False positive paradox

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The false positive paradox is a situation where the incidence of a condition is lower than the false positive rate of a test and therefore when the test shows that a condition exists, it is probable that the result is a false positive.

If there is a medical test that is accurate 99% of the time (in the sense that, if a subject has the disease, it is 99% likely to correctly indicate that she does, and if a subject does not have the disease, it is 99% likely to correctly indicate that she doesn't) about a disease that occurs in 1 out of 10,000 people, then the expected value of testing one million people would be the following:

Healthy and test indicates no disease (true negative)
$1,000,000 * (9999 / 10,000) * .99 = 989901$
Healthy and test indicates disease (false positive)
$1,000,000 * (9999 / 10,000) * .01 = 9999$
Unhealthy and test indicates disease (true positive)
$1,000,000 * (1 / 10,000) * .99 = 99$
Unhealthy and test indicates no disease (false negative)
$1,000,000 * (1 / 10,000) * .01 = 1$

If a patient received a positive response from the test the odds are ~99.02% (9999/10098) that he or she is healthy and the test is incorrect even though the test is "99% accurate" in the above sense.