A test is 99% accurate. You test positive. How likely are you sick?
A disease affects 1 in 1,000 people. A test for it is 99% accurate, correctly flagging 99% of sick people and correctly clearing 99% of healthy people. You take the test and get a positive result. What's the actual probability you have the disease?
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Only about 9%, not 99%. Out of 1,000 people, roughly 1 truly sick person tests positive, but about 10 of the 999 healthy people also test positive by the test's 1% error rate, so positives outnumber true cases roughly 10 to 1. Ignoring the disease's rarity, the 'base rate', in favor of the test's accuracy is the base rate fallacy, a cornerstone of Bayesian reasoning popularized for general audiences by psychologist Gerd Gigerenzer.
— Gerd Gigerenzer, Calculated Risks: How to Know When Numbers Deceive You — Simon & Schuster, 2002
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