Comparing multiple comparisons: practical guidance for choosing the best multiple comparisons test.

Abstract

Multiple comparisons tests (MCTs) include the statistical tests used to compare groups (treatments) often following a significant effect reported in one of many types of linear models. Due to a variety of data and statistical considerations, several dozen MCTs have been developed over the decades, with tests ranging from very similar to each other to very different from each other. Many scientific disciplines use MCTs, including >40,000 reports of their use in ecological journals in the last 60 years. Despite the ubiquity and utility of MCTs, several issues remain in terms of their correct use and reporting. In this study, we evaluated 17 different MCTs. We first reviewed the published literature for recommendations on their correct use. Second, we created a simulation that evaluated the performance of nine common MCTs. The tests examined in the simulation were those that often overlapped in usage, meaning the selection of the test based on fit to the data is not unique and that the simulations could inform the selection of one or more tests when a researcher has choices. Based on the literature review and recommendations: planned comparisons are overwhelmingly recommended over unplanned comparisons, for planned non-parametric comparisons the Mann-Whitney-Wilcoxon U test is recommended, Scheffé’s S test is recommended for any linear combination of (unplanned) means, Tukey’s HSD and the Bonferroni or the Dunn-Sidak tests are recommended for pairwise comparisons of groups, and that many other tests exist for particular types of data. All code and data used to generate this paper are available at: https://github.com/stevemidway/MultipleComparisons.