Berry K.J., Johnston J.E., Mielke P.W.Jr. The Measurement of Association. A Permutation Statistical Approach

New York: Springer, 2018. — 661 p.This research monograph utilizes exact and Monte Carlo permutation statistical methods to generate probability values and measures of effect size for a variety of measures of association. Association is broadly defined to include measures of correlation for two interval-level variables, measures of association for two nominal-level variables or two ordinal-level variables, and measures of agreement for two nominal-level or two ordinal-level variables. Additionally, measures of association for mixtures of the three levels of measurement are considered: nominal-ordinal, nominal-interval, and ordinal-interval measures. Numerous comparisons of permutation and classical statistical methods are presented.
Unlike classical statistical methods, permutation statistical methods do not rely on theoretical distributions, avoid the usual assumptions of normality and homogeneity of variance, and depend only on the data at hand. This book takes a unique approach to explaining statistics by integrating a large variety of statistical methods, and establishing the rigor of a topic that to many may seem to be a nascent field. This topic is relatively new in that it took modern computing power to make permutation methods available to those working in mainstream research.
Written for a statistically informed audience, it is particularly useful for teachers of statistics, practicing statisticians, applied statisticians, and quantitative graduate students in fields such as psychology, medical research, epidemiology, public health, and biology. It can also serve as a textbook in graduate courses in subjects like statistics, psychology, and biology.Definition of Measurement
Definition of Association
Symmetry and Asymmetry
Cross-Classification
Correlation, Association, and Agreement
Criteria for Measures of Association
Degree of Association
The Choice of a Measure of Association
Overview of Chaps Through
CodaPermutation Statistical Methods
Permutation Statistical Tests
Exact Permutation Tests
An Exact Permutation Analysis
A Second Exact Permutation Analysis
Monte Carlo Permutation Statistical Tests
A Monte Carlo Resampling Analysis
A Second Monte Carlo Resampling Analysis
Moment-Approximation Permutation Tests
A Moment-Approximation Analysis
Comparisons of the Three Permutation Approaches
A Second Moment-Approximation Analysis
Tests of Independence
Tests of Goodness of Fit
Permutation and Parametric Statistical Tests
Permutation Tests and Random Sampling
Permutation Tests and Normality
Permutation Tests and Small Sample Sizes
Permutation Tests and Data Dependency
Advantages of Permutation Methods
Calculation Efficiency
High-Speed Computing
Analysis with Combinations
Permutation Analysis
Mathematical Recursion
A Recursion
Recursion with an Arbitrary Initial Value
Variable Components of a Test StatisticNominal-Level Variables, I
Pearson's ϕ Measure of Association
Pearson's ϕ and rxy
Tschuprov's T Measure of Association
Cramér's V Measure of Association
Pearson's C Measure of Association
Maximum Arrangement of Cell Frequencies
Application to r x c x s Contingency Tables
Measures of Effect Size
Likelihood-Ratio Tests
Method
Illustration of the Resampling Procedure
Illustration of the Chi-squared Calculations
Illustration of the Likelihood-Ratio Calculations
Chi-squared Goodness-of-Fit Tests
Chi-squared Goodness-of-Fit
Likelihood-Ratio Goodness-of-Fit
Other Goodness-of-Fit Tests
Partition Theory
Algorithm
Computational Efficiency
Chi-squared and Correlation for r c Tables
Orthonormal Row Weights
Orthonormal Column Weights
Correlation and Chi-squared
Analysis with Shadow TablesCodaNominal-Level Variables, II
Hypergeometric Probability Values
Goodman and Kruskal's λa and λb Measures
λa and λb Analyses
Goodman and Kruskal's ta and tb Measures
Analysis for ta
Analysis for tb
An Asymmetric Test of Homogeneity
The Measurement of Agreement
Robinson's Measure of Agreement
The Intraclass Correlation Coefficient
Scott's π Measure of Agreement
Cohen's κ Measure of Agreement
Application with Multiple Judges
McNemar's Q Test for Change
Cochran's Q Test for Change
A Measure of Effect Size for Cochran's Q Test
A Chance-Corrected Measure of Effect Size
Advantages of the Measure of Effect Size
Leik and Gove's dNc Measure of Association
Observed Contingency Table
Expected Contingency Table
Maximized Contingency Table
Calculation of Leik and Gove's dNc
A Matrix Occupancy Problem
Analysis
