Multiple Comparison Procedures in Linear Models

Abstract

Multiplicity is a difficult and ubiquitous problem. The problem of evaluating multiple experimental questions occurs in many areas of applications, such as, for example, in clinical trials assessing more than one outcome variable, or in agricultural field experiments comparing several irrigation systems. If multiple null hypotheses are tested simultaneously, the probability of declaring effects when none exists increases beyond the nominal type I error level used for the individual comparisons. In this paper we review multiple comparison procedures in the linear model framework. We use the multcomp package from $\mathsf{R}$ to illustrate the methods with a linear regression example.