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Nonparametric Statistical Methods Using R

Book Description

A Practical Guide to Implementing Nonparametric and Rank-Based Procedures

Nonparametric Statistical Methods Using R covers traditional nonparametric methods and rank-based analyses, including estimation and inference for models ranging from simple location models to general linear and nonlinear models for uncorrelated and correlated responses. The authors emphasize applications and statistical computation. They illustrate the methods with many real and simulated data examples using R, including the packages Rfit and npsm.

The book first gives an overview of the R language and basic statistical concepts before discussing nonparametrics. It presents rank-based methods for one- and two-sample problems, procedures for regression models, computation for general fixed-effects ANOVA and ANCOVA models, and time-to-event analyses. The last two chapters cover more advanced material, including high breakdown fits for general regression models and rank-based inference for cluster correlated data.

The book can be used as a primary text or supplement in a course on applied nonparametric or robust procedures and as a reference for researchers who need to implement nonparametric and rank-based methods in practice. Through numerous examples, it shows readers how to apply these methods using R.

Table of Contents

  1. Preliminaries
  2. Preface
  3. Chapter 1 Getting Started with R
    1. 1.1 R Basics
      1. 1.1.1 Data Frames and Matrices
    2. 1.2 Reading External Data
    3. 1.3 Generating Random Data
    4. 1.4 Graphics
    5. 1.5 Repeating Tasks
    6. 1.6 User Defined Functions
    7. 1.7 Monte Carlo Simulation
    8. 1.8 R packages
    9. 1.9 Exercises
      1. Figure 1.1
      2. Figure 1.2
  4. Chapter 2 Basic Statistics
    1. 2.1 Introduction
    2. 2.2 Sign Test
    3. 2.3 Signed-Rank Wilcoxon
      1. 2.3.1 Estimation and Confidence Intervals
      2. 2.3.2 Computation in R
    4. 2.4 Bootstrap
      1. 2.4.1 Percentile Bootstrap Confidence Intervals
      2. 2.4.2 Bootstrap Tests of Hypotheses
    5. 2.5 Robustness*
    6. 2.6 One- and Two-Sample Proportion Problems
      1. 2.6.1 One-Sample Problems
      2. 2.6.2 Two-Sample Problems
    7. 2.7 <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" class="cItalic">&#967;</span><span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" class="cSuperscript">2</span> Tests Tests
      1. 2.7.1 Goodness-of-Fit Tests for a Single Discrete Random Variable
        1. Confidence Intervals
      2. 2.7.2 Several Discrete Random Variables
        1. Confidence Intervals
      3. 2.7.3 Independence of Two Discrete Random Variables
        1. Confidence Intervals
      4. 2.7.4 McNemar’s Test
    8. 2.8 Exercises
      1. Figure 2.1
      2. Figure 2.2
      1. Table 2.1
  5. Chapter 3 Two-Sample Problems
    1. 3.1 Introductory Example
    2. 3.2 Rank-Based Analyses
      1. 3.2.1 Wilcoxon Test for Stochastic Ordering of Alternatives
      2. 3.2.2 Analyses for a Shift in Location
        1. Normal Scores
      3. 3.2.3 Analyses Based on General Score Functions
      4. 3.2.4 Linear Regression Model
    3. 3.3 Scale Problem
    4. 3.4 Placement Test for the Behrens–Fisher Problem
      1. Discussion
    5. 3.5 Efficiency and Optimal Scores*
      1. 3.5.1 Efficiency
    6. 3.6 Adaptive Rank Scores Tests
    7. 3.7 Exercises
      1. Figure 3.1
      2. Figure 3.2
      3. Figure 3.3
      4. Figure 3.4
      5. Figure 3.5
      6. Figure 3.6
      7. Figure 3.7
      8. Figure 3.8
      1. Table 3.1
      2. Table 3.2
  6. Chapter 4 Regression I
    1. 4.1 Introduction
    2. 4.2 Simple Linear Regression
    3. 4.3 Multiple Linear Regression
      1. 4.3.1 Multiple Regression
      2. 4.3.2 Polynomial Regression
    4. 4.4 Linear Models*
      1. 4.4.1 Estimation
      2. 4.4.2 Diagnostics
      3. 4.4.3 Inference
      4. 4.4.4 Confidence Interval for a Mean Response
    5. 4.5 Aligned Rank Tests*
    6. 4.6 Bootstrap
    7. 4.7 Nonparametric Regression
      1. 4.7.1 Polynomial Models
      2. 4.7.2 Nonparametric Regression
    8. 4.8 Correlation
