Truth-seeking series · № 1

Bayes & base rates

You tested positive. How worried should you be?

A screening test for a disease is 90% accurate at catching it, and wrongly flags 9% of healthy people. About 1 in 100 people actually have the disease. Your result comes back positive.

Most people — including, in repeated studies, most physicians — say the chance you're sick is around 90%. Watch what happens when you make the people countable.

How common is the disease? 1%

Test catches the sick (sensitivity) 90%

Test wrongly flags the healthy 9%

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sick and flagged — true positives healthy but flagged — false alarms sick but missed healthy and cleared

Why intuition fails here

The trap is base-rate neglect: "90% accurate" describes the test, not you. Because healthy people vastly outnumber sick ones, even a small false-alarm rate mints a big pile of false positives — often bigger than the pile of true ones. Your real question is: of everyone holding a positive result, how many are actually sick?

When Gerd Gigerenzer's group posed this puzzle as percentages, most doctors got it badly wrong. Posed as natural frequencies — "of 1,000 people, 10 are sick, 9 get caught, 89 healthy people get flagged…" — most got it right. Same math, different packaging. Counting people beats multiplying probabilities.

The move generalizes far past medicine: a hiring signal, a fraud detector, a drug-dog alert, a vibe about a startup. Before trusting any detector, ask how rare the thing it detects is. A test's accuracy is not the probability that the alarm is right.