Adaptive Tests of Significance Using Permutations of Residuals With - R and Sa

Informationen zum Autor Thomas W. O'gorman , PhD, is Associate Professor in the Department of Mathematical Sciences at Northern Illinois University. Dr. O'Gorman's current research focuses on the analysis of adaptive methods for performing statistical tests and confidence intervals. Klappentext Provides the tools needed to successfully perform adaptive tests across a broad range of datasetsAdaptive Tests of Significance Using Permutations of Residuals with R and SAS illustrates the power of adaptive tests and showcases their ability to adjust the testing method to suit a particular set of data. The book utilizes state-of-the-art software to demonstrate the practicality and benefits for data analysis in various fields of study.Beginning with an introduction, the book moves on to explore the underlying concepts of adaptive tests, including:* Smoothing methods and normalizing transformations* Permutation tests with linear methods* Applications of adaptive tests* Multicenter and cross-over trials* Analysis of repeated measures data* Adaptive confidence intervals and estimatesThroughout the book, numerous figures illustrate the key differences among traditional tests, nonparametric tests, and adaptive tests. R and SAS software packages are used to perform the discussed techniques, and the accompanying datasets are available on the book's related website. In addition, exercises at the end of most chapters enable readers to analyze the presented datasets by putting new concepts into practice.Adaptive Tests of Significance Using Permutations of Residuals with R and SAS is an insightful reference for professionals and researchers working with statistical methods across a variety of fields including the biosciences, pharmacology, and business. The book also serves as a valuable supplement for courses on regression analysis and adaptive analysis at the upper-undergraduate and graduate levels. "Each chapter provides detailed information on R and SAS code, respectively. Moreover, each chapter closes with illustrating exercises (without solutions). This is ideal for researchers who wish to implement anadaptive test of significance for their specific problem." ( Biometrical Journal , 1 May 2013) Zusammenfassung Provides the tools needed to successfully perform adaptive tests across a broad range of datasets Adaptive Tests of Significance Using Permutations of Residuals with R and SAS illustrates the power of adaptive tests and showcases their ability to adjust the testing method to suit a particular set of data. Inhaltsverzeichnis Preface xv 1 Introduction 1 1.1 Why Use Adaptive Tests? 1 1.2 A Brief History of Adaptive Tests 2 1.3 The Adaptive Test of Hogg, Fisher, and Randies 5 1.4 Limitations of Rank-Based Tests 8 1.5 The Adaptive Weighted Least Squares Approach 9 1.6 Development of the Adaptive WLS Test 12 2 Smoothing Methods and Normalizing Transformations 15 2.1 Traditional Estimators of the Median and the Interquartile Range 15 2.2 Percentile Estimators that Use the Smooth Cumulative Distribution Function 16 2.3 Estimating the Bandwidth 21 2.4 Normalizing Transformations 23 2.5 The Weighting Algorithm 27 2.6 Computing the Bandwidth 30 2.7 Examples of Transformed Data 37 3 A Two-Sample Adaptive Test 43 3.1 A Two-Sample Model 44 3.2 Computing the Adaptive Weights 45 3.3 The Test Statistics for Adaptive Tests 47 3.4 Permutation Methods for Two-Sample Tests 50 3.5 An Example of a Two-Sample Test 54 3.6 R Code for the Two-Sample Test 56 3.7 Level of Significance of the Adaptive Test 61 3.8 Power of the Adaptive Test 63 3.9 Sample Size Estimation 65 3.10 A SAS Macro for the Adaptive Test 68 3.11 Modifications for One-Tailed Tests 70 3.12 Justification of the We...

