Hi,

If you want to use a binomial distribution:

p=38/50=0.76

P( x > 44 ) = 0.0106530. 44/50=0.88

P( x > 45 ) = 0.0279590. too big, bigger than 0.025 (0.05/2).

P(x<33)=0.0384254. too big

P(x<32)= 0.0190879.. 32/50=0.64

So the confidence interval includes the edges is: [0.64,0.88]

But I'm not sure if this is the best method.

http://users.stat.ufl.edu/~aa/articles/agresti_coull_1998.pdf
Generally, I would only expect that the accurate method will always be more correct than any approximation.

I can't say the attached article is very clear to me.

You may say that since it is discrete distribution it makes sense to get only CI from discrete values.

**The problem I can see with using the binomial distribution **is that the discrete value is based on

**estimated **probability, so actually thew values between the discrete results of the binomial are also possible values.

So because of the discrete results, the binomial CI produces a bigger confidence interval with a bigger

**actual confidence level **which is bigger than the

**required confidence level.**
The method called exact (that

**checkthebias mentioned) ** is actually Clopper-Pearson based on the Beta distribution, which is as I understand also an approximation?

I checked in R (library(Hmisc), there are also other options) and didn't see they use the binomial distribution as an option. (Normal / Clopper-Pearson, Wilson)

In

https://www.rdocumentation.org/packages/Hmisc/versions/4.2-0/topics/binconf they write :

"Following Agresti and Coull, the

**Wilson interval **is to be preferred and so is the default."

So what is the most accurate method for confidence interval?

@Miner @Dason
Why no binomial? is it what I wrote above?