Glossary term
Sensitivity
The share of people who truly have a condition that a test correctly flags as positive.
Visual intuition
3 in 100
before new evidence
Sensitivity is scored only on the 3 who truly have it
Of these 100 people, only the 3 highlighted truly have the condition. Sensitivity asks one question about them alone: what share would the test catch? The other 97 — and the false alarms they can raise — do not enter it.
Formula
sensitivity = true positives / everyone who truly has it
Example
Testing 10,000 people where 10 truly have the condition, a 99%-sensitive test flags about all 10 true cases; at 80% sensitivity it would miss 2 of them.
How It Works
Sensitivity is scored only on the people who truly have the condition: of the 3 in this crowd who do, what share does the test flag? A 99%-sensitive test catches 99 of every 100 true cases and misses 1 — a . What sensitivity deliberately ignores is everyone else: a test can catch every true case and still bury you in false alarms from the healthy majority. Guarding against those is 's job, and the pairing is why a 99%-sensitive, 99%-specific test still yields about 100 false positives for every 10 true ones when only 1 in 1,000 people has the condition.
Concepts
Base Rates
The background frequency of something before you consider new evidence. A strong signal can still produce many false alarms when the thing being tested for is rare, because there are many more non-cases than cases. Good reasoning combines the new signal with the base rate.
Conditional Probability
The probability of something after new information changes what is still possible. The important move is to update the denominator: cases ruled out by the new information should no longer be counted. Many mistakes happen when people keep using the original odds after the situation has narrowed.
