The Simpson's paradox unraveled
Open Access
- 31 March 2011
- journal article
- research article
- Published by Oxford University Press (OUP) in International Journal of Epidemiology
- Vol. 40 (3), 780-785
- https://doi.org/10.1093/ije/dyr041
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.Keywords
This publication has 27 references indexed in Scilit:
- Causal Directed Acyclic Graphs and the Direction of Unmeasured Confounding BiasEpidemiology, 2008
- Estimation of the causal effects of time-varying exposuresPublished by Taylor & Francis ,2008
- ConfoundingPublished by Wiley ,2008
- A Structural Approach to Selection BiasEpidemiology, 2004
- Causal diagrams for empirical researchBiometrika, 1995
- The Amalgamation and Geometry of Two-by-Two Contingency TablesThe Annals of Statistics, 1987
- Assessing Sensitivity to an Unobserved Binary Covariate in an Observational Study with Binary OutcomeJournal of the Royal Statistical Society Series B: Statistical Methodology, 1983
- A reversal paradox.Psychological Bulletin, 1981
- On Simpson's Paradox and the Sure-Thing PrincipleJournal of the American Statistical Association, 1972
- The Interpretation of Interaction in Contingency TablesJournal of the Royal Statistical Society Series B: Statistical Methodology, 1951