The false positive contradiction in terms may be a statistical result where false positive tests are additional probable than true positive tests, occurring once the population incorporates a low incidence of a condition and also the incidence rate is below the false positive rate. The likelihood of a positive check results determined not solely by the accuracy of the check however by the characteristics of the sampled population. Once the incidence, the proportion of those who have a given condition, is lower than the test's false positive rate, even tests that have an awfully low probability of giving a false positive in an individual case can give additional false than true positives overall. So, in a society with only a few infected people fewer proportionately than the check provides false positives there can really be more who check positive for an illness incorrectly and do not have it than people who check positive accurately and do.
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Scope and Importance
In medical testing, and more generally in binary classification, a false positive is when a test result indicates that a condition such as a disease is present (the result is positive), but it is not in fact present (the result is false), while a false negative is when a test result indicates that a condition is not present (the result is negative), but it is in fact present (the result is false). These are the two kinds of errors in a binary test, and are contrasted with a correct result, either a true positive or a true negative. These are also known in medicine as a false positive diagnosis (resp. false negative diagnosis), and in statistical classification as a false positive error (resp. false negative error).
In essence, the rate of false positives limits the effectiveness of any predictive system. The process of attempting to eliminate false positives is inherently one of diminishing return: even with no expense spared, the effort to eliminate false positives runs into boundaries of signal noise and generation of false positives.
To the degree that financial markets are ultimately predictive systems, this suggests a systemic cause of "unexpected" market crashes: signal noise and the intrinsic generation of false positives lead to a false sense of confidence in the system's stability and its ability to predict continued stability. There are only few international conferences focusing on false positive statistics and the ones entailing them are mainly concentrating on Biometrics and digital society.
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This page was last updated on December 1, 2023