The Simpson's paradox unraveled

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


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.

Publication types

  • Comparative Study
  • Research Support, N.I.H., Extramural

MeSH terms

  • Confounding Factors, Epidemiologic*
  • Data Interpretation, Statistical*
  • Effect Modifier, Epidemiologic*
  • Epidemiologic Research Design
  • Humans
  • Models, Statistical
  • Reproducibility of Results
  • Sensitivity and Specificity