Permutation Tests for Stochastic Ordering and ANOVA

by Basso, Dario; Pesarin, Fortunato; Salmaso, Luigi; Solari, Aldo

• ISBN13: 9780387859552
• ISBN10: 0387859551
• Format: Paperback
• Copyright: 2009-04-20
• Publisher: Springer Verlag

Summary

Permutation testing for multivariate stochastic ordering and ANOVA designs is a fundamental issue in many scientific fields such as medicine, biology, pharmaceutical studies, engineering, economics, psychology, and social sciences. This book presents new advanced methods and related R codes to perform complex multivariate analyses. The prerequisites are a standard course in statistics and some background in multivariate analysis and R software.

Author Biography

Dario Basso is a Post Doctoral Fellow at the Department of Management and Engineering of University of Padova. His main research interests include permutation tests and design of experiments. Fortunato Pesarin is Full Professor of Statistics at the Department of Statistics of the University of Padova. His main research interests include nonparametric methods, boot-strap methods, and permutation tests. He has published a leading book on multivariate permutation tests based on nonparametric combination methodology. Luigi Salmaso is Associate Professor of Statistics at the Department of Management and Engineering of the University of Padova. His main research interests include permutation methods, multiple tests, and design of experiments. He has published more than 70 papers on permutation methods and design of experiments in international peer-reviewed journals. Aldo Solari is a Post Doctoral Fellow at the Department of Chemical Process Engineering of the University of Padova. His main research interest is resampling based multiple testing methods.

Table of Contents

Preface	p. v
Permutation Tests	p. 1
Introduction	p. 1
Basic Construction	p. 4
Properties	p. 7
Multivariate Permutation Tests	p. 10
Properties of the Nonparametric Combination Tests	p. 17
Examples	p. 18
Univariate Permutation Tests	p. 18
The Nonparametric Combination Methodology	p. 22
Multiple Testing	p. 25
Multiple Comparisons	p. 32
Stochastic Ordering
Ordinal Data	p. 39
Introduction	p. 39
Testing Whether Treatment is "Better" than Control	p. 42
Conditional Distribution	p. 43
Linear Test Statistics: Choice of Scores	p. 44
Applications with R functions	p. 51
Concordance Monotonicity	p. 53
Applications with R functions	p. 55
Multiple Testing	p. 55
Independent Binomial Samples	p. 57
Applications with R functions	p. 60
Comparison of Several Treatments when the Response is Ordinal	p. 62
Multivariate Ordinal Data	p. 65
Introduction	p. 65
Standardized Test Statistics	p. 72
Multiple Testing on Endpoints and Domains	p. 74
Analysis of the FOB Data	p. 76
Violations of Stochastic Order	p. 78
Multivariate Continuous Data	p. 85
Introduction	p. 85
Testing Superiority	p. 86
Testing Superiority and Noninferiority	p. 93
Applications with R functions	p. 96
Several Samples	p. 97
Applications with R functions	p. 101
Nonparametric ANOVA
Nonparametric One-Way ANOVA	p. 105
Overview of Nonparametric One-Way ANOVA	p. 106
Permutation Solution	p. 107
Synchronizing Permutations	p. 110
A Comparative Simulation Study for One-Way ANOVA	p. 113
Testing for Umbrella Alternatives	p. 114
Simple Stochastic Ordering Alternatives	p. 116
Permutation Test for Umbrella Alternatives	p. 119
The Mack and Wolfe Test	p. 120
A Comparative Simulation Study	p. 122
Applications with R	p. 126
One-Way ANOVA with R	p. 127
Umbrella Alternatives with R	p. 129
Synchronized Permutation Tests in Two-way ANOVA	p. 133
Introduction	p. 133
The Test Statistics	p. 135
Constrained and Unconstrained Synchronized Permutations	p. 136
Properties of the Synchronized Permutation Test Statistics	p. 140
Uncorrelatedness Among Synchronized Permutation Tests	p. 140
Unbiasedness and Consistency of Synchronized Permutation Tests	p. 143
Power Simulation Study	p. 146
Multiple Comparisons	p. 149
Examples and Use of R Functions	p. 154
Applications with R Functions	p. 156
Examples	p. 166
Further Developments	p. 168
Unbalanced Two-Way ANOVA Designs	p. 168
Two-Way MANOVA	p. 170
Permutation Tests for Unreplicated Factorial Designs	p. 173
Brief Introduction to Unreplicated 2K Full Factorial Designs	p. 174
Loughin and Noble's Test	p. 176
The TF Test	p. 180
The (Basso and Salmaso) TP Test	p. 184
The (Basso and Salmaso) Step-up TP	p. 186
Calibrating the Step-up Tp	p. 192
A Comparative Simulation Study	p. 195
Examples with R	p. 198
Calibrating the Step-up Tp with R	p. 204
References	p. 207
Index	p. 215
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