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    $\begingroup$ Although this is what I also usually cite (+1), I am not sure whether or not one needs to revise this recommendation by one decimal place, given the recent recommendation of Valen Johnson in PNAS: "Make 0.005 the default level of significance [...]. Associate highly significant test results with P values that are less than 0.001." $\endgroup$ Commented Dec 7, 2013 at 14:28
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    $\begingroup$ Good answer. There's no style guides and no real standards in my fields, at least not for p-values. I do interdisciplinary work but I guess computer science and HCI would be the field for this. I think APA style would be where authors would turn, since the methods are generally borrowed from cognitive psych or other areas that the APA would cover. $\endgroup$ Commented Dec 7, 2013 at 20:04
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    $\begingroup$ Particle physics uses a $5\sigma$ rule (you might have seen it in the news with the confirmation of the Higgs boson), which blows way past this limit (being smaller even than $p < 10^{-6}$). Standards differ by area! $\endgroup$ Commented May 20, 2014 at 4:51
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    $\begingroup$ @Glen_b: Good point about $5\sigma$ in particle physics, but I guess what you wrote in your answer about sensitivity to assumptions etc. explains (or is at least part of the reason) why they report sigmas (i.e. basically $z$-statistic) instead of $p$-values. Once the $p$-value is below $0.0001$ or something (my usual advice is to report as many zeroes as one feels comfortable to print without switching to exponential notation), it's probably more meaningful to look at $z$-value than at $p$-value. $\endgroup$ Commented Feb 12, 2017 at 10:00
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    $\begingroup$ This is an awful recommendation. Any serious research field should be able to prove their hypothesis with p-values way under 0.001. This may be saying more about psichology than about p-values $\endgroup$ Commented Jun 19, 2019 at 13:35