A Positive Doesn't Always Mean Yes
by Anonymous · ⭐ 0 · 🍴 0
🧪 You test positive on a 99%-accurate test. What is the chance it is real? Line up ten thousand people and the answer appears — if 1 person in 1,000 has it, then 10 of the 10 real cases test positive, and 100 of the 9,990 clear people test positive too. That is 110 positives in all, of which only 10 are real: 9%. There are so many clear people that the false positives swamp the real ones. 📉 Second, the curve. Without touching the test at all, changing only «how rare it is» moves the answer from 9% to 92%. Meanwhile raising «the share of true cases caught» from 80% to 100% barely moves it — what decides the answer is not the test but the rarity. 📬 Third, spotting it. With three tests that are all equally 99% accurate, 1-in-1,000, 1-in-100 and 1-in-10 give 9%, 50% and 92%. This app was made with code too · Remix it with the numbers of a test you know.
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About this app
This interactive lesson explains why a positive result from a 99%-accurate test does not always mean the condition is truly present. Use a 10,000-person table to compare true positives and false positives, then explore how prevalence changes the share of positives that are real. A final quiz compares identical tests at prevalence rates of 1 in 1,000, 1 in 100, and 1 in 10.
Use cases
- Students learning conditional probability and base rates
- Teachers demonstrating false positives with a visual example
- Adults building statistical and critical-thinking skills
- Anyone interpreting medical or screening test results
Features
- Interactive 10,000-person outcome table
- Sliders for prevalence, sensitivity, and specificity
- Curve showing how prevalence affects the positive predictive value
- Comparison quiz using three identical 99%-accurate tests
- Reset, retry, tab navigation, and sound controls