The 99% Accurate Test Riddle Almost No One Gets Right
A medical test for a rare disease has sensitivity 99% and specificity 99%. The disease prevalence is 1%. If your result is positive, what is the closest estimate of the probability you actually have the disease?
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What is the answer to the 99% accurate medical test riddle?
About 50%. With 1% disease prevalence, a 99% accurate test produces roughly equal numbers of true and false positives, so a positive result means only about a 50% chance you're actually sick.
Why isn't the answer 99% if the test is 99% accurate?
Because the disease is rare. Out of 10,000 people, 100 sick give 99 true positives, but 9,900 healthy give 99 false positives. True positives are only about half of all positives, so the real chance is around 50%.
What is the false positive paradox?
It's the surprising result that even a highly accurate test can give mostly false alarms when a condition is rare, because the huge healthy population produces many false positives.