how to interpret disallowed values in confidence intervals I am doing simple binomial confidence intervals. e.g 19% of my sample has feature X, so my 95% confidence interval is [8,37] i.e. I'm 95% confident that between 8 and 37% of the population has this feature. 
But what if 4% of the sample has feature Y and my numerical 95% CI is [-12,20]. Clearly -12% is nonsensical, so is my confidence interval then [0,20] or do I somehow have to add back the -12 to get [0,32]? Intuitively I don't like the idea of [0 ... at all, as the sample is part of the population and I've got some positives already so 0% is theoretically impossible. If my CI (0, 20] then my intuition tells me that I've got too few cases in there, i.e. that this is not 95% confidence. But I don't have any mathematical basis for that intuition.
This is a very small corner of some social science research so I'm only looking for straightforward answers... thank you
 A: When calculating a confidence interval for a proportion, there are a number of different methods that can be used.  The simplest formula, which is the Wald confidence interval, relies on an approximation, which is why it can sometimes result in one or more confidence limits outside of $[0,1]$.
When this occurs, it is common practice to truncate the affected confidence limit so that the interval remains within $[0,1]$.  To address the first question of whether to include a $0$ or $1$ endpoint in such a case, it is not of much consequence:  unless the observed proportion is actually $0$ or $1$, it doesn't make much sense to include that value as you said, not any more than it makes sense to include values less than $0$ or greater than $1$.  But this isn't really the biggest issue:  coverage probability is much more important.
For the reason you identify, the Wald CI definitely has inferior performance and does not attain the nominal coverage probability when the observed proportion is "close to" $0$ or $1$.  This is well documented in the statistical literature, but as the audience here is social science, I will not illustrate in more detail here. However, the remedy is not so crude as to simply move the interval over while keeping it the same width.  While intuitively appealing, it lacks mathematical and statistical rigor.
An alternative that guarantees the nominal coverage probability in all cases is the Clopper-Pearson (exact) interval, which is assured to have limits within $[0,1]$, but a penalty is paid for requiring at least the nominal coverage:  inability to "spend" all the Type I error; i.e., if you want an interval with $95\%$ confidence of containing the true proportion, the actual coverage probability will strictly exceed it because anything smaller would not assure at least $95\%$ confidence.
A number of compromises between the two extremes that have been described and used.  One that is relatively easy to compute is the Wilson score interval.  Another is the Agresti-Coull interval.  Either of these, while not assuring the nominal coverage probability, are substantially superior to the Wald interval for interval estimation of the population parameter.
