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by Donald T. Campbell and David A. Kenny

Edition: 99Copyright: 1999

Publisher: Guilford Press

Published: 1999

International: No

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Regression toward the mean is a complex statistical principle that plays a crucial role in any research involving the measurement of change. This primer is designed to help researchers more fully understand this phenomenon and avoid common errors in interpretation. The book presents new methods of graphing regression toward the mean, facilitating comprehension with a wealth of figures and diagrams. Special attention is given to applications related to program or treatment evaluation. Numerous concrete examples illustrate the ways researchers all too often attribute effects to an intervention or other causal variable without considering regression artifacts as an alternative explanation for change. Also discussed are instances when problems are actually created, instead of solved, by "correction" for regression toward the mean. Throughout, the authors strive to use nontechnical language and to keep simulations and formulas as accessible as possible.

**1. Graphical Introduction**

From the Scatter Plot to the Correlation Coefficient

The Pair-Link and Galton Squeeze Diagrams

Backward Prediction

Biology and Regression toward the Mean

A Golden Oldie: McNemar's Illustration

Conclusion

**2. Mathematical and Special Cases**

Generalization to the Case with Unequal Means and Variances

Formal Definition and Formulas

Frequently Asked Questions about Regression toward the Mean

Conclusion

**3. Regression Artifacts Due to Extreme Group Selection**

Pre-Post Design and Regression Artifacts

Examples

Conclusion

**4. Regression Artifacts Due to Matching**

Detailed Illustration of the Limits of Matching

Direction of Bias

Conclusion

**5. Regression Artifacts Due to Statistical "Equating"**

Look at the "Treatment Effect" on the Covariate

Illustration of the Bias in Statistical Equating

Direction of Bias

When Statistical Equating Works

Alternatives to Statistical Equating

Examples

Conclusion

**6. Regression Artifacts in Change Scores**

Correlations with Change Scores

Reliability of Change Scores

The Measurement of Change

Correlates of Change

Conclusion

**7.Regression Artifacts in Time-Series Studies**

The Connecticut Crackdown on Speeding

The Offset Effect of Psychotherapy

Time Series of HIV Treatment in Clinical Trials

ARIMA Modeling and Regression Artifacts

Conclusion

**8. Regression Artifacts in Longitudinal Studies**

Over-Time Correlational Structure

Regression Artifacts in Multiwave Studies

Conclusion

**9. Cross-Lagged Panel Correlation Analysis**

What Is CLPC Analysis

Complications in CLPC Analysis

The Rogosa Critique

CLPC as a Special Case of the Multitrait-Multimethod Matrix Model

Conclusion

**10. Conclusion**

Common Sense and Data Analysis: A Brief Epistemological Exegesis

Time-Reversed Analysis

Graphical Display of Results

The Importance of Research Design

Careful Consideration of Plausible Rival Hypotheses

Regression and Prediction

Conclusion

Glossary of Terms

Glossary of Symbols

Appendix A: Dice-Rolling Program and Data Sets Used as Illustrations

Appendix B: The Computation of Autocorrelations

Summary

Regression toward the mean is a complex statistical principle that plays a crucial role in any research involving the measurement of change. This primer is designed to help researchers more fully understand this phenomenon and avoid common errors in interpretation. The book presents new methods of graphing regression toward the mean, facilitating comprehension with a wealth of figures and diagrams. Special attention is given to applications related to program or treatment evaluation. Numerous concrete examples illustrate the ways researchers all too often attribute effects to an intervention or other causal variable without considering regression artifacts as an alternative explanation for change. Also discussed are instances when problems are actually created, instead of solved, by "correction" for regression toward the mean. Throughout, the authors strive to use nontechnical language and to keep simulations and formulas as accessible as possible.

