Permutation Statistical Methods with R

Preface
Acknowledgments
Contents
1 Introduction
	1.1 Overviews of Chaps. 2–11
	1.2 Chapter 2
	1.3 Chapter 3
	1.4 Chapter 4
	1.5 Chapter 5
	1.6 Chapter 6
	1.7 Chapter 7
	1.8 Chapter 8
	1.9 Chapter 9
	1.10 Chapter 10
	1.11 Chapter 11
	1.12 Summary
	1.13 Preview of Chap. 2
	References
2 The R Programming Language
	2.1 R and RStudio, What are They About?
		2.1.1 What is R?
		2.1.2 Using R: Interactive Versus ``Batch'' Mode
		2.1.3 Installing R
		2.1.4 RStudio
		2.1.5 R Help
		2.1.6 R Manuals and Books
	2.2 Beginning R and RStudio
		2.2.1 Preliminaries
		2.2.2 R as a Simple Calculator
		2.2.3 Arrow Keys for Using Previous Commands
		2.2.4 Variables
		2.2.5 The Assignment Operator
		2.2.6 Using Variables in Expressions
		2.2.7 Removing Variables—Using R Functions
		2.2.8 Mathematical Functions
		2.2.9 Nesting of Commands
		2.2.10 Numerical Representations
	2.3 Vectors
		2.3.1 Creating Vector Variables
		2.3.2 Using Subscripts: Vector Indexing
		2.3.3 Adding and Removing Vector Elements
		2.3.4 Doing Mathematics with Vectors
		2.3.5 Missing Values
		2.3.6 Random Numbers
		2.3.7 Basic Statistical Functions
	2.4 Basic R Data Types
		2.4.1 Coercion
		2.4.2 Numeric Data
		2.4.3 Logical Data
		2.4.4 Integer Data
		2.4.5 Character Data
		2.4.6 Learning More About Variables
	2.5 Matrices
		2.5.1 Creating Matrices
		2.5.2 Characteristics of a Matrix
		2.5.3 Applying Functions to Query Matrices
		2.5.4 Manipulating Matrices
		2.5.5 Naming Rows and Columns
		2.5.6 Adding New Rows or Columns to Matrices
	2.6 Arrays: More Than Two Dimensions
	2.7 Factors
		2.7.1 Factor Functions
		2.7.2 Useful Data Manipulations with Factors
	2.8 Lists
		2.8.1 Referencing List Elements
		2.8.2 Manipulating Lists
		2.8.3 Search Path Attachment
	2.9 Data Frames
		2.9.1 Viewing and Selecting Data Frame Elements
		2.9.2 Computing Statistics
		2.9.3 Sorting Data Frames
		2.9.4 R's Sorting Functions
		2.9.5 Adding Rows or Columns to Data Frames
		2.9.6 Creating a New Data Frame
		2.9.7 Editing Values in a Data Frame
	2.10 Saving Work
		2.10.1 Setting and Getting Folder Pathways
		2.10.2 Session History Files
		2.10.3 R Scripts
		2.10.4 Workspace Files
		2.10.5 Writing External Text Files
	2.11 Reading External Text Files
		2.11.1 Reading Files Holding a Single Variable
		2.11.2 Reading Tables of Data with Many Variables
	2.12 Downloading and Installing Packages
	2.13 Programming Structures in R
		2.13.1 The Comment
		2.13.2 Writing Your Own Functions
		2.13.3 Conditional Statements
		2.13.4 Loops
		2.13.5 Writing Interactive Code
	2.14 Summary
	2.15 Preview of Chap. 3
	References
3 Permutation Statistical Methods
	3.1 Introduction
	3.2 A Brief History of Permutation Methods
		3.2.1 The 1920s
		3.2.2 The 1930s
		3.2.3 The 1940s
		3.2.4 The 1950s
		3.2.5 The 1960s
		3.2.6 The 1970s
		3.2.7 The 1980s
		3.2.8 The 1990s
		3.2.9 The 2000s
		3.2.10 The 2010s
	3.3 The Neyman–Pearson Population Model
	3.4 The Fisher–Pitman Permutation Model
		3.4.1 Exact Permutation Tests
		3.4.2 Monte Carlo Permutation Tests
	3.5 Permutation and Parametric Statistical Tests
		3.5.1 The Assumption of Random Sampling
		3.5.2 The Assumption of Normality
	3.6 Advantages of Permutation Methods
	3.7 Calculation Efficiency
		3.7.1 High-Speed Computing
		3.7.2 Analysis with Combinations
		3.7.3 Mathematical Recursion
