Viewing Simpson’s Paradox

Well known Simpson’s paradox is puzzling and surprising for many, especially for the empirical researchersand users of statistics. However there is no surprise as far as mathematical details areconcerned. A lot more is written about the paradox but most of them are beyond the grasp of suchusers. This short article is about explaining the phenomenon in an easy way to grasp using simplealgebra and geometry. The mathematical conditions under which the paradox can occur are madeexplicit and a simple geometrical illustration is used to describe it. We consider the reversal of theassociation between two binary variables, say, X and Y by a third binary variable, say, Z. We showthat it is always possible to define Z algebraically for non-extreme dependence between X and Y,therefore occurrence of the paradox depends on identifying it with a practical meaning for it in agiven context of interest, that is up to the subject domain expert. And finally we discuss the paradoxin predictive contexts since in literature it is argued that the paradox is resolved using causal reasoning