Maths

Why a treatment can win in every group and still lose overall: Simpson's paradox

Bar chart: treatment A beats B in small and large stones, but B beats A overall
30seconds
The 30-second version

Treatment B beats Treatment A overall, yet A wins for small stones and for large stones. That is Simpson's paradox, and it is real data from a kidney-stone study.

The trick is the mix: most of A's patients had the hard large stones, most of B's had easy small ones. Drag the sliders to change who gets which treatment and watch the winner flip, then see why the same effect showed up in Berkeley's 1973 admissions figures.

Deep dive · 4 min
Deep dive · 4 min

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