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Adaptive Tests of Significance Using Permutations of Residuals with R and SAS

Book Description

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.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Dedication
  5. Contents
  6. PREFACE
  7. CHAPTER 1: INTRODUCTION
    1. 1.1 WHY USE ADAPTIVE TESTS?
    2. 1.2 A BRIEF HISTORY OF ADAPTIVE TESTS
    3. 1.3 THE ADAPTIVE TEST OF HOGG, FISHER, AND RANDLES
    4. 1.4 LIMITATIONS OF RANK-BASED TESTS
    5. 1.5 THE ADAPTIVE WEIGHTED LEAST SQUARES APPROACH
    6. 1.6 DEVELOPMENT OF THE ADAPTIVE WLS TEST
  8. CHAPTER 2: SMOOTHING METHODS AND NORMALIZING TRANSFORMATIONS
    1. 2.1 TRADITIONAL ESTIMATORS OF THE MEDIAN AND THE INTERQUARTILE RANGE
    2. 2.2 PERCENTILE ESTIMATORS THAT USE THE SMOOTH CUMULATIVE DISTRIBUTION FUNCTION
    3. 2.3 ESTIMATING THE BANDWIDTH
    4. 2.4 NORMALIZING TRANSFORMATIONS
    5. 2.5 THE WEIGHTING ALGORITHM
    6. 2.6 COMPUTING THE BANDWIDTH
    7. EXERCISES
  9. CHAPTER 3: A TWO-SAMPLE ADAPTIVE TEST
    1. 3.1 A TWO-SAMPLE MODEL
    2. 3.2 COMPUTING THE ADAPTIVE WEIGHTS
    3. 3.3 THE TEST STATISTICS FOR ADAPTIVE TESTS
    4. 3.4 PERMUTATION METHODS FOR TWO-SAMPLE TESTS
    5. 3.5 AN EXAMPLE OF A TWO-SAMPLE TEST
    6. 3.6 R CODE FOR THE TWO-SAMPLE TEST
    7. 3.7 LEVEL OF SIGNIFICANCE OF THE ADAPTIVE TEST
    8. 3.8 POWER OF THE ADAPTIVE TEST
    9. 3.9 SAMPLE SIZE ESTIMATION
    10. 3.10 A SAS MACRO FOR THE ADAPTIVE TEST
    11. 3.11 MODIFICATIONS FOR ONE-TAILED TESTS
    12. 3.12 JUSTIFICATION OF THE WEIGHTING METHOD
    13. 3.13 COMMENTS ON THE ADAPTIVE TWO-SAMPLE TEST
    14. EXERCISES
  10. CHAPTER 4: PERMUTATION TESTS WITH LINEAR MODELS
    1. 4.1 INTRODUCTION
    2. 4.2 NOTATION
    3. 4.3 PERMUTATIONS WITH BLOCKING
    4. 4.4 LINEAR MODELS IN MATRIX FORM
    5. 4.5 PERMUTATION METHODS
    6. 4.6 PERMUTATION TEST STATISTICS
    7. 4.7 AN IMPORTANT RULE OF TEST CONSTRUCTION
    8. 4.8 A PERMUTATION ALGORITHM
    9. 4.9 A PERFORMANCE COMPARISON OF THE PERMUTATION METHODS
    10. 4.10 DISCUSSION
    11. EXERCISES
  11. CHAPTER 5: AN ADAPTIVE TEST FOR A SUBSET OF COEFFICIENTS IN A LINEAR MODEL
    1. 5.1 THE GENERAL ADAPTIVE TESTING METHOD
    2. 5.2 SIMPLE LINEAR REGRESSION
    3. 5.3 AN EXAMPLE OF A SIMPLE LINEAR REGRESSION
    4. 5.4 MULTIPLE LINEAR REGRESSION
    5. 5.5 AN EXAMPLE OF A TEST IN MULTIPLE REGRESSION
    6. 5.6 CONCLUSIONS
    7. EXERCISES
  12. CHAPTER 6: MORE APPLICATIONS OF ADAPTIVE TESTS
    1. 6.1 THE COMPLETELY RANDOMIZED DESIGN
    2. 6.2 TESTS FOR RANDOMIZED COMPLETE BLOCK DESIGNS
    3. 6.3 ADAPTIVE TESTS FOR TWO-WAY DESIGNS
    4. 6.4 DEALING WITH UNEQUAL VARIANCES
    5. 6.5 EXTENSIONS TO MORE COMPLEX DESIGNS
    6. EXERCISES
  13. CHAPTER 7: THE ADAPTIVE ANALYSIS OF PAIRED DATA
    1. 7.1 INTRODUCTION
    2. 7.2 THE ADAPTIVE TEST OF MIAO AND GASTWIRTH
    3. 7.3 AN ADAPTIVE WEIGHTED LEAST SQUARES TEST
