means, trimmed means, M-estimators, medians, etc. In our paper we compared a number of recently developed statistics with respect to their ability to control Type I errors when data were nonnormal, heterogeneous and the design was unbalanced. We examined: (1) the use of a preliminary test for symmetry which determines whether data should be trimmed symmetrically or asymmetrically, (2) the use of two different transformations to eliminate skewness, (3) the accuracy of assessing statistical significance with a bootstrap methodology and (4) statistics which utilized a robust measure of the typical score that empirically determined whether data should be trimmed, and, if so, in which direction, and by what amount. Though the fifty-six procedures we examined were remarkably robust to extreme forms of heterogeneity and nonnormality, we recommend a number o