Hsu J.C. Multiple comparisons: theory and methods

Springer Science+Business Media, 1996. — 277 p. — ISBN: 978-0-412-98281-1.Multiple Comparisons introduces simultaneous statistical inference and covers the theory and techniques for all-pairwise comparisons, multiple comparisons with the best, and multiple comparisons with a control. The author describes confidence intervals methods and stepwise exposes abuses and misconceptions, and guides readers to the correct method for each problem. Discussions also include the connections with bioequivalence, drug stability, and toxicity studies. Real data sets analyzed by computer software packages illustrate the applications presented.Introduction to simultaneous statistical inference
The one-way model
Modeling
Simultaneous confidence intervals
Simultaneous testing
Unequal variances
Nonparametric methods
Deduced inference versus direct inference
Exercises
Classification of multiple comparison methods
Types of multiple comparisons inference
Strength of multiple comparisons inference
Inferential tasks of multiple comparison methods
Choosing a multiple comparison method
Exercises
Multiple comparisons with a control
One-sided multiple comparisons with a control
Two-sided multiple comparisons with a control
Nonparametric methods
Other approaches to stepwise testing
Appendix: detailed proofs
Exercises
Multiple comparisons with the best
Constrained multiple comparison with the best
Unconstrained multiple comparisons with the best
Nonparametric methods
Exercises
All-pairwise comparisons
Balanced one-way model
Unbalanced one-way model
Nonparametric methods
Exercises
Abuses and misconceptions 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
Exercises
Some useful probabilistic inequalities
An inequality for conditionally independent random variabies
The Bonferroni inequality
Slepian's inequality
Sidak's inequality
The Hunter-Worsley Inequality
Some useful geometric lemmas
Projecting spheres
Projecting rectangles
Deriving confidence sets by pivoting tests
Sample size computations
Sample size computation for Tukey's MCA method
Sample size computation for MCB
Sample size computation for Dunnett's MCC method
An Example
Accessing computer codes
Online access to codes
Critical value computations
Sample size computations
Tables of critical values