    4. 7.4 AN EXAMPLE USING PAIRED DATA
    5. 7.5 SIMULATION STUDY
    6. 7.6 SAMPLE SIZE ESTIMATION
    7. 7.7 DISCUSSION OF TESTS FOR PAIRED DATA
    8. EXERCISES
  14. CHAPTER 8: MULTICENTER AND CROSS-OVER TRIALS
    1. 8.1 TESTS IN MULTICENTER CLINICAL TRIALS
    2. 8.2 ADAPTIVE ANALYSIS OF CROSS-OVER TRIALS
    3. EXERCISES
  15. CHAPTER 9: ADAPTIVE MULTIVARIATE TESTS
    1. 9.1 THE TRADITIONAL LIKELIHOOD RATIO TEST
    2. 9.2 AN ADAPTIVE MULTIVARIATE TEST
    3. 9.3 AN EXAMPLE WITH TWO DEPENDENT VARIABLES
    4. 9.4 PERFORMANCE OF THE ADAPTIVE TEST
    5. 9.5 CONCLUSIONS FOR MULTIVARIATE TESTS
    6. EXERCISES
  16. CHAPTER 10: ANALYSIS OF REPEATED MEASURES DATA
    1. 10.1 INTRODUCTION
    2. 10.2 THE MULTIVARIATE LR TEST
    3. 10.3 THE ADAPTIVE TEST
    4. 10.4 THE MIXED MODEL TEST
    5. 10.5 TWO-SAMPLE TESTS
    6. 10.6 TWO-SAMPLE TESTS FOR PARALLELISM
    7. 10.7 TWO-SAMPLE TESTS FOR GROUP EFFECT
    8. 10.8 AN EXAMPLE OF REPEATED MEASURES DATA
    9. 10.9 DEALING WITH MISSING DATA
    10. 10.10 CONCLUSIONS AND RECOMMENDATIONS
    11. EXERCISES
  17. CHAPTER 11: RANK-BASED TESTS OF SIGNIFICANCE
    1. 11.1 THE QUEST FOR POWER
    2. 11.2 TWO-SAMPLE RANK TESTS
    3. 11.3 THE HFR TEST
    4. 11.4 SIGNIFICANCE LEVEL OF ADAPTIVE TESTS
    5. 11.5 BÜNING'S ADAPTIVE TEST FOR LOCATION
    6. 11.6 AN ADAPTIVE TEST FOR LOCATION AND SCALE
    7. 11.7 OTHER ADAPTIVE RANK TESTS
    8. 11.8 MAXIMUM TEST
    9. 11.9 DISCUSSION
    10. EXERCISES
  18. CHAPTER 12: ADAPTIVE CONFIDENCE INTERVALS AND ESTIMATES
    1. 12.1 THE RELATIONSHIP BETWEEN TESTS AND CONFIDENCE INTERVALS
    2. 12.2 THE ITERATIVE PROCEDURE OF GARTHWAITE
    3. 12.3 A 95% CONFIDENCE INTERVAL FOR THE DIFFERENCE BETWEEN POPULATION MEANS
    4. 12.4 A 95% CONFIDENCE INTERVAL FOR SLOPE
    5. 12.5 A GENERAL FORMULA FOR CONFIDENCE LIMITS
    6. 12.6 COMPUTING A CONFIDENCE INTERVAL USING R
    7. 12.7 COMPUTING A 95% CONFIDENCE INTERVAL USING SAS
    8. 12.8 ADAPTIVE ESTIMATION
    9. 12.9 ADAPTIVE ESTIMATION OF THE DIFFERENCE BETWEEN TWO POPULATION MEANS
    10. 12.10 ADAPTIVE ESTIMATION OF A SLOPE IN A MULTIPLE REGRESSION MODEL
    11. 12.11 COMPUTING AN ADAPTIVE ESTIMATE USING R
    12. 12.12 COMPUTING AN ADAPTIVE ESTIMATE USING SAS
    13. 12.13 DISCUSSION
    14. EXERCISES
  19. APPENDIX A: R CODE FOR UNIVARIATE ADAPTIVE TESTS
  20. APPENDIX B: SAS MACRO FOR ADAPTIVE TESTS
  21. APPENDIX C: SAS MACRO FOR MULTIPLE COMPARISONS PROCEDURES
  22. APPENDIX D: R CODE FOR ADAPTIVE TESTS WITH BLOCKING FACTORS
  23. APPENDIX E: R CODE FOR ADAPTIVE TEST WITH PAIRED DATA
  24. APPENDIX F: SAS MACRO FOR ADAPTIVE TEST WITH PAIRED DATA
  25. APPENDIX G: R CODE FOR MULTIVARIATE ADAPTIVE TESTS
  26. APPENDIX H: R CODE FOR CONFIDENCE INTERVALS AND ESTIMATES
  27. APPENDIX I: SAS MACRO FOR CONFIDENCE INTERVALS
  28. APPENDIX J: SAS MACRO FOR ESTIMATES
  29. REFERENCES
  30. INDEX