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buybuydandavis comments on The Universal Medical Journal Article Error - Less Wrong
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This post makes a point that is both correct and important, but Phil has clearly lost much of the audience and is ticked off besides, and I don't blame him.
I think we've got two issues. The general issue of how one tests a null hypothesis and what it does and does not mean to reject the null, and the particular issue of food dyes. The general issue seems important, while the particular could provide a helpful illustration of the general.
But I would think that someone else, and probably multiple someone's, have already plowed this ground. Jaynes must have an article on this somewhere.
Anyone got a good article?
Depends on what you want. You could probably get something useful out of my http://lesswrong.com/lw/g13/against_nhst/ collection.
Thanks. Interesting, but it doesn't really get at the heart of the problem here, of mistaken interpretation of a "failure to reject" result as confirmation of the null hypothesis, thereby privileging the null. That just shouldn't happen, but often does.
I saw the Gigerenzer 2004 paper (you're talking about the Null Ritual paper, right?) earlier today, and it rang a few bells. Definitely liked the chart about the delusions surrounding p=0.01. Appalling that even the profs did so poorly.
GG has another 2004 paper with a similar theme: The Journal of Socio-Economics 33 (2004) 587–606 Mindless statistics http://people.umass.edu/~bioep740/yr2009/topics/Gigerenzer-jSoc-Econ-1994.pdf
Isn't that a major criticism of NHST, that almost all users and interpreters of it reverse the conditionality - a fallacy/confusion pointed by Cohen, Gigerenzer, and almost every paper I cited there?
I think that's a separate mistake. This paper shows Pr[data|H0] > 0.05. The standard mistake you refer to switches this to falsely conclude Pr[H0|data] > 0.05. However, neither of these is remotely indicative of H0 being true.