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## Clopper Pearson Confidence Interval for One Proportion as an Option in Distribution Platform

It would be nice to have an option that Clopper-Pearson ("Exact") Intervals (and Bounds) be reported in the Distribution Platform, additionally to Score Confidence Intervals. This could be a setting in the Platform Preferences or an option under the red triangle menu for "Confidence Intervals" or additional Columns in "Confidence Intervals".

This is not a matter of arguing that one interval is better than the other (it is known that Clopper-Pearson Intervals are overly conservative) but rather a matter of offering a method that many people (and regulatory bodies) are familiar with.

There is a JMP "Calculators" Skript (under Help -> Sample Data -> Calculators -> Confidence Interval for One Proportion) that offers this type of interval, but it's not editable, e.g. if one is interested in the proportion of "Fails", these can only be labelled "Successes", and when working with raw data it doesn't recognise hidden and excluded rows.

There is a Discussion in the Community about this topic where one user provided a formula solution (from the Hahn & Meeker book on Statistical Intervals):

https://community.jmp.com/t5/Discussions/clopper-pearson-confidence-interval-for-proportion/m-p/1218...

It is nice to have at least these options, but for reporting purposes both workarounds are not a good option.

The following picture shows the Distribution Platform output on the left and the Calculators-tool (Clopper-Pearson) output on the right:

### Defect ID:

2 Comments
Level IV

Hello, Yes I couldn't agree with you more in regards to your suggestion.

Exact intervals are also more approriate for proportions close to 0% and 100% since they use the binomial distribution, whereas the Score CIs use the normal approximation (accurate for proprotions close to 50%, and where many use the 'rules of thumb' np(1-p) >5 and np>5).

Wald intervals [noting that a Score CI is an elaborated  version of the classic Wald] are based upon the fact that when sample size is large or PS is near 50%, the Normal distribution is a "reasonable" model of the Binomial, even if such an application is "not completely accurate."  (per reference 8 in  Reasonable Con Limits for Binomial Proportions by John Zorich)

Ref #8: H. Motulsky, Intuitive Biostatistics (New York, NY: Oxford University Press, 1995): p. 18.

I would go a step further and mimic the calculator's graphical display of the confidence interval in the Distribution Platform.  The graphical display is particularly helpful for clarifying and communicating the confidence bounds on an attribute CI (in the same way that that the tips of the mean diamonds so the confidence bound on a CI for variable data); also, if in Analyze>Distribution JMP offers the option to calculate several different intervals (not just the Score CI), then the intervals can be compared visually in terms of their coverage.  Finally, the visual display of the CIs would be most useful for visual diagnostic assessment on how similar (in a 'statistical sense') two different proportions are in relation to each other (in Analyze > Fit Y by X).  This is currently not a feature in Fit Y by X either.

Level III

I couldn't agree more!

Also, there should be an option to plot not the median for each category, but the interpolated data value closest to the average rank of the values in this category (i.e. the 0.0...01% confidence interval, anti-avgRank?).