Contrasts and Effect Sizes in Behavioral Research: A Correlational Approach

by Robert Rosenthal , Ralph L. Rosnow , Donald B. Rubin

• ISBN13: 9780521659802
• ISBN10: 0521659809
• Format: Paperback
• Copyright: 1999-12-28
• Publisher: Cambridge University Press

Summary

Contrasts are statistical procedures for asking focused questions of data. Compared to diffuse or omnibus questions, focused questions are characterized by greater conceptual clarity and greater statistical power when examining those focused questions. If an effect truly exists, we are more likely to discover it and to believe it to be real when asking focused questions rather than omnibus ones. Researchers, teachers of research methods and graduate students will be familiar with the principles and procedures of contrast analysis, but will also be introduced to a series of newly developed concepts, measures, and indices that permit a wider and more useful application of contrast analysis. This volume takes on this new approach by introducing a family of correlational effect size estimates.

Table of Contents

Preface	ix
Basic Concepts of Focused Procedures	1	(7)
Focused versus Omnibus Questions	1	(1)
An Example	1	(3)
Effect Sizes and Significance Levels	4	(2)
Review Questions	6	(2)
Basic Procedures for Two Groups	8	(29)
Comparing Two Groups	8	(1)
Correlation Effect Size (r)	9	(2)
Other Effect Sizes: Cohen's d and Hedges's g	11	(1)
Transforming Between Effect Size Measures	12	(1)
Counternull Value of an Effect Size	13	(1)
Counternull Value of a Point-Biserial r	14	(1)
Problems When Interpreting Effect Sizes	15	(2)
Binomial Effect Size Display	17	(1)
Relating BESD, r, and r2	17	(3)
Counternull Value of the BESD	20	(1)
The BESD with Dichotomous Outcome Variables	21	(4)
How Big an Effect Size Is ``Important''?	25	(3)
How Many Subjects? Considerations of Power	28	(2)
Extension to Unequal Sample Sizes in Two Groups	30	(5)
Review Questions	35	(2)
One-Way Contrast Analyses	37	(34)
Obtaining Significance Levels	37	(5)
Effect Size Correlations	42	(19)
The Four rs in the Meta-Analytic Context	61	(2)
Extension to Unequal Sample Sizes in Three or More Groups	63	(5)
Review Questions	68	(3)
Contrasts in Factorial Designs	71	(54)
Prologue	71	(1)
r alerting: A Preliminary Look at the Data	71	(2)
Obtaining Significance Levels	73	(1)
r contrast: The Maximally Partialed Correlation	74	(2)
Another Example of the Calculation of r alerting, Significance Levels, and r contrast	76	(3)
r alerting, Significance Levels, and r contrast in Multifactor Designs with Unequal Sample Sizes	79	(1)
r effect size	79	(3)
A More Detailed Example of the Calculation of r effect size and r effect size/NS	82	(2)
A Three-Factor Example	84	(4)
A Four-Factor Example	88	(4)
r BESD	92	(10)
Effect Size Estimation When Contrast Weights of 0 Are Set Aside	102	(11)
Extension to Unequal Sample Sizes in Factorial Designs	113	(8)
Preview	121	(1)
Review Questions	122	(3)
Contrasts in Repeated Measures	125	(26)
Intrinsically Repeated Measures Studies	125	(11)
Introduction to Nonintrinsically Repeated Measures Studies	136	(1)
Nonintrinsically Repeated Measures Studies: Significance Levels and r contrast	137	(5)
Nonintrinsically Repeated Measures Studies: Effect Size Correlations Other Than r contrast	142	(5)
Review Questions	147	(4)
Multiple Contrasts	151	(34)
Relationships among Contrasts	151	(8)
Examining the Difference between Contrasts	159	(11)
Unplanned Contrasts	170	(8)
Review Questions	178	(7)
Appendix A List of Equations	185	(6)
Chapter 2	185	(2)
Chapter 3	187	(2)
Chapter 4	189	(1)
Chapter 5	190	(1)
Chapter 6	190	(1)
Appendix B Statistical Tables	191	(14)
Table B.1 Table of Standard Normal Deviates (Z)	191	(1)
Table B.2 Extended Table of t	192	(4)
Table B.3 Table of F	196	(6)
Table B.4 Table of x2	202	(3)
References	205	(4)
Index	209