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Comparative Study
. 2011 Jun;40(3):780-5.
doi: 10.1093/ije/dyr041. Epub 2011 Mar 30.

The Simpson's paradox unraveled

Miguel A Hernán  1 , David Clayton, Niels Keiding
Affiliations
Comparative Study

The Simpson's paradox unraveled

Miguel A Hernán et al. Int J Epidemiol. 2011 Jun.

Abstract

Background: In a famous article, Simpson described a hypothetical data example that led to apparently paradoxical results.

Methods: We make the causal structure of Simpson's example explicit.

Results: We show how the paradox disappears when the statistical analysis is appropriately guided by subject-matter knowledge. We also review previous explanations of Simpson's paradox that attributed it to two distinct phenomena: confounding and non-collapsibility.

Conclusion: Analytical errors may occur when the problem is stripped of its causal context and analyzed merely in statistical terms.

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Figures

Figure 1
Figure 1
A collider C
Figure 2
Figure 2
A confounder C
Figure 3
Figure 3
A prognostic factor C
Figure 4
Figure 4
Conditions for collapsibility
See this image and copyright information in PMC

References

    1. Simpson EH. The interpretation of interaction in contingency tables. J R Stat Soc Ser B. 1951;13:238–41.
    1. Blyth CR. On Simpson's paradox and the sure-thing principle. J Am Stat Assoc. 1972;67:364–66.
    1. Messick DM, van de Geer JP. A reversal paradox. Psychol Bull. 1981;90:582–93.
    1. Good IJ, Mittal Y. The amalgamation and geometry of two-by-two contingency tables. Ann Stat. 1981;15:694–711.
    1. Pearl J. Causal diagrams for empirical research. Biometrika. 1995;82:669–710.

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