Researchers can adopt different measures of central tendency and test statistics to examine the effect of a treatment variable across groups (e.g., means, trimmed means, M-estimators, & medians. Recently developed statistics are compared with respect to their ability to control Type I errors when data were nonnormal, heterogeneous, and the design was unbalanced: (1) a preliminary test for symmetry which determines whether data should be trimmed symmetrically or asymmetrically, (2) two different transformations to eliminate skewness, (3) the accuracy of assessing statistical significance with a bootstrap methodology was examined, and (4) statistics that use 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 were examined. The 56 procedures considered were remarkably robust to extreme forms of heterogeneity and nonnormality. However, we recommend a number of Welch-James heteroscedastic statistics which are preceded by the Babu, Padmanaban, and Puri (1999) test for symmetry that either symmetrically trimmed 10% of the data per group, or asymmetrically trimmed 20% of the data per group, after which either Johnson's (1978) or Hall's (1992) transformation was applied to the statistic and where significance was assessed through bootstrapping. Close competitors to the best methods were found that did not involve a transformation.
Keselman, H. J.; Wilcox, Rand R.; Othman, Abdul R.; and Fradette, Katherine
"Trimming, Transforming Statistics, And Bootstrapping: Circumventing the Biasing Effects Of Heterescedasticity And Nonnormality,"
Journal of Modern Applied Statistical Methods:
2, Article 38.
Available at: http://digitalcommons.wayne.edu/jmasm/vol1/iss2/38