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Confusion of the inverse, also called the conditional probability fallacy, is a logical fallacy whereupon a conditional probability is equivocated with its inverse [1].
In one study, physicians were asked what the chances of malignancy with a 1% prior probability of occurring and a positive test result from a diagnostic known to be 80% accurate with a 10% false positive rate for that type of test [2]. 95 out of 100 physicians responded the probability of malignancy would be around 75%, apparently because the physicians believed that the chances of malignancy given a positive test result were approximately the same as the chances of a positive test result given malignancy.
The correct probability of malignancy given a positive test result as stated above is 7.5%, derived via Bayes' theorem:
- Other examples
- Hard drug users tend to use marijuana; therefore, marijuana users tend to use hard drugs (the first probability is marijuana use given hard drug use, the second is hard drug use given marijuana use) [3]
- Most accidents occur within 25 miles from home; therefore, you are safest when you are far from home [4]
- Terrorists tend to have an engineering background; so, engineers have a tendency towards terrorism [5]
For other errors in conditional probability, see the Monty Hall problem and the base rate fallacy. Compare to illicit conversion.
Notes
References
- Eddy, David M. (1982). Probabilistic reasoning in clinical medicine: Problems and opportunities. In D. Kahneman, P. Slovic and A. Tversky (Eds.) Judgment under uncertainty: Heuristics and biases (pp. 249-267). New York: Cambridge University Press.
- Hastie, Reid; Robyn Dawes (2001). Rational Choice in an Uncertain World. ISBN 076192275X.
- Plous, Scott (1993). The Psychology of Judgment and Decisionmaking. ISBN 0070504776.
