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

[gerd]

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):  clopper-pearson confidence interval for proportion 

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:

[PatrickGiuliano]

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.

[Knut]

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?).

[PatrickGiuliano]

@Knut  Interesting idea!  Can I ask why this option would be useful in your world? (practically speaking).

[PatrickGiuliano]

It turns out that this was requested by @david_arteta  and solved by @mpb  a long time ago (JMP-11) in the context of manually constructing column formulas: clopper-pearson confidence interval for proportion 

This feature is probably long overdue to be native in JMP (along with the currently generated Score CI's in the Distribution Platform), since the confidence intervals are pretty fundamental in certain contexts and industries.  As I understand it, the FDA "accepts" this interval estimation method in medical device development (submission) activities.   

[HappyUser]

Hello!

I have been working with a very talented JMP Technical Support representative.  He has helped me validate a solution that is needed in our workforce to test and evaluate SMALL sample size events. 

It would be of great support to us if you could include the following solution into the next version of JMP.  Our workforce uses the JMP license and will continue to do so in the future.

Solution requested to be implemented in next version of JMP:

Clopper Pearson Confidence Interval for one proportion USING the Beta Quantile () formula.

In the meantime, I will be scripting in JMP to create an add-in.  

Thank you to your team and your tech support which has given over the top support.

[PatrickGiuliano]

Hello @HappyUser,  Thank you for your support and the kind words for JMP Technical Support -- I echo your request per this Wish List Item -- we have captured this request for consideration in a future version of JMP. @PatrickGiuliano 

[Sarah-Sylvestre]

Hi @gerd, thank you for your suggestion! We have captured your request and will take it under consideration.