Multiple Comparison Methods for Means

Abstract

Abstract. 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

Uncertainties of the Gravity Recovery and Climate Experiment time-variable gravity-field solutions based on three-cornered hat method

“…Subsequently, a follow-up test was conducted to identify which processing center presented uncertainties resulting from a different distribution. The relative performance pertaining to the 91 river basins by the multiple-comparison test, based on the Tukey-Kramer procedure, 61 is shown in Figs. 8(c) and 8(d) (TCH and ensemble mean based errors, respectively).…”

Estimación Tier II de emisión de metano entérico en hatos de vacas lactantes en Querétaro, México

“…La sexta lactancia contempló los registros de seis o más lactancias. Las medias de los estimadores de los parámetros de la función gamma incompleta, DL, s, Y, Y max y el pico de producción se compararon con la prueba Tukey-Kramer para modelos desbalanceados (18) y siendo la variable explicativa el número de capacity of complex lactation curve models, those like the incomplete gamma function are recommended, unless mechanistic details are needed for extended lactation curves (> 800 d) (15) . The formula used here was:…”

“…Para fines del cálculo de la E m , se estimó el peso correspondiente a las lactancias 1, 2 y 3 imbalanced models (18) , with lactation number as the explanatory variable. The contrast between primiparous and multiparous cows was also tested.…”

Misuse of multiple comparison tests and underuse of contrast procedures in aquaculture publications

“…The merit of each of these tests over the others has extensively been discussed (Montgomery, 1997;Steel et al, 1997), and is beyond the scope of this paper. However, with qualitative independent factors showing a structure, statistical procedures exist which lead to more meaningful conclusions on treatment effects; furthermore, pairwise multiple comparison tests should not be used on quantitative main factors and factorial interaction terms as this leads to misinterpretation of research results and flawed conclusions (Gates, 1991;Montgomery, 1997;Olsen, 2003;Petersen, 1977;Rafter et al, 2002;Saville, 1990;Steel et al, 1997).…”

“…Then, the results section was examined in order to make sure that the procedures used to analyze the treatment means, following ANOVA or multiple factor ANOVA, conform to what was planned in the materials and methods section. Also, we checked whether or not the presentation and interpretation of results were in accordance with the appropriate statistical practice described previously (Gates, 1991;Montgomery, 1997;Petersen, 1977;Rafter et al, 2002;Steel et al, 1997).…”