Graphical Representations of Tukey's Multiple Comparison Method

Abstract

Tukey's multiple comparison method is widely implemented in statistical packages. We list the inferential and perceptual tasks a graphical representation of Tukey's method may be required to perform, and show that the most commonly used graphical representations (underlining, line-by-line plotting, notched boxplots, and comparison circles) are all lacking in some respect. A new graphical representation, based on the mean-mean scatterplot, is proposed instead. This representation performs all the inferential and perceptual tasks not only in an unbalanced one-way model, but also in a general linear model. An event-driven, color-graphics implementation is presented. Finally, issues for future research, such as color perception and comparative experimentation, are briefly discussed.