Permutation Tests for Stochastic Ordering and ANOVA (eBook)

Preface 5
Contents 10
Permutation Tests 13
Introduction 13
Basic Construction 16
Properties 19
Multivariate Permutation Tests 22
Properties of the Nonparametric Combination Tests 29
Examples 30
Univariate Permutation Tests 30
The Nonparametric Combination Methodology 34
Multiple Testing 37
Multiple Comparisons 44
Part I Stochastic Ordering 48
Ordinal Data 49
Introduction 49
Testing Whether Treatment is ``Better'' than Control 52
Conditional Distribution 53
Linear Test Statistics: Choice of Scores 54
Applications with R functions 61
Concordance Monotonicity 63
Applications with R functions 65
Multiple Testing 65
Independent Binomial Samples 67
Applications with R functions 70
Comparison of Several Treatments when the Response is Ordinal 72
Multivariate Ordinal Data 75
Introduction 75
Standardized Test Statistics 82
Multiple Testing on Endpoints and Domains 84
Analysis of the FOB Data 86
Violations of Stochastic Order 88
Multivariate Continuous Data 95
Introduction 95
Testing Superiority 96
Testing Superiority and Noninferiority 103
Applications with R functions 106
Several Samples 107
Applications with R functions 111
Part II Nonparametric ANOVA 112
Nonparametric One-Way ANOVA 113
Overview of Nonparametric One-Way ANOVA 114
Permutation Solution 115
Synchronizing Permutations 118
A Comparative Simulation Study for One-Way ANOVA 121
Testing for Umbrella Alternatives 122
Simple Stochastic Ordering Alternatives 124
Permutation Test for Umbrella Alternatives 127
The Mack and Wolfe Test 128
A Comparative Simulation Study 130
Applications with R 134
One-Way ANOVA with R 135
Umbrella Alternatives with R 137
Synchronized Permutation Tests in Two-way ANOVA 141
Introduction 141
The Test Statistics 143
Constrained and Unconstrained Synchronized Permutations 144
Properties of the Synchronized Permutation Test Statistics 148
Uncorrelatedness Among Synchronized Permutation Tests 148
Unbiasedness and Consistency of Synchronized Permutation Tests 151
Power Simulation Study 154
Multiple Comparisons 157
Examples and Use of R Functions 162
Applications with R Functions 164
Examples 174
Further Developments 176
Unbalanced Two-Way ANOVA Designs 176
Two-Way MANOVA 178
Permutation Tests for Unreplicated Factorial Designs 181
Brief Introduction to Unreplicated 2K Full Factorial Designs 182
Loughin and Noble's Test 184
The TF Test 188
The (Basso and Salmaso) TP Test 192
The (Basso and Salmaso) Step-up TP 194
Calibrating the Step-up Tp 200
A Comparative Simulation Study 203
Examples with R 206
Calibrating the Step-up TP with R 212
References 214
Index 221