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Simpson's Paradox and Experimental Research

Ameringer, Suzanne; Serlin, Ronald C.; Ward, Sandra

doi: 10.1097/NNR.0b013e318199b517

Background: Experimental research in nursing has increased considerably in recent years. To improve the quality of such research, it is critical to reduce threats to internal validity. One threat that has received inadequate attention in the nursing literature is Simpson's paradox-a case of extreme confounding that can lead to erroneous conclusions about the effects of an experimental intervention. In fact, it can lead to a conclusion about an intervention effect that is the opposite of the correct inference.

Approach: The aims of this study were to describe Simpson's paradox, provide a hypothetical example, and discuss approaches to avoiding the paradox.

Results: The paradox is due to the combination of an overlooked confounding variable and a disproportionate allocation of that variable among experimental groups. Different designs and analysis approaches that can be used to avoid the paradox are presented.

Discussion: Simpson's paradox can be avoided by selecting an appropriate experimental design and analysis that incorporates the confounding variable in such a way as to obtain unconfounded estimates of treatment effects, thus more accurately answering the research question.

Suzanne Ameringer, PhD, RN, is Assistant Professor, Virginia Commonwealth University, Richmond.

Ronald C. Serlin, PhD, is Chair, Department of Educational Psychology; and Sandra Ward, PhD, RN, FAAN, is Helen Denne Schulte Professor, University of Wisconsin-Madison.

Accepted for publication October 16, 2008.

Corresponding author: Suzanne Ameringer, PhD, RN, School of Nursing, Virginia Commonwealth University, 1100 East Leigh Street, Richmond, VA 23219 (e-mail:

© 2009 Lippincott Williams & Wilkins, Inc.