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Hi group!

is there functionality in JMP 11 for calculation of Clopper-Pearson exact confidence intervals for a proportion?

If I am not wrong, the manual only mentions this method for sample size calculations.

Thanks,

Dave

Re: clopper-pearson confidence interval for proportion

Note that the solution solution already covered uses the Fisher-Snedecor distribution (aka F-distribution), which is perfectly appropriate and highly accurate to approximate the binomial.  Here is an additional publication reference which details the calculations for Clopper-Pearson and includes another method (using the Beta Equation, from p. 38 of Krishnamoorthy, K., Handbook of statistical distributions with applications, (c) 2006 Chapman& Hall, CRC Press) which works equally well.

LCL = 

UCL = 

 

where C = confidence desired or required, k = number observed events, and N = total number of possible events.

https://www.johnzorich.com/s/Reasons-for-Using-the-Coefficient-of-Determination-by-John-Zorich.pdf

 

(Example attached in JMP).

Re: clopper-pearson confidence interval for proportion

Dear Kevin,

thanks for your suggestion. I have calculated Wilson Score CI's previously, but sometimes it is a matter of who is to review the information and their preferences. Such is the case of some regulatory bodies, and, unfortunately, I am in no position to argue.

Best,

Dave

Re: clopper-pearson confidence interval for proportion

This is probably going to open a can of worms, but that's never stopped me before... 

The Clopper-Pearson confidence intervals have been shown (Agresti, A. and Coull, B.A.(1998); "Approximate is Better Than Exact for Interval Estimation of Binomial Proportions"; The American Statistician Vol. 52 No .2; pp. 119-126) to have coverage probabilities that are overly conservative, especially in the tails.

That paper recommends Wilson Score Intervals, which are calculated natively in JMP in the Distribution platform.  Since I usually find myself thinking about "average" coverage performance of confidence intervals, and not "worst-possible" coverage performance, I tend to prefer the Wilson Score CI's.

Clopper-Pearson is the historical "gold standard", but I recommend you cast off the yoke of convention and go Wilson Score.  Plus, no formulae are required.

Re: clopper-pearson confidence interval for proportion

You can build the formulas in JMP for upper and lower confidence limits (2-sided or 1-sided) following Hahn and Meeker's book Statistical Intervals sections 6.2.2 and 6.2.5. Very useful book.

Lower 2-sided 100(1-alpha)% confidence limit for p = x/n:

Upper 2-sided 100(1-alpha)% confidence limit for p = x/n:

For 1-sided limits replace alpha/2 by alpha.