      1. 4.8.1 Pearson’s Correlation Coefficient
      2. 4.8.2 Kendall’s <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" class="cItalic">&#964;</span><span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" class="cIsub">K</span>
      3. 4.8.3 Spearman’s <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" class="cItalic">&#961;</span><span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" class="cIsub">s</span>
      4. 4.8.4 Computation and Examples
    9. 4.9 Exercises
      1. Figure 4.1
      2. Figure 4.2
      3. Figure 4.3
      4. Figure 4.4
      5. Figure 4.5
      6. Figure 4.6
      7. Figure 4.7
      8. Figure 4.8
      9. Figure 4.9
      10. Figure 4.10
      11. Figure 4.11
      12. Figure 4.12
      13. Figure 4.13
      1. Table 4.1
  7. Chapter 5 ANOVA and ANCOVA
    1. 5.1 Introduction
    2. 5.2 One-Way ANOVA
      1. 5.2.1 Multiple Comparisons
      2. 5.2.2 Kruskal–Wallis Test
    3. 5.3 Multi-Way Crossed Factorial Design
      1. 5.3.1 Two-Way
      2. 5.3.2 <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" class="cItalic">k</span>-Way-Way
    4. 5.4 ANCOVA*
      1. 5.4.1 Computation of Rank-Based ANCOVA
        1. Computation of Rank-Based ANCOVA for a One-Way Layout
        2. Computation of Rank-Based ANCOVA for a <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" class="cItalic">k</span>-Way Layout-Way Layout
    5. 5.5 Methodology for Type III Hypotheses Testing*
    6. 5.6 Ordered Alternatives
    7. 5.7 Multi-Sample Scale Problem
    8. 5.8 Exercises
      1. Figure 5.1
      2. Figure 5.2
      3. Figure 5.3
      4. Figure 5.4
      5. Figure 5.5
      6. Figure 5.6
      7. Figure 5.7
  8. Chapter 6 Time to Event Analysis
    1. 6.1 Introduction
    2. 6.2 Kaplan–Meier and Log Rank Test
      1. 6.2.1 Gehan’s Test
    3. 6.3 Cox Proportional Hazards Models
    4. 6.4 Accelerated Failure Time Models
    5. 6.5 Exercises
      1. Figure 6.1
      2. Figure 6.2
      3. Figure 6.3
      4. Figure 6.4
      5. Figure 6.5
      6. Figure 6.6
      1. Table 6.1
      2. Table 6.2
      3. Table 6.3
      4. Table 6.4
  9. Chapter 7 Regression II
    1. 7.1 Introduction
    2. 7.2 High Breakdown Rank-Based Fits
      1. Stars Data
        1. 7.2.1 Weights for the HBR Fit
    3. 7.3 Robust Diagnostics
      1. 7.3.1 Graphics
      2. 7.3.2 Procedures for Differentiating between Robust Fits
      3. 7.3.3 Concluding Remarks
    4. 7.4 Weighted Regression
    5. 7.5 Linear Models with Skew Normal Errors
      1. 7.5.1 Sensitivity Analysis
      2. 7.5.2 Simulation Study
    6. 7.6 A Hogg-Type Adaptive Procedure
    7. 7.7 Nonlinear
      1. 7.7.1 Implementation of the Wilcoxon Nonlinear Fit
      2. 7.7.2 R Computation of Rank-Based Nonlinear Fits
      3. 7.7.3 Examples
        1. The 4 Parameter Logistic Model
      4. 7.7.4 High Breakdown Rank-Based Fits
    8. 7.8 Time Series
      1. 7.8.1 Order of the Autoregressive Series
    9. 7.9 Exercises
      1. Figure 7.1
      2. Figure 7.2
      3. Figure 7.3
      4. Figure 7.4
      5. Figure 7.5
      6. Figure 7.6
      7. Figure 7.7
      8. Figure 7.8
      9. Figure 7.9
      10. Figure 7.10
      11. Figure 7.11
      12. Figure 7.12
      13. Figure 7.13
      14. Figure 7.14
      15. Figure 7.15
      16. Figure 7.16
      17. Figure 7.17
      1. Table 7.1
      2. Table 7.2
      3. Table 7.3
      4. Table 7.4
  10. Chapter 8 Cluster Correlated Data
    1. 8.1 Introduction
    2. 8.2 Friedman’s Test
    3. 8.3 Joint Rankings Estimator
      1. 8.3.1 Estimates of Standard Error
        1. Compound Symmetric
        2. Empirical
        3. Sandwich Estimator
      2. 8.3.2 Inference
      3. 8.3.3 Examples
        1. Simulated Dataset
        2. Crabgrass Data
        3. Electric Resistance Data
    4. 8.4 Robust Variance Component Estimators
    5. 8.5 Multiple Rankings Estimator
      1. Estimation of Scale
      2. Inference
    6. 8.6 GEE-Type Estimator
      1. 8.6.1 Weights
      2. 8.6.2 Link Function
      3. 8.6.3 Working Covariance Matrix
      4. 8.6.4 Standard Errors
      5. 8.6.5 Examples
    7. 8.7 Exercises
      1. Figure 8.1
      2. Figure 8.2
      3. Figure 8.3
      1. Table 8.1
  11. Bibliography