Steven D. Levitt: pwned by the base rate fallacy?
Statistics is full of terms that fool people, because they seem intuitively to mean something very simple, while in fact they mean something equally simple, but radically different. And in the rich lexicon of statistical misunderstanding, few terms are more misleading than "false positive rate".
You take a medical test for Condition X and it comes back positive. Bad news — you have Condition X, right? Not so fast — the test is sometimes wrong. How often? Well, there's a "false positive rate" of 10%. OK, so that means that there's a 10% chance that your positive test result is false, and therefore a 90% chance that you have Condition X, right?
No. Wrong, wrong, wrong.
In this situation, your chances of having Condition X are probably not 9 out of 10, but more like 1 in 10 — or maybe 1 in 1,000 or 1 in 100,000 or even less. Without some additional information, we can't tell what the odds are — but they're almost certainly smaller than 9 in 10, and probably a very great deal smaller. Listen up, and I'll explain.
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