A 99% Accurate Test Can Still Be Wrong 99% of the Time for Rare Conditions
If a condition affects only 1 in 10,000 people and a test has 99% sensitivity and 99% specificity (a 1% false-positive rate), testing positive gives just ~1% true odds of having it.
🧪 Bayes Theorem
Bayesian Inference & Diagnostics
For a 1-in-10,000 rarity with a 99% accurate test, about what % of positives are actually true?
Known as the Base Rate Fallacy, ignoring prior rarity lets false positives swamp true positives.
📊 Statistics
Bayes Theorem
Why / How?
Scientific Mechanism
Bayes' Theorem shows why ignoring the base rate traps our intuition. Out of 10,000 tested people, 1 truly sick person tests positive—while 1% of the 9,999 healthy people (~100 people) receive false positives. Only 1 out of those ~101 positive alerts is real.
Why It Matters
Known as the Base Rate Fallacy, ignoring prior rarity lets false positives swamp true positives.
