False positive paradox

The false positive paradox is a statistical result where false positive tests are more probable than true positive tests, occurring when the overall population has a low incidence of a condition and the incidence rate is lower than the false positive rate. The probability of a positive test result is determined not only by the accuracy of the test but by the characteristics of the sampled population.[1] When the incidence, the proportion of those who have a given condition, is lower than the test's false positive rate, even tests that have a very low chance of giving a false positive in an individual case will give more false than true positives overall.[2] So, in a society with very few infected people--fewer proportionately than the test gives false positives--there will actually be more who test positive for a disease incorrectly and don't have it than those who test positive accurately and do. The paradox has surprised many.[3] It is especially counter-intuitive when interpreting a positive result in a test on a low-incidence population after having dealt with positive results drawn from a high-incidence population.[2] If the false positive rate of the test is higher than the proportion of the new population with the condition, then a test administrator whose experience has been drawn from testing in a high-incidence population may conclude from experience that a positive test result usually indicates a positive subject, when in fact a false positive is far more likely to have occurred.