Editing Binomial distribution (section)

==== Agresti–Coull method ====
{{Main|Binomial proportion confidence interval#Agresti–Coull interval}}
<ref name=Agresti1988>{{Citation |last1=Agresti |first1=Alan |last2=Coull |first2=Brent A. |date=May 1998 |title=Approximate is better than 'exact' for interval estimation of binomial proportions |url = http://www.stat.ufl.edu/~aa/articles/agresti_coull_1998.pdf |journal=The American Statistician |volume=52 |issue=2 |pages=119–126 |access-date=2015-01-05 |doi=10.2307/2685469 |jstor=2685469 }}</ref>
: <math> \tilde{p} \pm z \sqrt{ \frac{ \tilde{p} ( 1 - \tilde{p} )}{ n + z^2 } }</math>

Here the estimate of {{math|''p''}} is modified to
: <math> \tilde{p}= \frac{ n_1 + \frac{1}{2} z^2}{ n + z^2 } </math>

This method works well for {{math|''n'' > 10}} and {{math|''n''<sub>1</sub> ≠ 0, ''n''}}.<ref>{{cite web|last1=Gulotta|first1=Joseph|title=Agresti-Coull Interval Method|url=https://pellucid.atlassian.net/wiki/spaces/PEL/pages/25722894/Agresti-Coull+Interval+Method#:~:text=The%20Agresti%2DCoull%20Interval%20Method,%2C%20or%20per%20100%2C000%2C%20etc|website=pellucid.atlassian.net|access-date=18 May 2021}}</ref> See here for <math>n\leq 10</math>.<ref>{{cite web|title=Confidence intervals|url=https://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm|website=itl.nist.gov|access-date=18 May 2021}}</ref> For {{math|1=''n''<sub>1</sub> = 0, ''n''}} use the Wilson (score) method below.