Table of Contents

**1. Graphical Introduction**

From the Scatter Plot to the Correlation Coefficient

The Pair-Link and Galton Squeeze Diagrams

Backward Prediction

Biology and Regression toward the Mean

A Golden Oldie: McNemar's Illustration

Conclusion

**2. Mathematical and Special Cases**

Generalization to the Case with Unequal Means and Variances

Formal Definition and Formulas

Frequently Asked Questions about Regression toward the Mean

Conclusion

**3. Regression Artifacts Due to Extreme Group Selection**

Pre-Post Design and Regression Artifacts

Examples

Conclusion

**4. Regression Artifacts Due to Matching**

Detailed Illustration of the Limits of Matching

Direction of Bias

Conclusion

**5. Regression Artifacts Due to Statistical "Equating"**

Look at the "Treatment Effect" on the Covariate

Illustration of the Bias in Statistical Equating

Direction of Bias

When Statistical Equating Works

Alternatives to Statistical Equating

Examples

Conclusion

**6. Regression Artifacts in Change Scores**

Correlations with Change Scores

Reliability of Change Scores

The Measurement of Change

Correlates of Change

Conclusion

**7.Regression Artifacts in Time-Series Studies**

The Connecticut Crackdown on Speeding

The Offset Effect of Psychotherapy

Time Series of HIV Treatment in Clinical Trials

ARIMA Modeling and Regression Artifacts

Conclusion

**8. Regression Artifacts in Longitudinal Studies**

Over-Time Correlational Structure

Regression Artifacts in Multiwave Studies

Conclusion

**9. Cross-Lagged Panel Correlation Analysis**

What Is CLPC Analysis

Complications in CLPC Analysis

The Rogosa Critique

CLPC as a Special Case of the Multitrait-Multimethod Matrix Model

Conclusion

**10. Conclusion**

Common Sense and Data Analysis: A Brief Epistemological Exegesis

Time-Reversed Analysis

Graphical Display of Results

The Importance of Research Design

Careful Consideration of Plausible Rival Hypotheses

Regression and Prediction

Conclusion

Glossary of Terms

Glossary of Symbols

Appendix A: Dice-Rolling Program and Data Sets Used as Illustrations

Appendix B: The Computation of Autocorrelations

Publisher Info

Publisher: Guilford Press

Published: 1999

International: No

Published: 1999

International: No

**1. Graphical Introduction**

From the Scatter Plot to the Correlation Coefficient

The Pair-Link and Galton Squeeze Diagrams

Backward Prediction

Biology and Regression toward the Mean

A Golden Oldie: McNemar's Illustration

Conclusion

**2. Mathematical and Special Cases**

Generalization to the Case with Unequal Means and Variances

Formal Definition and Formulas

Frequently Asked Questions about Regression toward the Mean

Conclusion

**3. Regression Artifacts Due to Extreme Group Selection**

Pre-Post Design and Regression Artifacts

Examples

Conclusion

**4. Regression Artifacts Due to Matching**

Detailed Illustration of the Limits of Matching

Direction of Bias

Conclusion

**5. Regression Artifacts Due to Statistical "Equating"**

Look at the "Treatment Effect" on the Covariate

Illustration of the Bias in Statistical Equating

Direction of Bias

When Statistical Equating Works

Alternatives to Statistical Equating

Examples

Conclusion

**6. Regression Artifacts in Change Scores**

Correlations with Change Scores

Reliability of Change Scores

The Measurement of Change

Correlates of Change

Conclusion

**7.Regression Artifacts in Time-Series Studies**

The Connecticut Crackdown on Speeding

The Offset Effect of Psychotherapy

Time Series of HIV Treatment in Clinical Trials

ARIMA Modeling and Regression Artifacts

Conclusion

**8. Regression Artifacts in Longitudinal Studies**

Over-Time Correlational Structure

Regression Artifacts in Multiwave Studies

Conclusion

**9. Cross-Lagged Panel Correlation Analysis**

What Is CLPC Analysis

Complications in CLPC Analysis

The Rogosa Critique

CLPC as a Special Case of the Multitrait-Multimethod Matrix Model

Conclusion

**10. Conclusion**

Common Sense and Data Analysis: A Brief Epistemological Exegesis

Time-Reversed Analysis

Graphical Display of Results

The Importance of Research Design

Careful Consideration of Plausible Rival Hypotheses

Regression and Prediction

Conclusion

Glossary of Terms

Glossary of Symbols

Appendix A: Dice-Rolling Program and Data Sets Used as Illustrations

Appendix B: The Computation of Autocorrelations