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Jan 2 at 17:10 comment added whuber Glen_b's answer at stats.stackexchange.com/a/319653/919 looks straightforward and simple to me: the general formula is clearly stated in the second line and simplified to $-\log(\alpha)/n$ in the fourth line.
Jan 2 at 16:54 comment added emaxx "Rule of −log(α)" is beautiful, thanks! Would be useful if promoted to an answer because all of these other questions just hide this under a ton of formulas and other considerations.
Jan 2 at 16:45 comment added whuber You might find it more useful to refer to this as the "Rule of $-log(\alpha).$" For 95% confidence, alpha = 5% while for 99% confidence alpha = 1%. It is a short step from that to remembering the underlying principle, as discussed in any of the derivations, which is simply the definition of a confidence limit.
Jan 2 at 16:19 comment added emaxx The links give an overwhelming number of different formulas, but for posterity stats.stackexchange.com/a/34102/455846 says the answer is the "rule of 4.6".
Jan 2 at 16:09 history duplicates list edited whuber duplicates list edited from Sample size when one hypothesis is overwhelming to Sample size when one hypothesis is overwhelming, Using Rule of Three to obtain confidence interval for a binomial population, Is this a valid way to construct a confidence interval?, Revisiting the Rule of Three
Jan 2 at 16:08 history closed Harvey Motulsky
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whuber
Duplicate of Sample size when one hypothesis is overwhelming
Jan 2 at 16:08 comment added whuber Search for "Rule of Three" log.
Jan 2 at 15:58 comment added emaxx I've added the detail that the given event didn't happen in the given sample. Thanks.
Jan 2 at 15:57 history edited emaxx CC BY-SA 4.0
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Jan 2 at 15:56 history edited emaxx CC BY-SA 4.0
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Jan 2 at 15:55 comment added Harvey Motulsky The rule of three is for a situation where the outcome is an event that happens or not (not measured variable) and the event did not occur in the n observations. If you are asking for the corresponding value for 99% CI, please add those details to your question.
S Jan 2 at 15:38 review First questions
Jan 2 at 16:11
S Jan 2 at 15:38 history asked emaxx CC BY-SA 4.0