Multiple Comparisons: Theory and methods

Multiple comparisons are the comparisons of two or more treatments. These may be treatments of a disease, groups of subjects, or computer systems, for example. Statistical multiple comparison methods are used heavily in research, education, business, and manufacture to analyze data, but are often used incorrectly. This book exposes such abuses and misconceptions, and guides the reader to the correct method of analysis for each problem. Theories for all pairwise comparisons, multiple comparison with the best, and multiple comparison with a control are discussed, and methods giving statistical inference in terms of confidence intervals, confident directions, and confident inequalities are described. Applications are illustrated with real data. Included are recent mentods empowered by modern computers. Multiple Comparisons will be valued by researchers and graduate students interested in the theory of multiple comparisons, as well as those invloved in data analysis in bilogical and social sciences, medicine, business and engineering. It will also interest professional and consulting statisticians in the pharmaceutical industry, and quality control engineers in manufacturing companies.

Table of Contents:

Introduction to simultaneous statistical inference

The one way model

Modeling

Simultaneous confidence intervals

Simultaneous testing

Unequal variances

Nonparametric methods

Deduced inference versus direct inference

Classification of multiple comparison methods

1. Types of multiple comparisons inference
2. Strength of multiple comparisons inference
3. Inferential tasks of multiple comparison methods
4. Choosing a multiple comparison method

Multiple comparisons with a control

1-sided multiple comparisons with a control

2-sided multiple comparisons with a control

Nonparametric methods

Other approaches to stepwise testing

Multiple comparisons with the best

Constrained multiple comparison with the best

Unconstrained multiple comparison with the best

Nonparametric methods

All-pairwise comparisons

Balanced one-way model

Unbalanced one-way model

Nonparametric methods

Common abuses in multiple comparisons

Not adjusting for multiplicity

Inflation of strength of inference

Conditional inference

Post hoc comparisons

Recommendations

Multiple comparisons in the general linear model

Models with one way structure

Multiple comparisons with a control

Multiple comparisons with the best

All-pairwise comparisons

Scheffe's method for all contrasts

Nonparametric methods

Two-way mixed models

One-way repeated measurement models

Appendix A: Some useful probabilistic inequalities

An inequality for conditionally independent random variables

The Bonferroni inequality

Slepian's inequality

Sidak's Inequality

The Hunter-Worsley Inequality

Appendix B: Some useful geometric lemmas

Projecting spheres

Projecting rectangles

Deriving confidence sets by pivoting tests

Appendix C: Sample size calculations

Sample size calculation for Tukey's method of MCA

Sample size calculation for MCB

Sample size calculation for Dunnett's MCC method

An example

Appendix D: Accessing computer codes

Critical value computations

Sample size computations

Online access to codes

Appendix E: Tables of critical values

---