Multiple Comparison Methods for Means

Multiple comparison methods (MCMs) are used to investigate differences between pairs of population means or, more generally, between subsets of population means using sample data. Although several such methods are commonly available in statistical software packages, users may be poorly informed about the appropriate method(s) to use and/or the correct way to interpret the results. This paper classifies the MCMs and presents the important methods for each class. Both simulated and real data are used to compare methods, and emphasis is placed on correct application and interpretation. We include suggestions for choosing the best method. Mathematica programs developed by the authors are used to compare MCMs. By taking advantage of Mathematica's notebook structure, an interested student can use these programs to explore the subject more deeply. The programs and examples used in the article are available at http://www.cs.gasou.edu/faculty/rafter/MCMM/.