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This book successfully introduces readers to the theory and applicability of adaptive tests, reviews the main contributions in the field, and provides readers with the tools needed to implement the statistical methodology. It focuses on adaptive tests of significance, which are more powerful than traditional tests.
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)
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 Tests for Parallelism 212
10.7 Two–Sample Tests for Group Effect 219
10.8 An Example of Repeated Measures Data 223
10.9 Dealing with Missing Data 227
10.10 Conclusions and Recommendations 229
11 Rank–Based Tests of Significance 235
11.1 The Quest for Power 235
11.2 Two–Sample Rank Tests 236
11.3 The HFR Test 242
11.4 Significance Level of Adaptive Tests 243
11.5 Biining′s Adaptive Test for Location 244
11.6 An Adaptive Test for Location and Scale 245
11.7 Other Adaptive Rank Tests 247
11.8 Maximum Test 248
11.9 Discussion 249
12 Adaptive Confidence Intervals and Estimates 253
12.1 The Relationship Between Tests and Confidence Intervals 253
12.2 The Iterative Procedure of Garthwaite 254
12.3 Confidence Interval for a Difference 259
12.4 A 95% Confidence Interval for Slope 263
12.5 A General Formula for Confidence Limits 264
12.6 Computing a Confidence Interval Using R 266
12.7 Computing a 95% Confidence Interval Using SAS 268
12.8 Adaptive Estimation 268
12.9 Adaptive Estimation of the Difference Between Two Population Means 271
12.10 Adaptive Estimation of a Slope in a Multiple Regression Model 272
12.11 Computing an Adaptive Estimate Using R 274
12.12 Computing an Adaptive Estimate Using SAS 278
12.13 Discussion 278
Exercises 279
Appendix A: R Code for Univariate Adaptive Tests 283
Appendix B: SAS Macro for Adaptive Tests 287
Appendix C: SAS Macro for Multiple Comparisons Procedures 299
Appendix D: R Code for Adaptive Tests with Blocking Factors 303
Appendix E: R Code for Adaptive Test with Paired Data 305
Appendix F: SAS Macro for Adaptive Test with Paired Data 309
Appendix G: R Code for Multivariate Adaptive Tests 313
Appendix H: R Code for Confidence Intervals and Estimates 317
Appendix I: SAS Macro for Confidence Intervals 321
Appendix J: SAS Macro for Estimates 329
References 333
Index 341
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.
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. 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 estimates
Throughout 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.
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