I'm studying sampling distributions and confidence intervals for proportions and all is well. However, I don't understand what the standard error of a sample proportion is about. I know about the standard deviation of a sampling distribution, but not the standard error of a sample proportion. If we draw a sample and get a proportion, what does the standard error do for us? I know we can calculate margins of errors with it to construct confidence intervals, but why would a sampled proportion deviate? Am I missing something?
I could easily draw a sampling distribution model, but what about a sample proportion?