title: The Simpson's paradox unraveled.
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.
  
  
  CONCLUSIONS
  Analytical errors may occur when the problem is stripped of its causal context and analyzed merely in statistical terms.
authors: Department of Epidemiology, Harvard School of Public Health, Harvard-MIT Division of Health Sciences and Technology, Boston, MA 02115, USA. miguel_hernan@post.havard.edu
authors: Miguel A
authors: MA
authors: Hernán
authors: David
authors: D
authors: Clayton
authors: Niels
authors: N
authors: Keiding
mesh_terms: D015986:Confounding Factors, Epidemiologic; D003627:Data Interpretation, Statistical; D015987:Effect Modifier, Epidemiologic; D015340:Epidemiologic Research Design; D006801:Humans; D015233:Models, Statistical; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity