I have two related questions:
a) Is there any other way to calculate a confidence interval for the proportion, in addition to the "classical" form?
b) Can we apply this "classical" method when the proportion was calculated from a weighted data base?
I will put in context these questions so you can better understand me.
Reviewing the methodology applied on a survey (http://fra.europa.eu/sites/default/files/fra-2014-vaw-survey-technical-report-1_en.pdf) I found a table showing proportions and their confidence intervals. I calculated the confidence intervals by myself using the "classical" formula, because they looked excesively wide, and they didn't match. The only explanation I can find is that these proportions have been calculated from a weighted base data. But I'm not convinced with this self-explanation, since the "classical" formula takes into account the size of the sample, and that has not changed with the weighting.
Why my confidence intervals don't match with those shown in the table? This question is what led me to ask the two questions above.
Can please anybody help me?