Nonparametric Statistical Methods Using R (2nd Edition – Kloke & McKean) | Complete eBook PDF

,Designed cover image: © John Kloke and Joseph McKean
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DOI: 10.1201/9781003039617

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,Contents


Preface xiii

Preface from the First Edition xv

1 Introduction 1
1.1 Data and Notation . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Data Types in R . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Vector and Matrix Notation . . . . . . . . . . . . . . . 3
1.1.3 Data Frames . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.4 Ranks . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . 11
1.3.1 Estimates of Center: Sample Mean and Sample Median 13
1.4 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4.1 Single Line Functions . . . . . . . . . . . . . . . . . . 17
1.4.2 Level and Power of a Statistical Test . . . . . . . . . . 17
1.4.3 Functions . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5 Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.6 Density Estimation . . . . . . . . . . . . . . . . . . . . . . . 24
1.6.1 Some Details . . . . . . . . . . . . . . . . . . . . . . . 26
1.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2 One-Sample Problems 33
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2 One-Sample Proportion Problems . . . . . . . . . . . . . . . 33
2.3 Sign Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3.1 Power Simulation . . . . . . . . . . . . . . . . . . . . . 37
2.4 Signed-Rank Wilcoxon . . . . . . . . . . . . . . . . . . . . . 39
2.4.1 Estimation and Confidence Intervals . . . . . . . . . . 40
2.4.2 Computation in R . . . . . . . . . . . . . . . . . . . . 42
2.4.3 Density Estimation Revisited . . . . . . . . . . . . . . 44
2.5 Adjustments for Ties . . . . . . . . . . . . . . . . . . . . . . 45
2.5.1 Sign Test . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.5.2 Signed-Rank Wilcoxon . . . . . . . . . . . . . . . . . . 47
2.6 Confidence Interval Based Estimates of Standard Errors . . . 48
2.7 Asymptotic Tests . . . . . . . . . . . . . . . . . . . . . . . . 52

, viii Contents

2.7.1 Signed-Rank Wilcoxon Test . . . . . . . . . . . . . . . 53
2.7.2 Sign Test . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.8 Bootstrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.8.1 Percentile Bootstrap Confidence Intervals . . . . . . . 57
2.8.2 Bootstrap Tests of Hypotheses . . . . . . . . . . . . . 58
2.9 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.10 Power and Sample Size Determination . . . . . . . . . . . . . 63
2.10.1 Power of One-Sample Rank-Based Tests . . . . . . . . 63
2.10.2 Sample Size Determination . . . . . . . . . . . . . . . 66
2.10.3 Randomized Paired Design . . . . . . . . . . . . . . . 68
2.10.4 Sign Test . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.10.5 Sample Size Determination for Estimation . . . . . . . 71
2.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3 Two-Sample Problems 79
3.1 Introductory Example . . . . . . . . . . . . . . . . . . . . . . 79
3.2 Rank-Based Analyses . . . . . . . . . . . . . . . . . . . . . . 81
3.2.1 Wilcoxon Test for Stochastic Ordering of Alternatives 81
3.2.2 Analyses for a Shift in Location . . . . . . . . . . . . . 84
3.2.3 Analyses Based on General Score Functions . . . . . . 89
3.2.4 Linear Regression Model . . . . . . . . . . . . . . . . . 91
3.3 Sign Scores Two-Sample Analysis . . . . . . . . . . . . . . . 94
3.3.1 Mood’s Median Test . . . . . . . . . . . . . . . . . . . 94
3.3.2 Estimation of the Shift in Location . . . . . . . . . . . 98
3.4 Adjustments for Ties . . . . . . . . . . . . . . . . . . . . . . 100
3.5 Scale Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.6 Placement Test for the Behrens–Fisher Problem . . . . . . . 106
3.6.1 Estimation of a Shift Parameter, ∆ . . . . . . . . . . . 109
3.6.2 Classical Behrens–Fisher Model . . . . . . . . . . . . . 110
3.7 Efficiency and Optimal Scores . . . . . . . . . . . . . . . . . 114
3.7.1 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.8 Adaptive Rank Scores Tests . . . . . . . . . . . . . . . . . . 120
3.9 Power and Sample Size Determination for Rank-Based Tests 123
3.9.1 Power of Rank-Based Tests . . . . . . . . . . . . . . . 124
3.9.2 Sample Size Determination . . . . . . . . . . . . . . . 128
3.10 k-Nearest Neighbors and Cross-Validation . . . . . . . . . . 134
3.11 Kaplan–Meier and Log-Rank Test . . . . . . . . . . . . . . . 139
3.11.1 Gehan’s Test . . . . . . . . . . . . . . . . . . . . . . . 144
3.11.2 Composite Outcomes . . . . . . . . . . . . . . . . . . . 145
3.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147