Simpson's Paradox

Simpson's paradox is the unsettling situation where a trend that appears in every subgroup reverses when the subgroups are combined (or vice versa). The aggregate story and the within-group story point in opposite directions.

It happens because a lurking confounder is distributed unevenly across the groups. The paradox is really a question disguised as a contradiction: which view is correct depends on the causal structure, not the arithmetic. If the grouping variable is a confounder, trust the within-group result; if it is a mediator or collider, the answer changes — so you cannot resolve it from the numbers alone.