		3.7.4 Variable Components of a Test Statistic
		3.7.5 Holding an Array Constant
	3.8 Summary
	3.9 Preview of Chap. 4
	References
4 Central Tendency and Variability
	4.1 Introduction
	4.2 Data Storage Modes and Structures
	4.3 Statistical Graphics
	4.4 The Sample Mode
		4.4.1 R Script for the Sample Mode
	4.5 The Sample Mean
		4.5.1 R Script for the Sample Mean
	4.6 The Sample Median
		4.6.1 R Script for the Sample Median
	4.7 The Sample Standard Deviation and Variance
		4.7.1 R Script for the Sample Standard Deviation
	4.8 The Mean Absolute Deviation
		4.8.1 R Script for the Mean Absolute Deviation
	4.9 An Alternative Approach to Dispersion Measures
		4.9.1 Pairwise Differences: Standard Deviation
		4.9.2 R Script for the Sample Standard Deviation
	4.10 Summary
	4.11 Preview of Chap. 5
	Reference
5 One-Sample Tests
	5.1 Introduction
	5.2 Student's One-Sample t Test
	5.3 A Permutation Approach
	5.4 The Relationship Between Test Statistics t and δ
	5.5 Test Statistics t and δ
		5.5.1 R Script for Student's t Test
		5.5.2 R Script for Test Statistic δ
		5.5.3 R Script for an Exact Student's t Test
		5.5.4 The Choice Between Test Statistics t and δ
	5.6 The Measurement of Effect Size
		5.6.1 R Script for the Expected Value of δ
	5.7 Detailed Calculations for Statistics δ and µδ
		5.7.1 Comparisons of Effect Size Measures
		5.7.2 R Script for the  Measure of Effect Size
	5.8 Measures of Effect Size
		5.8.1 R Script for Measures of Effect Size
	5.9 Analyses with v = 2 and v = 1
		5.9.1 An Exact Analysis with v = 2
		5.9.2 R Script for Test Statistic δ
		5.9.3 The Assumption of Normality
		5.9.4 An Exact Analysis with v = 1
	5.10 Exact and Monte Carlo Analyses
		5.10.1 A Monte Carlo Analysis with v = 2
		5.10.2 R Script for a Monte Carlo Analysis
		5.10.3 An Exact Analysis with v = 2
		5.10.4 A Monte Carlo Analysis with v = 1
		5.10.5 An Exact Analysis with v = 1
	5.11 Rank-Score Permutation Analyses
		5.11.1 The Wilcoxon Signed-Ranks Test
		5.11.2 A Permutation Approach
		5.11.3 An Example Analysis
		5.11.4 R Script for Wilcoxon's Signed-Ranks Test
		5.11.5 An Exact Analysis with v = 2
		5.11.6 The Relationship Between Statistics T and δ
		5.11.7 R Script for a Monte Carlo Probability Value
		5.11.8 An Exact Analysis with v = 1
	5.12 Summary
	5.13 Preview of Chap. 6
	References
6 Two-Sample Tests
	6.1 Introduction
	6.2 Two-Sample Tests
		6.2.1 Student's Two-Sample t Test
	6.3 A Permutation Approach
		6.3.1 The Relationship Between Statistics t and δ
	6.4 Test Statistics t and δ
		6.4.1 R Script for a Test of Homogeneity
		6.4.2 R Script for Student's t Test
		6.4.3 A Permutation Approach
		6.4.4 R Script for Test Statistic δ
	6.5 Measures of Effect Size
		6.5.1 Comparisons of Effect Size Measures
		6.5.2 R Script for Measures of Effect Size
	6.6 Analyses with v = 2 and v = 1
		6.6.1 An Exact Analysis with v = 2
		6.6.2 Measures of Effect Size
		6.6.3 An Exact Analysis with v = 1
	6.7 Exact and Monte Carlo Analyses
		6.7.1 A Monte Carlo Analysis with v = 2
		6.7.2 R Script for a Monte Carlo Analysis
		6.7.3 Measures of Effect Size
		6.7.4 A Monte Carlo Analysis with v = 1
	6.8 Rank-Score Permutation Analyses
		6.8.1 The Wilcoxon–Mann–Whitney Test
		6.8.2 R Script for the Wilcoxon Rank-Sum Test
		6.8.3 An Exact Analysis with v = 2
		6.8.4 R Script for an Exact Wilcoxon Test
