False positive
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A false positive, also called false alarm, exists when a test reports, incorrectly, that it has found a signal where none exists in reality. Detection algorithms of all kinds often create false alarms. For example, optical character recognition (OCR) software may detect an 'a' where there are only some dots that look like an a to the algorithm being used. In statistical hypothesis testing, a false positive test which rejects the null hypothesis when it is true is called a Type I error. The false positive rate equals 1 minus the sensitivity of the test.
When developing detection algorithms (that is, tests) there is a tradeoff between false positives and false negatives (in which an actual match is not detected). That is, an algorithm can often be made more sensitive at the risk of introducing more false positives, or it can be made more restrictive, at the risk of rejecting true positives. The risk of Type I errors must be balanced against the risk of Type II errors (false negatives which fail to reject the null hypothesis when it is false). Usually there is some threshold of how close a match to a given sample must be achieved before the algorithm reports a match. The higher this threshold, the fewer false positives and the more false negatives.
False positives are a significant issue in medical testing. In some cases, there are two or more tests that can be used, one of which is simpler and less expensive, but less accurate, than the other. For example, the simplest tests for HIV and hepatitis in blood have a significant rate of false positives. These tests are used to screen out possible blood donors, but more expensive and more precise tests are used in medical practice, to determine whether a person is actually infected with these viruses.
False positives are also problematic in biometric scans, such as retina scans or facial recognition, when the scanner incorrectly identifies someone as matching a known person, either a person who is entitled to enter the system, or a suspected criminal.
False positives can produce serious and counterintuitive problems when the condition being searched for is rare. If a test has a false positive rate of one in ten thousand, but only one in a million samples (or people) is a true positive, most of the "positives" detected by the test will be false. The probability that an observed positive result is a false positive may be calculated, and the problem of false positives demonstrated, using Bayes' theorem.