Suppose there is a test for a tuberculosis and it's given to every schoolkid in the US. Then it's found that 99% of the positive results were actually false positives; the kid was fine but the test said they were sick.
Many people would interpret this to mean that the test has low accuracy. Not so - its accuracy is still pretty high, but there are simply very few kids who actually do have tuberculosis out there, so the number of positive results is simply very low.
For example, if the test is given to 10 million kids and it returns the correct result 99.9% of the time (regardless of the kid's health) and 100 kids in the country have tuberculosis, the test will have 100 or 99 or 98 correct positive results and about 10,000 incorrect positive results. 99% of positive results will be wrong results, even though the test was actually very accurate.
[Via Quora]
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