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“A masterful presentation reflecting many years of research and study. It should prove to be valuable to any researcher who has even a basic understanding of statistical analysis.”

—International Journal of Consumer Studies


“Aguinis has produced the most comprehensive single-source treatment on the topic of why and how to conduct moderated regression analysis for categorical moderators. The book presents very clear steps for how to test for moderators, but is more than a cookbook in that it also explores in detail the underlying assumptions; issues that will affect interpretation (e.g., homogeneity of variance and power); and solutions to frequently encountered problems. Examples from different types of research problems help clarify the analytical strategy, and presentation of the software for examining underlying issues is very valuable. Aguinis also provides excellent coverage of the literature surrounding the analytical strategy. This volume is an excellent reference for any researcher or student interested in studying interactions with categorical variables.”

—Sheldon Zedeck, PhD, Department of Psychology, University of California, Berkeley


“This book presents a complete and current treatment of a topic of great importance to management and organizational studies researchers. Strengths of the book include the use of an integrative example with data that is available to readers, and the clear presentation style. The treatment of homogeneity of error variance and statistical power problems is especially impressive and provides readers with practical guidance for dealing with these issues. This book will be an excellent resource for any researcher who works with regression models.”

—Larry J. Williams, PhD, Center for the Advancement of Research Methods and Analysis, School of Business, Virginia Commonwealth University


“Aguinis has provided an extraordinarily understandable guide to conducting tests of moderation by categorical variables. The book contains clear examples for running the analyses, checking assumptions, and interpreting the results. This book is an excellent resource for courses on regression analysis at both the undergraduate and graduate levels, and for individuals who need a refresher on moderator analysis.”

—Lois Tetrick, PhD, Department of Psychology, George Mason University

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Table of Contents

1. What Is a Moderator Variable and Why Should We Care?

Why Should We Study Moderator Variables?

Distinction between Moderator and Mediator Variables

Importance of A Priori Rationale in Investigating Moderating Effects

Conclusions

2. Moderated Multiple Regression

What Is MMR?

Endorsement of MMR as an Appropriate Technique

Pervasive Use of MMR in the Social Sciences: Literature Review

Conclusions

3. Performing and Interpreting Moderated Multiple Regression Analysis Using Computer Programs

Research Scenario

Data Set

Conducting an MMR Analysis Using Computer Programs: Two Steps

Output Interpretation

Conclusions

4. Homogeneity of Error Variance Assumption

What Is the Homogeneity of Error Variance Assumption?

Two Distinct Assumptions: Homoscedasticity and Homogeneity of Error Variance

Is It a Big Deal to Violate the Assumption?

Violation of the Assumption in Published Research

How to Check If the Homogeneity Assumption Is Violated

What to Do When the Homogeneity of Error Variance Assumption Is Violated

ALTMMR: Computer Program to Check Assumption Compliance and Compute Alternative Statistics If Needed

Conclusions

5. MMR’s Low-Power Problem

Statistical Inferences and Power

Controversy Over Null Hypothesis Significance Testing

Factors Affecting the Power of All Inferential Tests

Factors Affecting the Power of MMR

Effect Sizes and Power in Published Research

Implications of Small Observed Effect Sizes for Social Science Research

Conclusions

6. Light at the End of the Tunnel: How to Solve the Low-Power Problem

How to Minimize the Impact of Factors Affecting the Power of All Inferential Tests

How to Minimize the Impact of Factors Affecting the Power of MMR

Conclusions

7. Computing Statistical Power

Usefulness of Computing Statistical Power

Empirically Based Programs

Theory-Based Program

Relative Impact of the Factors Affecting Power

Conclusions

8. Complex MMR Models

MMR Analyses Including a Moderator Variable with More Than Two Levels

Linear Interactions and Non-linear Effects: Friends or Foes?

Testing and Interpreting Three-Way and Higher-Order Interaction Effects

Conclusions

9. Further Issues in the Interpretation of Moderating Effects

Is the Moderating Effect Practically Significant?

The Signed Coefficient Rule for Interpreting Moderating Effects

The Importance on Identifying Criterion and Predictor A Priori

Conclusions

10. Summary and Conclusions

Moderators and Social Science Theory and Practice

Use of Moderated Multiple Regression

Homogeneity of Error Variance Assumption

Low Statistical Power and Proposed Remedies

Complex MMR Models

Assessing Practical Significance

Conclusions

Appendix A. Computation of Bartlett’s (1937) \ital\M\ital\ Statistic

Appendix B. Computation of James’s (1951) \ital\J\ital\ Statistic

Appendix C. Computation of Alexander’s (Alexander & Govern, 1994) \ital\A\ital\ Statistic

Appendix D. Computation of Modified \ital\f\ital\\superscript\2\superscript\

Appendix E. Theory-Based Power Approximation

References

Name Index

Subject Index

1. What Is a Moderator Variable and Why Should We Care?

Why Should We Study Moderator Variables?

