Editing 2545: Bayes' Theorem
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β | For example, if a test has a 100% sensitivity (first line, all those affected receive a positive result) and a 99% specificity (second line, 1% of the unaffected also receive a positive result), the interpretation of a positive test depends on the prevalence of the disease in the population. In the example case, the prevalence is 0.1% (third column), so that when the test result is positive (1% of the tests, left column) the subject is actually unaffected nine | + | For example, if a test has a 100% sensitivity (first line, all those affected receive a positive result) and a 99% specificity (second line, 1% of the unaffected also receive a positive result), the interpretation of a positive test depends on the prevalence of the disease in the population. In the example case, the prevalence is 0.1% (third column), so that when the test result is positive (1% of the tests, left column) the subject is actually unaffected nine time out of ten. Although this would be a very performant test, given the relative prevalences involved it will produce overwhelmingly false positives among all positive results. (But, in this example, all those told they are not in danger — almost a hundred times more individuals than test positive — are correctly notified.) |
For this same example, the Bayesian formula gives : | For this same example, the Bayesian formula gives : |