		6.8.5 An Exact Analysis with v = 1
	6.9 Summary
	6.10 Preview of Chap. 7
	References
7 Matched-Pairs Tests
	7.1 Introduction
	7.2 Matched-Pairs Tests
		7.2.1 Student's Matched-Pairs t Test
	7.3 A Permutation Approach
		7.3.1 The Relationship Between Statistics t and δ
	7.4 Test Statistics t and δ
		7.4.1 R Script for Student's Matched-Pairs t Test
		7.4.2 An Exact Analysis
		7.4.3 R Script for an Exact Matched-Pairs Test
	7.5  Measures of Effect Size
		7.5.1 Comparisons of Effect Size Measures
		7.5.2 R Script for Measures of Effect Size
	7.6 Analyses with v = 2 and v = 1
		7.6.1 An Exact Analysis with v = 2
		7.6.2 R Script for an Exact Student's t Test
		7.6.3 An Exact Analysis with v = 1
		7.6.4 A Comparison of v = 2 and v = 1
	7.7 Exact and Monte Carlo Analyses
		7.7.1 A Monte Carlo Analysis with v = 2
		7.7.2 R Script for a Monte Carlo Analysis
		7.7.3 An Exact Analysis with v = 2
		7.7.4 A Monte Carlo Analysis with v = 1
		7.7.5 An Exact Analysis with v = 1
	7.8 Rank-Score Permutation Analyses
		7.8.1 The Wilcoxon Signed-Ranks Test
		7.8.2 R Script for Wilcoxon's Signed-Ranks Test
		7.8.3 An Exact Analysis with v = 2
		7.8.4 R Script for an Exact Signed-Ranks Test
		7.8.5 The Relationship Between Statistics T and δ
		7.8.6 An Exact Analysis with v = 1
	7.9 Summary
	7.10 Preview of Chap. 8
	References
8 Completely-Randomized Designs
	8.1 Introduction
	8.2 Fisher's F-Ratio Test
	8.3 A Permutation Approach
	8.4 The Relationship Between Statistics F and δ
	8.5 Test Statistics F and δ
		8.5.1 The Bartlett Test for Homogeneity
		8.5.2 R Script for Bartlett's Test of Homogeneity
		8.5.3 The Analysis of Variance
		8.5.4 R Script for an Analysis of Variance
		8.5.5 An Alternative to R Function aov()
		8.5.6 A Permutation Approach
		8.5.7 R Script for Test Statistic δ
	8.6 Measures of Effect Size
		8.6.1 Comparisons of Effect Size Measures
		8.6.2 R Script for Measures of Effect Size
	8.7 Analyses with v = 2 and v = 1
		8.7.1 The Analysis of Variance
		8.7.2 A Monte Carlo Analysis with v = 2
		8.7.3 Measures of Effect Size
		8.7.4 A Monte Carlo Analysis with v = 1
	8.8 Exact and Monte Carlo Analyses
		8.8.1 The Analysis of Variance
		8.8.2 A Monte Carlo Analysis with v = 2
		8.8.3 Measures of Effect Size
		8.8.4 A Monte Carlo Analysis with v = 1
	8.9 Rank-score Permutation Analyses
		8.9.1 The Kruskal–Wallis Rank-sum Test
		8.9.2 R Script for the Kruskal–Wallis Rank-sum Test
		8.9.3 A Monte Carlo Analysis with v = 2
		8.9.4 R Script for a K–W Probability Value
	8.10 Summary
	8.11 Preview of Chap. 9
	References
9 Randomized-Blocks Designs
	9.1 Introduction
	9.2 Randomized-Blocks Analysis of Variance
		9.2.1 Fisher's F-Ratio Test Statistic
	9.3 A Permutation Approach
	9.4 The Relationship Between Statistics F and δ
	9.5 Test Statistics F and δ
		9.5.1 R Script for a Randomized-Blocks Analysis
		9.5.2 An Exact Analysis with v = 2
		9.5.3 R Script for a Permutation Analysis
	9.6 Measures of Effect Size
		9.6.1 An Example Analysis
		9.6.2 R Script for Three Measures of Effect Size
	9.7 Analyses with v = 2 and v = 1
		9.7.1 A Monte Carlo Analysis with v = 2
		9.7.2 R Script for a Monte Carlo Analysis
		9.7.3 Measures of Effect Size
		9.7.4 A Monte Carlo Analysis with v = 1
	9.8 A Larger Monte Carlo Analysis
		9.8.1 A Monte Carlo Analysis with v = 2
		9.8.2 Measures of Effect Size
