The Simpson's paradox unraveled
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.