On Multiple Comparisons in R *

The multiplicity problem arises when several inferences are considered simultaneously as a group. If each inference has a 5% error rate, then the error rate over the entire group can be much higher than 5%. This article shows practical examples of multiple comparisons procedures that control the error of making any incorrect inference. The multcomp package for the R statistical environment allows for multiple comparisons of parameters whose estimates are generally correlated, including comparisons of k groups in general linear models. The package has many common multiple comparison procedures “hard-coded”, including Dunnett, Tukey, sequential pairwise contrasts, comparisons with the average, changepoint analysis, Williams’, Marcus’, McDermott’s, and tetrad contrasts. In addition, a free input interface for the contrast matrix allows for more general comparisons. The comparisons themselves are not restricted to balanced or simple designs. Instead, the package is designed to provide general multiple comparisons, thus allowing for covariates, nested effects, correlated means, likelihood-based estimates, and missing values. For the homoscedastic normal linear models, the functions in the package account for the correlations between test statistics by using the exact multivariate t-distribution. The resulting procedures are therefore more powerful than the Bonferroni and Holm methods; adjusted p-values for ∗This document is based on an article published in R News