Distinction between Moderator and Mediator Variables

Importance of A Priori Rationale in Investigating Moderating Effects

Conclusions

2. Moderated Multiple Regression

What Is MMR?

Endorsement of MMR as an Appropriate Technique

Pervasive Use of MMR in the Social Sciences: Literature Review

Conclusions

3. Performing and Interpreting Moderated Multiple Regression Analysis Using Computer Programs

Research Scenario

Data Set

Conducting an MMR Analysis Using Computer Programs: Two Steps

Output Interpretation

Conclusions

4. Homogeneity of Error Variance Assumption

What Is the Homogeneity of Error Variance Assumption?

Two Distinct Assumptions: Homoscedasticity and Homogeneity of Error Variance

Is It a Big Deal to Violate the Assumption?

Violation of the Assumption in Published Research

How to Check If the Homogeneity Assumption Is Violated

What to Do When the Homogeneity of Error Variance Assumption Is Violated

ALTMMR: Computer Program to Check Assumption Compliance and Compute Alternative Statistics If Needed

Conclusions

5. MMR’s Low-Power Problem

Statistical Inferences and Power

Controversy Over Null Hypothesis Significance Testing

Factors Affecting the Power of All Inferential Tests

Factors Affecting the Power of MMR

Effect Sizes and Power in Published Research

Implications of Small Observed Effect Sizes for Social Science Research

Conclusions

6. Light at the End of the Tunnel: How to Solve the Low-Power Problem

How to Minimize the Impact of Factors Affecting the Power of All Inferential Tests

How to Minimize the Impact of Factors Affecting the Power of MMR

Conclusions

7. Computing Statistical Power

Usefulness of Computing Statistical Power

Empirically Based Programs

Theory-Based Program

Relative Impact of the Factors Affecting Power

Conclusions

8. Complex MMR Models

MMR Analyses Including a Moderator Variable with More Than Two Levels

Linear Interactions and Non-linear Effects: Friends or Foes?

Testing and Interpreting Three-Way and Higher-Order Interaction Effects

Conclusions

9. Further Issues in the Interpretation of Moderating Effects

Is the Moderating Effect Practically Significant?

The Signed Coefficient Rule for Interpreting Moderating Effects

The Importance on Identifying Criterion and Predictor A Priori

Conclusions

10. Summary and Conclusions

Moderators and Social Science Theory and Practice

Use of Moderated Multiple Regression

Homogeneity of Error Variance Assumption

Low Statistical Power and Proposed Remedies

Complex MMR Models

Assessing Practical Significance

Conclusions

Appendix A. Computation of Bartlett’s (1937) \ital\M\ital\ Statistic

Appendix B. Computation of James’s (1951) \ital\J\ital\ Statistic

Appendix C. Computation of Alexander’s (Alexander & Govern, 1994) \ital\A\ital\ Statistic

Appendix D. Computation of Modified \ital\f\ital\\superscript\2\superscript\

Appendix E. Theory-Based Power Approximation

References

Name Index

Subject Index

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About the Author

Herman Aguinis, PhD, is the Avram Tucker Distinguished Scholar and Professor of Management at George Washington University School of Business. Previously, he served on the faculties of the Kelley School of Business at Indiana University and the University of Colorado Denver Business School. In addition, he has been a visiting scholar at universities around the world. His research is interdisciplinary and addresses human capital acquisition, development, deployment, and research methods and analysis. Widely published, Dr. Aguinis currently serves as associate editor of the Annual Review of Organizational Psychology and Organizational Behavior. He is a Fellow of the Academy of Management, the American Psychological Association, the Association for Psychological Science, and the Society for Industrial and Organizational Psychology, and has been inducted into the Society of Organizational Behavior and the Society for Research Synthesis Methodology. His work has been recognized with numerous awards.

• Author's website

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Audience

Students, researchers, and practitioners in psychology, management, business, education, and other social and behavioral science disciplines. Suitable for readers with only a basic knowledge of inferential statistics.

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Course Use

Serves as an invaluable supplemental text in advanced undergraduate statistics and methods courses and in graduate courses addressing multiple regression or the general linear model.