	9.9 Rank-Score Permutation Analyses
		9.9.1 Friedman's Analysis of Variance for Ranks
		9.9.2 R Script for Friedman's Rank-Sum Test
		9.9.3 A Monte Carlo Analysis with v = 2
		9.9.4 R Script for Friedman's Rank-Sum Test
		9.9.5 A Monte Carlo Analysis with v = 1
	9.10 Summary
	9.11 Preview of Chap. 10
	References
10 Correlation and Association
	10.1 Introduction
	10.2 Linear Correlation
		10.2.1 A Permutation Approach
	10.3 The Relationship Between Statistics rxy and δ
	10.4 An Example Analysis
		10.4.1 R Script for Pearson's Correlation Coefficient
		10.4.2 An Exact Permutation Analysis
		10.4.3 R Script for an Exact Analysis
		10.4.4 R Script for a Monte Carlo Analysis
	10.5 A Measure of Effect Size
		10.5.1 A Monte Carlo Permutation Analysis
	10.6 Spearman's Rank-Order Correlation Coefficient
		10.6.1 The Relationship Between Statistics rs and δ
		10.6.2 R Script for Spearman's Rank Correlation
		10.6.3 A Monte Carlo Permutation Analysis
		10.6.4 R Script for a Monte Carlo Analysis
		10.6.5 R Script for an Exact Analysis
	10.7 Kendall's τa Measure of Association
		10.7.1 An Example
		10.7.2 The Relationship Between Kendall's S and δ
		10.7.3 R Script for Kendall's τa Coefficient
		10.7.4 A Monte Carlo Permutation Analysis
		10.7.5 R Script for a Monte Carlo Analysis
		10.7.6 An Exact Permutation Analysis
		10.7.7 R Script for an Exact Analysis
	10.8 Kendall's τb Measure of Association
		10.8.1 Example Analysis
		10.8.2 R Script for Kendall's τb Coefficient
		10.8.3 R Script for a Monte Carlo Analysis
		10.8.4 An Exact Permutation Analysis
		10.8.5 R Script for an Exact Analysis
	10.9 The Analysis of Contingency Tables
		10.9.1 R Script for Analyzing a Contingency Table
	10.10 Spearman's Footrule Agreement Measure
		10.10.1 The Relationship Between mathcalR and
		10.10.2 A Monte Carlo Analysis
		10.10.3 R Script for an Exact Analysis
	10.11 The Relationship Between mathcalR and S
	10.12 Summary
	10.13 Preview of Chap. 11
	References
11 Chi-Squared and Related Measures
	11.1 Introduction
	11.2 Chi-Squared Goodness-of-Fit Tests
		11.2.1 Example
		11.2.2 R Script for Pearson's Goodness-of-Fit Test
		11.2.3 A Monte Carlo Permutation Analysis
		11.2.4 R Script for a Monte Carlo Probability Value
	11.3 Measures of Effect Size
		11.3.1 Pearson's χ2 Measure of Effect Size
		11.3.2 R Code for a χ2 Measure of Effect Size
		11.3.3 Wilks' G2 Measure of Effect Size
		11.3.4 R Code for a G2 Measure of Effect Size
		11.3.5 A Chance-Corrected Measure of Effect Size
		11.3.6 R Code for a Chance-Corrected Measure
	11.4 Chi-Squared Test of Independence
		11.4.1 Example
		11.4.2 R Script for Pearson's Test of Independence
		11.4.3 A Measure of Effect Size
		11.4.4 R Script for Cramér's Measure of Effect Size
	11.5 A Chance-Corrected Measure of Effect Size
		11.5.1 Illustration of a Chance-Corrected Measure
		11.5.2 A Maximum Chi-Squared Procedure
		11.5.3 R Script for a Measure of Effect Size
		11.5.4 A Monte Carlo Probability Value
		11.5.5 R Script for a Monte Carlo Probability Value
	11.6 Fisher's Exact Probability Test
		11.6.1 Example Analysis
		11.6.2 R Script for Fisher's Exact Probability Test
		11.6.3 A Recursion Example
		11.6.4 Recursion with an Arbitrary Origin
		11.6.5 R Script for Fisher's Exact Probability Test
	11.7 Summary
	References
Author Index
Subject Index