A medical test provides evidence about whether a health condition is present. Its result changes belief through Bayesian updating, so accuracy alone does not determine how strongly a positive result should be trusted: the condition’s prior prevalence matters too. section 13.4
Interpret a test by separating these ideas:
- Sensitivity measures accuracy for people who have the condition; specificity measures accuracy for people who do not. section 13.4
- A rare condition can produce many false positives even when a test is 99.5% accurate. section 13.4
- The posterior probability combines the prior distribution with the likelihood of each test result. section 13.4
The Frob Syndrome test
Suppose 1 in 30,000 people has Frob Syndrome. A cheap test has 99.5% sensitivity and specificity. After a positive result, the modeled odds are 199 people with the syndrome to 29,999 without it—about 0.7%, not 99.5%. section 13.4
