steven0461 comments on Poll results: LW probably doesn't cause akrasia - Less Wrong
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Comments (104)
No, a 12% chance of seeing a correlation at least as strong. Confusion about p-values is endemic! Please be super-careful explaining what they mean! (Specifically, in this case, you don't want people thinking something like P(result | effect is real) = 1 and P(result | effect is false) = .12; I think that would be overstating the evidence.)
The issue isn't how many questions one is comparing, but rather what is the prior for this specific correlation. I don't think the prior for caffeine correlating with productivity is that low, and the .004 probably translates to pretty strong evidence. Of course, separately from that, you have to worry whether the correlation represents coffee -> productivity causation.
Steven, or others: if someone were to do a survey of e.g. Berkeley math majors, or others who seem similar to the LW population, what odds would you give on the caffeine/Anne correlation holding up? This might be a good subject for bets and rationality practice.
It sounds like a lot of effort for just one question. It would be easier to have someone transparently pick some science papers that people hadn't heard of, and then have people guess at what their conclusions were.
This is a good idea; however, it is possible to update fairly strongly on the fact that a paper on the subject in question was published.