Correlation : Parametric and Nonparametric Measures

by
Format: Paperback
Pub. Date: 2002-06-12
Publisher(s): Sage Publications, Inc
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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

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