Correlation : parametric and nonparametric measures / Peter Y. Chen, Paula M. Popovich.

Format:

Book

Author/Creator:

Chen, Peter Y.

Contributor:

Popovich, Paula M.

Series:

Quantitative applications in the social sciences ; no. 07-139.

Quantitative applications in the social sciences ; 139

Language:

English

Subjects (All):

Correlation (Statistics).

Physical Description:

vi, 95 pages : illustrations ; 22 cm.

Place of Publication:

Thousands Oaks, Calif. : Sage Publications, [2002]

Summary:

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, you will be able to compare and distinguish the concepts of similarity and relationship, identify the distinction between correlation and causation, and interpret correlations correctly.

Contents:

Characteristics of a Relationship 2

Correlation and Causation 3

Correlation and Correlational Methods 6

Choice of Correlation Indexes 7

2. The Pearson Product-Moment Correlation 9

Interpretation of Pearson's r 12

Assumptions of Pearson's r in Inferential Statistics 13

Sampling Distributions of Pearson's r 14

Properties of the Sampling Distribution of Pearson's r 15

Null Hypothesis Tests of [rho] = 0 16

Null Hypothesis Tests of [rho] = [rho subscript phi] 19

Confidence Intervals of [rho] 20

Null Hypothesis Test of [rho subscript 1] = [rho subscript 2] 20

Null Hypothesis Test for the Difference Among More Than Two Independent [rho]s 22

Null Hypothesis Test for the Difference Between Two Dependent Correlations 23

3. Special Cases of Pearson's r 25

Point-Biserial Correlation, r[subscript pb] 26

Phi Coefficient, [phi] 29

Spearman Rank-Order Correlation, r[subscript rank] 31

True Versus Artificially Converted Scores 33

Biserial Coefficient, r[subscript bis] 35

Tetrachoric Coefficient, r[subscript tet] 37

Eta Coefficient, [eta] 38

Other Special Cases of Pearson's r 40

4. Applications of Pearson's r 41

Application I Effect Size 42

Application II Power Analysis 43

Application III Meta-Analysis 46

Application IV Utility Analysis 49

Application V Reliability Estimates 50

Application VI Validation 52

5. Factors Affecting the Size and Interpretation of Pearson's r 55

Shapes of Distributions 55

Sample Size 56

Outliers 56

Restriction of Range 57

Nonlinearity 61

Aggregate Samples 63

Ecological Inference 67

Measurement Error 68

Third Variables 69

6. Other Useful Nonparametric Correlations 78

C and Cramer's V Coefficients 79

Kendall's [tau] Coefficient 82

Kendall's [tau subscript b] and Stuart's [tau subscript c] Coefficients 84

Goodman and Kruskal's [gamma] Coefficient 86

Kendall's Partial Rank-Order Correlation, [tau subscript XY.Z] 87.

Notes:

Includes bibliographical references (pages 93-94).

ISBN:

0761922288

OCLC:

49576427