Pairwise comparisons for small samples from normal mixtures : the unexpected role of skewness

Music City Center 

This paper simulates the performance of two pairwise comparison procedures when distributions are normal mixtures (sometimes exhibiting heteroscedasticity and/or skewness). The two procedures are Tukey's (1949) using the Hayter-Fisher (1986) adjustment (HFF) compared to a novel procedure we name EHF that adjusts for heteroscedasticity based on the methods of Brown-Forsythe (1974), Mehrotra (1997), and Games-Howell (1976). The heterogeneity adjustments of EHF provide the expected protection against Type I errors but with a loss of power. The HFF procedure is acceptably robust and more powerful in most cases, with the exception being small sample sizes, extreme heteroscedasticity, and maximized difference in skewness and kurtosis among the populations. The direction of skewness, along with the configuration of means, surprisingly effects the power of the procedures resulting from the effect of the skewness on the correlation of mean square treatment (MST) and mean square error (MSE), the numerator and denominator in analysis of variance (ANOVA) F tests.

ANOVA methods

power and robustness

computer simulation procedures

assumption violations 

Quality and Productivity Section