Correlation - Chen, Peter Y

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Résumé :
Correlations, in general, and the Pearson product-moment correlation in particular, can be used for many research purposes, ranging from describing a relationship between two variables as a descriptive statistic to examining a relationship between two variables in a population as an inferential statistic, or to gauge the strength of an effect, or to conduct a meta-analytic study. How can correlation be more effectively used so that one doesn't misinterpret the data? This book reveals how to do this by examining Pearson r from its conceptual meaning, to assumptions, special cases of the Pearson r, the biserial coefficient and tetrachoric coefficient estimates of the Pearson r, its uses in research (including effect size, power analysis, meta-analysis, utility analysis, reliability estimates and validation), factors that affect the Pearson r, and finally to additional nonparametric correlation indexes. After reading this book, the reader will be able to compare and distinguish the concepts of similarity and relationship, identify the distinction between correlation and causation, and to interpret correlations correctly. ...

Biographie:
The goals of my research programs are to improve the quality of individual well-being, and to build a healthy workplace and society that enhance the safety and health of workers and their families. A healthy workplace or a healthy society is one in which all constituents are able to exercise their talents and gifts to achieve high performance as well as maintain psychological and physical well-being. In order to understand how to effectively build a healthy society and a healthy organization, I have taken an interdisciplinary approach over years to explore the ways of maximizing organizational as well as societal productivity, and optimizing individual potentials to pursue healthier, more secure, and safer lives. My past field and military experience have convinced me that there will be much more efficient options available if one is open to different approaches and ideas, and utilize their strengths to solve problems.

Sommaire:
Ch 1. Introduction
Characteristics of a Relationship
Correlation and Causation
Correlation and Causation
Correlation and Correlational Methods
Choice of Correlation Indexes
Ch 2. The Pearson Product-Moment Correlation
Interpretation of Pearson r
Assumptions of Pearson r in Inferential Statistics
Sampling Distributions of the Pearson r
Properties of the Sampling Distribution of the Pearson
Null Hypothesis Tests of r = 0
Null Hypothesis Tests of r = r?
Confidence Intervals of r
Null Hypothesis Test of r1 = r2
Null Hypothesis Test for the Difference Among More Than Two Independent r?s
Null Hypothesis Test for the Difference Between Two Dependent Correlations
Chapter 3: Special Cases of The Pearson r
Point-Biserial Correlation, rpb
Phi Coefficient, f
Spearman Rank-Order Correlation, rrank
True vs. Artificially Converted Scores
Biserial Coefficient,
Tetrachoric Coefficient,
Eta Coefficient,
Other Special Cases of the Pearson r
Chapter 4: Applications of the Pearson r
Application I: Effect Size
Application II: Power Analysis
Application III: Meta-Analysis
Application IV: Utility Analysis
Application V: Reliability Estimates
Application VI: Validation
Chapter 5: Factors Affecting the Size and Interpretation of the Pearson r
Shapes of Distributions
Sample Size
Outliers
Restriction of Range
Nonlinearity
Aggregate Samples
Ecological Inference
Measurement Error
Third Variables
Chapter 6: Other Useful Nonparametric Correlations
C and Cram?r?s V Coefficients
Kendall?s t Coefficient
Kendall?s tb and Stuart?s tc Coefficients
Goodman-Kruskal?s g Coefficient
Kendall?s Partial Rank-Order Correlation,
References
Lists of Tables
Lists of Figures
List of Appendixes
About the Authors