It Won Every Part, Then Lost the Total
by Anonymous · ⭐ 1 · 🍴 0
🏥 Two hospitals' surgery success rates. For mild cases it is A 93% against B 87%; for severe cases A 73% against B 69% — split, A leads in both. Pool them and it becomes A 77%, B 83%: the ranking flips. Not one of the four success rates was touched. All that changed is «who took more of which patients». 🔀 Second, the reason. Severe cases succeed less at either hospital, and 80% of A's patients are severe against only 20% of B's. The pooled number shows that gap, not skill. Set the two shares equal and it can «never» flip — what flips it is not the rates but the mix. 🔍 Third, the judgement. If you are a severe case, read the number for «your own group», not the total. This app was made with code too · Remix it with different shares.
About this app
An interactive lesson on Simpson’s paradox using two hospitals and two patient groups. Compare success rates for mild and severe cases separately, then adjust each hospital’s share of severe cases to see how the pooled ranking can reverse without changing any group-specific success rate. A final question reinforces why patients should compare outcomes for their own group rather than relying only on an overall percentage.
Use cases
- Students learning statistics and data interpretation
- Adults exploring critical thinking and numeracy
- Teachers demonstrating Simpson’s paradox in class
- Anyone practicing how to evaluate aggregated percentages
Features
- Interactive sliders for each hospital’s share of severe cases
- Separate and pooled success-rate comparisons for two hospitals
- Explanation of how case mix causes the ranking reversal
- Statement showing why equal group shares prevent the flip
- Multiple-choice question about choosing the relevant group-specific rate
- Three-tab lesson flow with reset and retry controls