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Base rate fallacy
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==== High-prevalence population ==== {| class="wikitable floatright" style="text-align:right;" ! Number<br />of people !! Infected !! Uninfected !! Total |- ! Test<br />positive | 400<br />(true positive) || 30<br />(false positive) | 430 |- ! Test<br />negative | 0<br />(false negative) || 570<br />(true negative) | 570 |- ! Total | 400 || 600 ! 1000 |} Imagine running an infectious disease test on a population ''A'' of 1,000 persons, of which 40% are infected. The test has a false positive rate of 5% (0.05) and a false negative rate of zero. The [[expected value|expected outcome]] of the 1,000 tests on population ''A'' would be: {{block indent|Infected and test indicates disease ([[true positive]]) {{block indent|1=1000 Γ {{sfrac|40|100}} = 400 people would receive a true positive}}}} {{block indent|Uninfected and test indicates disease (false positive) {{block indent|1=1000 Γ {{sfrac|100 β 40|100}} Γ 0.05 = 30 people would receive a false positive}} The remaining 570 tests are correctly negative.}} So, in population ''A'', a person receiving a positive test could be over 93% confident ({{sfrac|400|30 + 400}}) that it correctly indicates infection.
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