Correlation implies 25% likelihood of causation. Either A causes B, B causes A, C causes A and B, or chance.
In this post, Immerman wrote:
I *hate* seeing statistics abused. A 25% likelihood of causation is *not* implied. Yes, one of the four outcomes must be the case, but you don't know the relative probabilities of each. It's like grabbing a marble out of a bag containing red, green, blue, and yellow marbles - there's only four possibilities as to which color your marble is, but for all you know I filled the bag with blue marbles and just threw in a handful of the other colors, in which case it would be preposterous to claim a 25% chance of getting a red one.
I'm aware of the hyperbole in my illustration. They're probably not equally probable, but absent other evidence, one has to assume so. My point is that just because the probability isn't 100 percent doesn't mean it can always be treated as 0 percent. So if you want to plead false cause more effectively, explain why they're not equally probable. Be willing to discuss what further observations would be needed to show which of the four possibilities is most likely. But don't say "correlation does not imply causation" as if it were "correlation implies lack of causation" without providing evidence, as that's close to the fallacy fallacy and the black or white fallacy.
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