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I just would like to understand the basis and rational why 0.05 is widely used as the accepted value to decide rare or unlikely.

Is p-value threshold related with the confidence interval or +/- $2\sigma$ as the basis for 5%?

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    $\begingroup$ Both the $0.05$ and $2$ standard deviations came from RA Fisher who as a practical statistician doing field experiments (literally, at Rothamsted) had found this provided empirically useful criteria as to whether to investigate a question further. They are related in that $\Phi(1.96)\approx 0.975$ though not all statistical tests use the normal distribution. He also stated that other scientists might prefer to use other cutt-offs for their own reasons $\endgroup$
    – Henry
    Commented Sep 7, 2021 at 11:24
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    $\begingroup$ There's a saying: if you ask somebody in industry why they use $0.05$ they'll tell you "it's because that's what they were taught in school". If you ask somebody in academia why they teach $0.05$, it's because "that's what they use in industry". $\endgroup$
    – knrumsey
    Commented Sep 7, 2021 at 14:26

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I think that is the opposite. People first started to use 5% as the threshold for "rare" events. Then, since the 97.5-th percentile of the standard normal distribution is around 1.97, people also started to use the 2$\sigma$ rule for convenience.
In my understanding, choosing 5% in the first place is only a historical convention.
I would be interested in hearing other opinions, though.

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