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Statistics

Simpson's paradox: the safer hospital with worse overall survival

simpsons-paradoxconfoundingaggregation

Two hospitals report patient survival rates (survivors / admissions), split by how severe each patient's case was on arrival:

Routine casesCritical casesOverall
Mercy190/200 (95%)560/800 (70%)750/1000 (75%)
City850/900 (94.4%)65/100 (65%)915/1000 (91.5%)

Mercy has higher survival on routine cases (95% vs 94.4%) and on critical cases (70% vs 65%), yet City's overall survival rate is far higher (91.5% vs 75%).

Which hospital is safer, and explain the paradox.

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