Bias 13: Base Rate Fallacy

If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease, assuming you know nothing about the person’s symptoms or signs?

This question had been asked to 60 Harvard Medical students in 1978 by Schoemberger, Grayboys and Casscells. The average was 0.56 while the correct answer is 0.02. What happened?

The base rate fallacy is an error, a cognitive “jump”, that occurs when the conditional probability of event A knowing B is assessed without taking into account the prior probability of B.

In our example:

What most people do: They ignore the prior probability of disease prevalence so they consider that P(D/P)=P(P/D)

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Correct answer based on Bayes’ Theorem:

P(D/P)=P(D)*P(P/D)/P(P)= P(D)*P(P/D)/(P(H)*P(P/H)+P(D)*P(P/D))
=0,001*1/(0,001*1+0,05*0,999)
=2%

Base Rate Fallacy

Reference:
Gigerenzer, G. (1993). The bounded rationality of probabilistic mental models. In This chapter is based on a lecture delivered at Harvard University, Oct 2, 1991.. Taylor & Frances/Routledge.

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