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.