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This article in the Encyclopedia of Epidemiology explains Simpson’s paradox, an extreme form of confounding where the association between two variables in a full group is in the opposite direction of the association found within every subcategory of a third variable.
Simpson’s paradox can be problematic when not recognized, leading to naïve and misleading conclusions regarding effectiveness or other relations studied. Perhaps more ominously, knowledge of Simpson’s paradox can be intentionally used to present or emphasize results that support a desired conclusion, when that conclusion is not valid.
More generally, Simpson’s paradox has been shown to have implications for the philosophical study of causation and causal inference. In practical terms, it is prudent for both researchers and research consumers to be on guard for this potentially perilous paradox.