Right, but as I understand it, you don't need a file drawer effect to see that some of the experiments done in parapsychology still have devastatingly tiny p-values on their own, such as through the Stanford Research Institute.. So the file drawer effect isn't really the right way to challenge the analogy.

How is that?

I actually don't know what that means. Is sigma being used to indicate standard deviation? If so, then yes, there have been a number of parapsychology experiments that went in that range of accuracy - some moreso if I recall correctly. (It has been many years since I read into that stuff, so I could be misremembering.)

You need to provide links because I read a fair bit on the subject and don't recall this. If I came across such results my money would be on fraud of systematic error- not a statistical fluke.

So either parapsychology is ridiculous because it uses bad statistical methods (in which case there's a significant chance that this FTL finding is a statistical error), or we can trust the statistical methods that CERN used (which seems to force us to trust the statistical methods that parapsychologists use.)

This is the kind of "outside-view-taken to the extreme" attitude that just doesn't make sense. We know why the statistical results of para-psychological studies tend to not be trustworthy- publication bias, file drawer effect, exploratory research turned into hypothesis testing retroactively etc. If we didn't know why such statistical results couldn't be trusted the we would be compelled to seriously consider para-psychological claims. My claim is that those reasons don't apply to neutrino velocity measurements.