It looks like that is using the Clopper-Pearson Exact CI. Here is what I have used for calculating the upper confidence interval for alpha. Unfortunately, the theory on how it was derived has faded from my memory.
There are a couple of ways to imitate the Excel example directly using the JMP Binomial Distribution function. One way is to create a column with that formula and other columns for the independent variables and use the Profiler to achieve the target right hand side by varying the proportion p. The other way is to set it up as a nonlinear fit using p again to achieve the target right hand side. They both work.
Here is an example of the nonlinear approach. The script below creates a data table with same data as in the Excel example. Run the table script to calculate the confidence limits.
(I first tried a neat solution that included the nonlinear platform (invisibly) in a column formula to enable automatic calculation. It worked, but not always as JMP sometimes got stuck inside an apparently infinite loop.)
Yes, I tried that, it worked but it was a bit shaky. I did not save the script but the principle was something like this:
I used script that excluded all rows then a for loop where each iteration unexcludes the current row, run the nonlinear script (incl. saving the parameter value), and finally re-excludes the current row. However, sometimes I got erroneous results probably because the row exclusion/unexclusion completion was running ahead of completion the numerical nonlinear fitting. One could try to find the sweet spot using Wait()-commands or use some other way to force completion.
Another possibility would be to run the non-linear with a by-argument using column with unique ID for each row. and then loop through the different nonlinear objects to finish and get estimates: Something like
I figured out a way to do it that might be faster than using the nonlinear function. Takes about 12-18 tries in the loop before finding an acceptable value. Adjust the epsilon parameter to get higher or lower precision. Takes less than a second on a table of 2400 values!
The Chadd's formula and it's lower bound counterpart should give the same upper and lower bounds as the method in the nist manual. I'll look up the other bound if you are interested. That would require no coding at all except to create the column forumulas.
It may be worth mentioning that the "exact" calculation is not necessarily considered "best" in the sense that the resulting interval may be unnecessarily wide. Here are a couple of papers in PDF format that are readily available and which you may find interesting.