Wilson score confidence intervals are often used when estimating low prevalence rates. Similarly the finite population correction (FPC) is often used when the sample is a large proportion of the population (usually over 5%). My question is whether it is appropriate to use them together? If so, what is the correct FPC for Wilson score confidence intervals?
Why not use exact confidence intervals based on the hypergeometric distribution? You took a random sample (without replacement) of size n from a population of size N. In that population an unknown number K has some particular property. You observed k with that property in the sample. Now you just use the hypergeometric distribution to find the largest K such that the probability to observe k or less in the sample is at least 2.5%, and ...
Richard,
I must admit I was hoping for a fairly simple approximation but your suggestion works fine if I use an iterative approach especially if I use Wilson's to initialise the iteration. I used the hypergeometric function in excel. Unfortunately my version of excel does not have the cumulative function so it was a bit more laborious but not too bad as both sample size and prevalence were low. Many thanks for pointing me in the right direction.
Mario - I am a little dismayed that you are doing anything important in Excel, whose statistical routines are long known to be flawed, and which MS obstinately has never fixed. See http://homepages.ulb.ac.be/~gmelard/rech/compsstat37.pdf.
The authors state : The conclusion is that Microsoft did not make an attempt to fix all the errors in Excel, and this point needs to be made strongly. Microsoft continues to market a product that contains known statistical errors, some of them going back to Excel 4, released in 1994. This should be contrasted with what is found on some open source or free software packages, see McCullough (2004c) about Gnumeric and Yalta and Yalta (2010) about gretl.
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