math-lab

rates

Base rate fallacy

The test is accurate. The condition is rare. The name for that mix-up is the base rate fallacy.

The test is accurate, and the condition is rare. Of the alarms, how many are real?

Sick and positive Well and positive Sick and negative Well and negative

Lock a guess, then draw the crowd. Green rings are real alarms. Coral rings are false alarms.

What share of positive tests are real?
โ€”Positive tests in this crowd that are real
โ€”Positive tests that are real in the long run
โ€”True positives / all positives

Almost everyone is well, so a small false-alarm rate still flags many healthy people.

A positive test is more believable when the condition is common, and less believable when it is rare.

A rare crime. A match that is rare among innocent people can still turn up several times in a large city.

A door and a test. Monty showing a goat and a positive test both leave you to count everyone that result fits.