Correlation : Parametric and Nonparametric Measures

by Peter Y Chen

• ISBN13: 9780761922285
• ISBN10: 0761922288
• Format: Paperback
• Copyright: 2002-06-12
• Publisher: Sage Publications, Inc

Summary

How can correlation be more effectively used so that one does not 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.

Table of Contents

Series Editor's Introduction	v
Introduction	1	(8)
Characteristics of a Relationship	2	(1)
Correlation and Causation	3	(3)
Correlation and Correlational Methods	6	(1)
Choice of Correlation Indexes	7	(2)
The Pearson Product-Moment Correlation	9	(16)
Interpretation of Pearson's r	12	(1)
Assumptions of Pearson's r in Inferential Statistics	13	(1)
Sampling Distributions of Pearson's r	14	(1)
Properties of the Sampling Distribution of Pearson's r	15	(1)
Null Hypothesis Tests of ρ = 0	16	(3)
Null Hypothesis Tests of ρ = ρφ	19	(1)
Confidence Intervals of ρ	20	(1)
Null Hypothesis Test of ρ1 = ρ2	20	(2)
Null Hypothesis Test for the Difference Among More Than Two Independent ρs	22	(1)
Null Hypothesis Test for the Difference Between Two Dependent Correlations	23	(2)
Special Cases of Pearson's r	25	(16)
Point-Biserial Correlation, rpb	26	(3)
Phi Coefficient, φ	29	(2)
Spearman Rank-Order Correlation, rrank	31	(2)
True Versus Artificially Converted Scores	33	(2)
Biserial Coefficient, rbis	35	(2)
Tetrachoric Coefficient, rtet	37	(1)
Eta Coefficient, ηn	38	(2)
Other Special Cases of Pearson's r	40	(1)
Applications of Pearson's r	41	(14)
Application I: Effect Size	42	(1)
Application II: Power Analysis	43	(3)
Application III: Meta-Analysis	46	(3)
Application IV: Utility Analysis	49	(1)
Application V: Reliability Estimates	50	(2)
Application VI: Validation	52	(3)
Factors Affecting the Size and Interpretation of Pearson's r	55	(23)
Shapes of Distributions	55	(1)
Sample Size	56	(1)
Outliers	56	(1)
Restriction of Range	57	(4)
Nonlinearity	61	(2)
Aggregate Samples	63	(4)
Ecological Inference	67	(1)
Measurement Error	68	(1)
Third Variables	69	(9)
Other Useful Nonparametric Correlations	78	(10)
C and Cramer's V Coefficients	79	(3)
Kendall's τ Coefficient	82	(2)
Kendall's τb and Stuart's τc Coefficients	84	(2)
Goodman and Kruskal's γ Coefficient	86	(1)
Kendall's Partial Rank-Order Correlation, τXY.Z	87	(1)
Appendix I	88	(1)
Appendix 2	89	(1)
Appendix 3	90	(1)
Appendix 4	91	(2)
References	93	(2)
About the Authors	95