List of contents

Preface xv
 
1 Introduction 1
 
1.1 Why Use Adaptive Tests? 1
 
1.2 A Brief History of Adaptive Tests 2
 
1.3 The Adaptive Test of Hogg, Fisher, and Randies 5
 
1.4 Limitations of Rank-Based Tests 8
 
1.5 The Adaptive Weighted Least Squares Approach 9
 
1.6 Development of the Adaptive WLS Test 12
 
2 Smoothing Methods and Normalizing Transformations 15
 
2.1 Traditional Estimators of the Median and the Interquartile Range 15
 
2.2 Percentile Estimators that Use the Smooth Cumulative Distribution Function 16
 
2.3 Estimating the Bandwidth 21
 
2.4 Normalizing Transformations 23
 
2.5 The Weighting Algorithm 27
 
2.6 Computing the Bandwidth 30
 
2.7 Examples of Transformed Data 37
 
3 A Two-Sample Adaptive Test 43
 
3.1 A Two-Sample Model 44
 
3.2 Computing the Adaptive Weights 45
 
3.3 The Test Statistics for Adaptive Tests 47
 
3.4 Permutation Methods for Two-Sample Tests 50
 
3.5 An Example of a Two-Sample Test 54
 
3.6 R Code for the Two-Sample Test 56
 
3.7 Level of Significance of the Adaptive Test 61
 
3.8 Power of the Adaptive Test 63
 
3.9 Sample Size Estimation 65
 
3.10 A SAS Macro for the Adaptive Test 68
 
3.11 Modifications for One-Tailed Tests 70
 
3.12 Justification of the Weighting Method 70
 
3.13 Comments on the Adaptive Two-sample Test 71
 
4 Permutation Tests with Linear Models 75
 
4.1 Introduction 75
 
4.2 Notation 76
 
4.3 Permutations with Blocking 77
 
4.4 Linear Models in Matrix Form 77
 
4.5 Permutation Methods 78
 
4.6 Permutation Test Statistics 81
 
4.7 An Important Rule of Test Construction 82
 
4.8 A Permutation Algorithm 82
 
4.9 A Performance Comparison of the Permutation Methods 83
 
4.10 Discussion 84
 
5 An Adaptive Test for a Subset of Coefficients 87
 
5.1 The General Adaptive Testing Method 87
 
5.2 Simple Linear Regression 91
 
5.3 An Example of a Simple Linear Regression 93
 
5.4 Multiple Linear Regression 96
 
5.5 An Example of a Test in Multiple Regression 100
 
5.6 Conclusions 105
 
6 More Applications of Adaptive Tests 111
 
6.1 The Completely Randomized Design 111
 
6.2 Tests for Randomized Complete Block Designs 120
 
6.3 Adaptive Tests for Two-way Designs 127
 
6.4 Dealing with Unequal Variances 134
 
6.5 Extensions to More Complex Designs 140
 
7 The Adaptive Analysis of Paired Data 149
 
7.1 Introduction 149
 
7.2 The Adaptive Test of Miao and Gastwirth 151
 
7.3 An Adaptive Weighted Least Squares Test 153
 
7.4 An Example Using Paired Data 160
 
7.5 Simulation Study 161
 
7.6 Sample Size Estimation 163
 
7.7 Discussion of Tests for Paired Data 165
 
8 Multicenter and Cross-Over Trials 169
 
8.1 Tests in Multicenter Clinical Trials 170
 
8.2 Adaptive Analysis of Cross-over Trials 176
 
9 Adaptive Multivariate Tests 191
 
9.1 The Traditional Likelihood Ratio Test 191
 
9.2 An Adaptive Multivariate Test 192
 
9.3 An Example with Two Dependent Variables 196
 
9.4 Performance of the Adaptive Test 199
 
9.5 Conclusions for Multivariate Tests 203
 
10 Analysis of Repeated Measures Data 207
 
10.1 Introduction 207
 
10.2 The Multivariate LR Test 209
 
10.3 The Adaptive Test 209
 
10.4 The Mixed Model Test 210
 
10.5 Two-Sample Tests 211
 
10.6 Two-Sample

Report

"Each chapter provides detailed information on R and SAS code, respectively. Moreover, each chapter closes with illustrating exercises (without solutions). This is ideal for researchers who wish to implement anadaptive test of significance for their specific problem." ( Biometrical Journal , 1 May 2013)

Product details

• Authors: &apos, Thomas W. gorman, O&apos, O'Gorman, Thomas W O'Gorman, Thomas W. O'Gorman, Thomas W. O''gorman, Thomas W. (Northern Illinois University O''gorman, Tw O''gorman, O'Gorman Thomas W.
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 06.03.2012
• EAN: 9780470922255
• ISBN: 978-0-470-92225-5
• No. of pages: 384
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Statistik, Regressionsanalyse, Statistics, Biostatistik, Biostatistics, Statistics for Finance, Business & Economics, Finanz- u. Wirtschaftsstatistik, Regression Analysis