Good_Burning_Plastic comments on The Strangest Thing An AI Could Tell You - Less Wrong
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If you don't want to break the suspension of disbelief for any reader who is a particle physicist, you might want to increase the number of sigmas. A two-sigma surprise isn't "major", it's something that would happen almost 5% of the time even with a perfect model.
"Three sigmas confidence" is a pretty meaningless expression to start with.
Updated again to three nines.