In Agresti et al. (2008) "Simultaneous confidence intervals for comparing binomial parameter", it is suggested to use a studentized range distribution with a score statistic. However, exactly how you would compute a score statistic seems to be rather elusive. I've looked in "Intro to Categorical Data" by Agresti as well as "Intro to Mathematical Statistics" by Hogg et al. They go into the Wald method and Likelihood ratio, but they seem to gloss over the score method.

Some searching on Google has lead to a formula for the Wilson Score confidence interval for a proportion, but I've yet to find one for the difference of proportions.

I've found the R code written by Euijung Ryu that is referenced in the article, but it's quite complicated.


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