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]


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Accuracy paradox — The accuracy paradox for predictive analytics states that predictive models with a given level of accuracy may have greater predictive power than models with higher accuracy. It may be better to avoid the accuracy metric in favor of other metrics …   Wikipedia

  • Berry paradox — The Berry paradox is a self referential paradox arising from the expression the smallest possible integer not definable by a given number of words. Bertrand Russell, the first to discuss the paradox in print, attributed it to G. G. Berry, a… …   Wikipedia

  • Raven paradox — The Raven paradox, also known as Hempel s paradox or Hempel s ravens is a paradox proposed by the German logician Carl Gustav Hempel in the 1940s to illustrate a problem where inductive logic violates intuition. It reveals the problem of… …   Wikipedia

  • Omnipotence paradox — Part of a series on Atheism …   Wikipedia

  • Berry-Paradox — Das Berry Paradoxon (auch: Berry Paradox) ist ein selbstreferenzierendes Paradoxon, das sich aus dem Ausdruck „die kleinste ganze Zahl, die nicht durch eine gegebene Anzahl von Wörtern definierbar ist“ ergibt. Bertrand Russell, der sich als… …   Deutsch Wikipedia

  • Negative and positive atheism — A diagram showing the relationship between the definitions of weak/strong and implicit/explicit atheism. Explicit strong/positive atheists (in purple on the right) assert that at least one deity exists is a false statement. Explicit weak/negative …   Wikipedia

  • Banach–Tarski paradox — The Banach–Tarski paradox is a theorem in set theoretic geometry which states that a solid ball in 3 dimensional space can be split into several non overlapping pieces, which can then be put back together in a different way to yield two identical …   Wikipedia

  • List of statistics topics — Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… …   Wikipedia

  • Type I and type II errors — In statistics, the terms Type I error (also, α error, or false positive) and type II error (β error, or a false negative) are used to describe possible errors made in a statistical decision process. In 1928, Jerzy Neyman (1894 1981) and Egon… …   Wikipedia

  • Confusion of the inverse — Confusion of the inverse, also called the conditional probability fallacy, is a logical fallacy whereupon a conditional probability is equivocated with its inverse:[1] That is, given two events A and B, the probability Pr(A | B) is assumed to be… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”