Fisher's Exact Probability Test
Fisher's Exact Analysis of a Table
A Contingency Table
Larger Contingency Tables
Contingency Table
Analyses of Tables
Contingency TableOrdinal-Level Variables, I
Pairwise Measures of Ordinal Association
Permutation Statistical Methods
Kendall's τa Measure of Ordinal Association
Kendall's τb and Wilcoxon's W Measures
Stuart's τc Measure of Ordinal Association
Measures of Effect Size
Sharper Bounds
Goodman and Kruskal's γ Measure
Monotonicity
Somers' dyx and dxy Measures of Association
Comparisons of Pairwise Measures
Marginal Frequency Distributions
Whitfield's S Measure
Cureton's Rank-Biserial Correlation Coefficient
Relationships Among MeasuresSpearman's Rank-Order Correlation Coefficient
Spearman's Footrule Agreement Measure
Probability of Spearman's Footrule
Illustration with b = Independent Judges
Illustration with b = Independent Judges
Analysis
The Coefficient of Concordance
A Related Procedure
Analysis
Kendall's u Measure of Agreement
Exact Probability Values
Cohen's Weighted Kappa
Linear Weighting
Quadratic Weighting
Linear and Quadratic Weighting Compared
Weighted Kappa with Multiple Judges
Algorithm for r c s Contingency Tables
Quadratic Weighting
Advantages of Linear Weighting
Embedded Tables
Exact Variance Method
Resampling Contingency Table Method
Randomized-Block Method
with Three Judges
Resampling Contingency Table Method
Resampling-Block Method
Ridit Analysis
Calculations
Exact Permutation Procedures
Ridit AnalysisOrdinary Least Squares (OLS) Linear Regression
Univariate of OLS Regression
Multivariate of OLS Regression
Least Absolute Deviation (LAD) Regression
Illustration of Effects of Extreme Values
Distance
Leverage
Influence
Univariate of LAD Regression
Multivariate of LAD Regression
LAD Multivariate Multiple Regression
Analysis of Factor A
Analysis of Factor B
Comparison of OLS and LAD Linear Regression
Ordinary Least Squares (OLS) Analysis
Least Absolute Deviation (LAD) Analysis
Least Absolute Deviation (LAD) Analysis
Fisher's rxy to z Transformation
Normal Distribution
Symmetric Kappa Distribution
Confidence Intervals
Hypothesis Testing
Discussion
Problems with the Point-Biserial Coefficient
Biserial Linear Correlation
Intraclass Correlation
Interclass and Intraclass Linear Correlation
CodaMixed-Level Variables
Freeman's Index of Nominal-Ordinal Association
Agresti's Index of Nominal-Ordinal Association
Piccarreta's Index of Nominal-Ordinal Association
Comparisons Between and
Analysis
The Delta Method
Dichotomous Nominal-Level Variables
Whitfield's τ Measure of Association
Product-Moment Correlation Coefficient
The Correlation Ratio
Hays'
Mielke and Berry's
Biased Estimators
Dichotomous Nominal-Level Variables
Biserial Correlation
Improper Norming
Measures of Ordinal-Interval Association
Jaspen's Index of Ordinal-Interval Association
Interval-Level Dependent Variables
Univariate
Multivariate
Ordinal-Level Dependent Variables
Univariate
Multivariate
Nominal-Level Dependent Variables
Univariate
Mixed Dependent Variables
Multivariate
and Existing Statistics
Interval-Level Dependent Variable
Nominal-Level Dependent VariableFourfold Contingency Tables, I
Logical Models of Association
Fourfold Contingency Tables
Pearson's Mean-Square Measure of Association
Pearson's Tetrachoric Measure of Correlation
A Permutation Test for Tetrachoric Correlation
Exact and Asymptotic Probability Values
Yule's Q Measure of Association
Yule's Y Measure of Association
The Odds Ratio
Goodman–Kruskal's ta and tb Measures
with Goodman and Kruskal's ta
Goodman–Kruskal's ta, tb, and χ
Somers' dyx and dxy Measures
with Somers' dyx
with Somers' dxy
Percentage Differences
Kendall's τb Measure of Ordinal Association
Kendall's τb and Pearson's rxy Measures
An Alternative Proof
Pearson's Correlation Coefficient
Unstandardized Regression Coefficients
Pearson's ϕ and Cohen's κ MeasuresSymmetrical Fourfold Tables
Statistics ϕ, T, and V
Pearson's rxy Correlation Coefficient
Regression Coefficients
Leik and Gove's dNc Statistic
Goodman and Kruskal's ta and tb Statistics
Kendall's τb Statistic
Stuart's τc Statistic
Percentage Differences
Cohen's κ Statistic
Inter-relationships Among the Measures
Extended Fourfold Contingency Tables
The Mantel–Haenszel Test
Analysis
Measures of Effect Size
Maximum-Corrected Measure of Effect Size
Cohen's Kappa Measure
Unweighted Kappa
Weighted Kappa
Unweighted Kappa
Weighted Kappa
McNemar's Q Test for Change
Illustration
Cochran's Q Test for Change
Analysis of Contingency Tables
Contingency Table
Analysis of Contingency Tables
CodaEpilogue
Author Index
Subject Index