The direction of an association at the population-level may be reversed within the subgroups comprising that population—a striking observation called Simpson's paradox. When facing this pattern, psychologists often view it as anomalous. Here, we argue that Simpson's paradox is more common than conventionally thought, and typically results in incorrect interpretations—potentially with harmful consequences. We support this claim by reviewing results from cognitive neuroscience, behavior genetics, clinical psychology, personality psychology, educational psychology, intelligence research, and simulation studies. We show that Simpson's paradox is most likely to occur when inferences are drawn across different levels of explanation (e.g., from populations to subgroups, or subgroups to individuals). We propose a set of statistical markers indicative of the paradox, and offer psychometric solutions for dealing with the paradox when encountered—including a toolbox in R for detecting Simpson's paradox. We show that explicit modeling of situations in which the paradox might occur not only prevents incorrect interpretations of data, but also results in a deeper understanding of what data tell us about the world.
Keywords: paradox, measurement, reductionism, Simpson's paradox, statistical inference, ecological fallacy
Citation: Kievit RA, Frankenhuis WE, Waldorp LJ and Borsboom D (2013) Simpson's paradox in psychological science: a practical guide. Front. Psychol. 4:513. doi: 10.3389/fpsyg.2013.00513
Received: 04 May 2013; Accepted: 19 July 2013;
Published online: 12 August 2013.
Edited by:Joshua A. McGrane, The University of Western Australia, Australia
Reviewed by:Mike W. L. Cheung, National University of Singapore, Singapore
Copyright © 2013 Kievit, Frankenhuis, Waldorp and Borsboom. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Rogier A. Kievit, Medical Research Council - Cognition and Brain Sciences Unit, 15 Chaucer Rd, Cambridge, CB2 7EF, Cambridgeshire, UK e-mail: firstname.lastname@example.org