Thomas W. O'Gorman

Adaptive Tests

• Gebundenes Buch

Produktbeschreibung

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. Also included is coverage of smoothing methods in adaptive weighting, permutation of residuals, and within-block permutation methods, allowing the presented methods to be used directly with multicenter clinical trials as well as with randomized block designs. It is designed for professionals in a variety of fields, including biostatistics and pharmaceutical, agricultural, and business statistics, as well as a supplementary course book for courses in regression analysis and adaptive analysis.

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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.

Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 364
• Erscheinungstermin: 13. März 2012
• Englisch
• Abmessung: 240mm x 161mm x 24mm
• Gewicht: 632g
• ISBN-13: 9780470922255
• ISBN-10: 0470922257
• Artikelnr.: 34440607

Autorenporträt

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.

Inhaltsangabe

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