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MENTAL MODEL · M4128

False Positive Paradox

False Positive Paradox
TechnicalHigh supportProbability Theory
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Updated 2026-08-01

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INTRODUCTION

English translation pending.

CORE DEFINITION

A consequence of Bayes' theorem and a central case of base-rate neglect. If a disease affects one person in a thousand and a test is 99 percent accurate, a positive result still implies a low probability of disease, because the many healthy people who test falsely positive outnumber the few sick people who test correctly. The positive predictive value therefore depends on prevalence as much as on sensitivity and specificity. The same arithmetic governs fraud alerts, security screening, and any detection system applied to a rare event.

SCAFFOLDING EFFECT

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- Base-rate first: state the prevalence before reading any test result. - Predictive value check: compute what a positive actually implies instead of trusting accuracy. - Threshold design: raise specificity or stack independent tests when the prior is very low.

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The number of true positives equals prevalence times sensitivity, while false positives equal the large healthy population times the false-positive rate. When prevalence is tiny, the second product dwarfs the first even at high accuracy, so positives are mostly errors. The direction of conditional probability matters: the accuracy of a test given disease is not the probability of disease given a positive result.

MINIMUM ACTION

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Source support: Explicit

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    en.wikipedia.orghttps://en.wikipedia.org/wiki/Base_rate_fallacyZH · Explicit
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