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private_messaging comments on Rationality Quotes September 2013 - Less Wrong
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Or, for instance in the case of particle physics, it means the probability you are just looking at background. You are painting with an overly broad brush. Sure, p-values are overused, but there are situations where the p-value IS the right thing to look at.
Well, technically, the probability that you will end up with a result given that you are just looking at background. I.e. the probability that after the experiment you will end up looking at background thinking it is not background*, assuming it is all background.
It's really awkward to describe that in English, though, and I just assume that this is what you mean (while Bayesianists assume that you are conflating the two).