Timeline for Confidence interval around binomial estimate of 0 or 1
Current License: CC BY-SA 3.0
24 events
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| Dec 13, 2023 at 5:11 | history | edited | ttnphns |
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| Dec 13, 2023 at 4:42 | answer | added | Ben | timeline score: 5 | |
| Jul 30, 2019 at 20:24 | comment | added | AdamO | I discuss median unbiased intervals in an answer here. They work for proportions of exactly 1 or 0. | |
| Oct 9, 2018 at 18:52 | history | post merged (destination) | |||
| Oct 9, 2018 at 18:51 | comment | added | whuber♦ | As far as approximations go, what matters is the absolute number of successes in the dataset rather than the size of the dataset itself. | |
| Oct 9, 2018 at 18:23 | comment | added | jbowman | With 800 trials, the usual Normal approximation will work reasonably well down to about $p=0.015$ (my simulations indicated a 94.5% actual coverage of a 95% confidence interval.) At 1000 trials and $p=0.01$, the actual coverage was about 92.7% (all based on 100,000 replications.) So this is only an issue for very low $p$, given your trial count. | |
| Oct 9, 2018 at 18:19 | comment | added | AI2.0 |
For only getting the upper limit of the confidence interval with (1-$\alpha$ confidence level, we will just use B(1−$\alpha$;x+1,n−x) where x is the number of successes (or failures), n is the sample size. In python, we just use scipy.stats.beta.ppf(1−$\alpha$;x+1,n−x) . If this is TRUE, can we conclude that we are 1−$\alpha$ confident that the upper limit is bounded by the value we calculate from scipy.stats.beta.ppf(1−$\alpha$;x+1,n−x) ?
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| Oct 9, 2018 at 17:27 | comment | added | user158565 | Use Clopper–Pearson interval you linked. The general principle: Try Clopper–Pearson interval first. If computer cannot get the answer, try the approximation method, such as normal approximation. According to the current computer speed, I do not think we need approximation on most situations. | |
| Oct 9, 2018 at 17:21 | comment | added | AI2.0 | We usually have greater than 800 trials. We usually expect 0 to 0.1 for $\hat{p}$ | |
| Oct 9, 2018 at 17:06 | comment | added | jbowman | How close to zero is $\hat{p}$? Is it zero often, or on the order of 0.001, or 0.01, or ...? And how much data do you have? | |
| Oct 9, 2018 at 16:02 | answer | added | Jay Schyler Raadt | timeline score: 4 | |
| S Feb 4, 2017 at 19:15 | history | bounty ended | Tim | ||
| S Feb 4, 2017 at 19:15 | history | notice removed | Tim | ||
| S Feb 3, 2017 at 12:02 | history | bounty started | Tim | ||
| S Feb 3, 2017 at 12:02 | history | notice added | Tim | Reward existing answer | |
| S Mar 21, 2016 at 23:26 | history | bounty ended | gung - Reinstate Monica | ||
| S Mar 21, 2016 at 23:26 | history | notice removed | gung - Reinstate Monica | ||
| Mar 14, 2016 at 23:00 | history | tweeted | twitter.com/StackStats/status/709514627613327360 | ||
| Mar 14, 2016 at 21:58 | history | edited | amoeba | CC BY-SA 3.0 |
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| S Mar 14, 2016 at 21:39 | history | bounty started | gung - Reinstate Monica | ||
| S Mar 14, 2016 at 21:39 | history | notice added | gung - Reinstate Monica | Reward existing answer | |
| Jan 19, 2014 at 11:55 | vote | accept | Kasper | ||
| Jan 19, 2014 at 9:39 | answer | added | Karl Ove Hufthammer | timeline score: 76 | |
| Jan 19, 2014 at 8:38 | history | asked | Kasper | CC BY-SA 3.0 |