CHAPTER 1: Introduction to Design CHAPTER 2: Principles of Estimation and Inference: Means and Variance CHAPTER 3: Design and Analysis of Single-Factor Experiments: Completely Randomized Design CHAPTER 4: Single-Factor Experiments Having Repeated Measures on the Same Element CHAPTER 5: Design and Analysis of Factorial Experiments: Completely-Randomized Design CHAPTER 6: Factorial Experiments: Computational Procedures and Numerical Example CHAPTER 7: Multifactor Experiments Having Repeated Measures on the Same Element CHAPTER 8: Factorial Experiments in which Some of the Interactions are Confounded CHAPTER 9: Latin Squares and Related Designs CHAPTER 10: Analysis of Covariance
Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth of the results. For the analyses we use the R add-on package multcomp, which provides a convenient interface to the general approach adopted here.