When I input my data into OpenEpi for proportions, I get a proportion and a variety of possible confidence intervals to use. What is the difference between the Fisher Exact test and the Wilson Score? And when would I use each one?
You should expect to get different answers with these methods. Generally speaking, the Fisher Exact test is most suited to either very rare or very common outcomes, where the probability of being in one category is very low.
It's a somewhat more conservative measure than the Wilson Score, so if you don't meet those circumstances, the Wilson Score is more efficient.
This is a decent treatment of the subject: http://jansenlex.readyhosting.com/mwsug/2008/pharma/MWSUG-2008-P08.pdf