False positive paradox

False positive paradox

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 about a disease that occurs in 1 out of 10,000 people, then testing one million people would approximately yield the following results:

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 they are healthy and the test is incorrect even though the test is 99% accurate.

See also

* Prosecutor's fallacy

External links

* [http://findarticles.com/p/articles/mi_qa4089/is_200305/ai_n9252796/pg_2 Link to article discussing the paradox]

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