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33 – Statistical Software, Modeling, Graphics, and Hardware
Pairwise Comparisons of Means when Distributions are Normal Mixtures with Unequal Variance
Mary Whiteside
The University of Texas-Arlington
Mark Eakin
The University of Texas-Arlington
This paper extends the authors' earlier work on the power and robustness of multiple comparison procedures when assumptions of normality and equal variance do not hold to underlying distributions that are normal mixtures, violating both assumptions. Normal mixtures can represent an incorrectly specified design that results in a one-way layout rather than a two way design with a normally distributed response. We examine two approaches: ANOVA F followed by Tukey-Kramer comparisons with the Hayter-Fisher adjustment in degrees of freedom (HFF) and Mohtra's modification of the Brown-Forsythe F test (changing numerator degree of freedom as well as the Brown-Forsythe modification of the denominator degrees of freedom) followed by Games-Howell multiple comparisons which adjust Tukey-Kramer comparisons for unequal variances with the Hayter-Fisher adjustment (MEE). HFF is one of six approaches evaluated by Ramsey et.al.in "Pairwise comparisons of means under realistic nonnormality, unequal variances, outliers and equal sample sizes," February 2011. For the initial cases considered, MEE is the more conservative procedure, providing better coverage rates for simultaneous confidence intervals.