Base-Rate Neglect: What a Positive Checkup Really Means

Your annual checkup report arrives, and a tumor marker is flagged “positive.” Many people panic on the spot, search online, and read “this test is 95% accurate.” Their heart sinks: “So there’s a 95% chance something’s wrong?” Hold on — let’s work it out with the method from the last lesson.

Run the numbers

Suppose the condition this marker screens for affects 2% of people getting checkups, the test has 95% sensitivity, and a 5% false-positive rate. Picture 1,000 people getting a checkup:

• 20 have the condition, and 19 of them test positive;
• 980 are healthy, and 980 × 5% = 49 of them test positive too.

That’s 68 positives, of whom 19 are truly sick: 19 ÷ 68 ≈ 28%. Worth taking seriously — but a long way from “95% chance something’s wrong.”

What base-rate neglect is

Focusing on “how accurate is the test?” while forgetting “how common is this to begin with?” is base-rate neglect. It makes us overweight evidence about rare events.

The same positive result means very different things for different people. Take a high-risk group — people who already have symptoms and a family history — where, say, 20% have the condition:

• 200 are sick, and 190 test positive;
• 800 are healthy, and 40 test positive.

Now the posterior is 190 ÷ 230 ≈ 83%. Same test, but the conclusion jumps from roughly a third to over four in five — purely because of the base rate. Drag the base rate in the dot grid from 2% to 20% and watch the makeup of the positive group change completely.

That’s also why doctors usually recommend a retest after a positive screening. If the retest is positive too, and the two tests’ errors are unrelated, the probability climbs from about 28% to about 88%.

Not just checkups

“He wears glasses, loves reading, and speaks softly. Is he more likely a professor or an office worker?” Many people say professor. But office workers vastly outnumber professors, so even if only a small fraction fit the description, they can still outnumber the professors who do.

When you review a forecast and realize a vivid piece of evidence carried you away before you checked how common the outcome is, tag it as “base-rate neglect.”