Basso / Pesarin / Salmaso Permutation Tests for Stochastic Ordering and ANOVA

Theory and Applications with R
1. Auflage 2009
ISBN: 978-0-387-85956-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 194, 218 Seiten

Reihe: Lecture Notes in Statistics

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.

Autoren/Hrsg.

Basso, Dario

Pesarin, Fortunato

Salmaso, Luigi

Solari, Aldo

Inhaltsverzeichnis

1;Preface;5
2;Contents;10
3;Permutation Tests;13
3.1;Introduction;13
3.2;Basic Construction;16
3.3;Properties;19
3.4;Multivariate Permutation Tests;22
3.4.1;Properties of the Nonparametric Combination Tests;29
3.5;Examples;30
3.5.1;Univariate Permutation Tests;30
3.5.2;The Nonparametric Combination Methodology;34
3.6;Multiple Testing;37
3.7;Multiple Comparisons;44
4;Part I Stochastic Ordering;48
4.1;Ordinal Data;49
4.1.1;Introduction;49
4.1.2;Testing Whether Treatment is ``Better'' than Control;52
4.1.2.1;Conditional Distribution;53
4.1.2.2;Linear Test Statistics: Choice of Scores;54
4.1.2.3;Applications with R functions;61
4.1.2.4;Concordance Monotonicity;63
4.1.2.5;Applications with R functions;65
4.1.2.6;Multiple Testing;65
4.1.3;Independent Binomial Samples;67
4.1.3.1;Applications with R functions;70
4.1.4;Comparison of Several Treatments when the Response is Ordinal;72
4.2;Multivariate Ordinal Data;75
4.2.1;Introduction;75
4.2.2;Standardized Test Statistics;82
4.2.3;Multiple Testing on Endpoints and Domains;84
4.2.4;Analysis of the FOB Data;86
4.2.5;Violations of Stochastic Order;88
4.3;Multivariate Continuous Data;95
4.3.1;Introduction;95
4.3.2;Testing Superiority;96
4.3.3;Testing Superiority and Noninferiority;103
4.3.3.1;Applications with R functions;106
4.3.4;Several Samples;107
4.3.4.1;Applications with R functions;111
5;Part II Nonparametric ANOVA;112
5.1;Nonparametric One-Way ANOVA;113
5.1.1;Overview of Nonparametric One-Way ANOVA;114
5.1.2;Permutation Solution;115
5.1.2.1;Synchronizing Permutations;118
5.1.2.2;A Comparative Simulation Study for One-Way ANOVA;121
5.1.3;Testing for Umbrella Alternatives;122
5.1.4;Simple Stochastic Ordering Alternatives;124
5.1.5;Permutation Test for Umbrella Alternatives;127
5.1.5.1;The Mack and Wolfe Test;128
5.1.6;A Comparative Simulation Study;130
5.1.7;Applications with R;134
5.1.7.1;One-Way ANOVA with R;135
5.1.7.2;Umbrella Alternatives with R;137
5.2;Synchronized Permutation Tests in Two-way ANOVA;141
5.2.1;Introduction;141
5.2.2;The Test Statistics;143
5.2.3;Constrained and Unconstrained Synchronized Permutations;144
5.2.4;Properties of the Synchronized Permutation Test Statistics;148
5.2.4.1;Uncorrelatedness Among Synchronized Permutation Tests;148
5.2.4.2;Unbiasedness and Consistency of Synchronized Permutation Tests;151
5.2.5;Power Simulation Study;154
5.2.6;Multiple Comparisons;157
5.2.7;Examples and Use of R Functions;162
5.2.7.1;Applications with R Functions;164
5.2.7.2;Examples;174
5.2.8;Further Developments;176
5.2.8.1;Unbalanced Two-Way ANOVA Designs;176
5.2.8.2;Two-Way MANOVA;178
5.3;Permutation Tests for Unreplicated Factorial Designs;181
5.3.1;Brief Introduction to Unreplicated 2K Full Factorial Designs;182
5.3.2;Loughin and Noble's Test;184
5.3.3;The TF Test;188
5.3.4;The (Basso and Salmaso) TP Test;192
5.3.5;The (Basso and Salmaso) Step-up TP;194
5.3.5.1;Calibrating the Step-up Tp;200
5.3.6;A Comparative Simulation Study;203
5.3.7;Examples with R;206
5.3.7.1;Calibrating the Step-up TP with R;212
5.4;References;214
5.5;Index;221