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I think this statistical error is called confusion of the inverse: https://en.wikipedia.org/wiki/Confusion_of_the_inverse https://en.wikipedia.org/wiki/Confusio
by EForEndeavour 8y ago
I think this statistical error is called confusion of the inverse: https://en.wikipedia.org/wiki/Confusion_of_the_inverse https://en.wikipedia.org/wiki/Confusion_of_the_inverse
Confusion of the inverse is the assumption that the probability of A given B is equal to the probability of B given A. In symbols, the fallacy is falsely assuming P(A|B) = P(B|A). You have to use Bayes' Theorem to convert from a conditional probability to its inverse:
P(B|A)⋅P(A) = P(A|B)⋅P(B)
- paultopia 8y agoThe error has a name! I never knew! I just tell my students "you can't flip conditional probabilities like that."
- imgabe 8y agoThank you! I knew it had to do with Bayes' theorem. So much confusion in the world seems to come from the fact that people don't understand conditional probability.
- astazangasta 8y agoSticking my frequentist nose in here, this is maybe better described as the Base Rate Fallacy: https://en.m.wikipedia.org/wiki/Base_rate_fallacy https://en.m.wikipedia.org/wiki/Base_rate_fallacy
- EForEndeavour 8y agoNice, thanks! Though that page mentions and uses Bayes' Theorem a lot ;)
- handedness 8y agoThis type of faulty reasoning also frequently takes the form of affirming the consequent: https://en.wikipedia.org/wiki/Affirming_the_consequent https://en.wikipedia.org/wiki/Affirming_the_consequent (P→Q,Q)→P It happens often when people have a limited consideration set of possible causes, often due to a natural degree of ignorance or lack of experience relating to the subject matter area, e.g., a small child sees a wet sidewalk and assumes it rained, because they aren't yet aware of sprinklers (or garden hoses, etc.) (If rain→wet sidewalk, wet sidewalk)→rain The title alone might be clumsily restated as: (If amateur endurance athlete→rich, rich)→amateur endurance athlete