U�ytkownik "G Robin Edwards" <[EMAIL PROTECTED]> napisa� w wiadomo�ci news:[EMAIL PROTECTED] > In article <[EMAIL PROTECTED]>, sleszyk <[EMAIL PROTECTED]> wrote: > > <Snip> > > > I have another question about the proportion confidence interval: > > > With the above formula one can calcute the symmetrical interval, which > > is ok as long as the proportion is not too close to 0 or 1. However, > > from what I've heard the "real" CI is always asymmetrical (well, maybe > > except for p=0,5). > > > Does anybody know how to calculate an asymmetrical CI for a > > proportion? I've been looking for an answer on the web some time ago > > and couldn't find it. > > This is nicely and simply given in the latest edition of "Statistics with > Confidence", by Gardner and Altman, pages 45 to 56. The techniques and > worked examples are given, so that you can check your own implementation! > > It is published (in the UK) by the BMJ. Sorry, I don't have the ISBN. > > > Here's a precis of the method :- > > Let n = sample size and r = number of "events". Then p = r/n, > and let q = (1-p). Let A = required probability, say 0.05 for example. > Then 100*(1-A)% would represent the 95% interval. > > Let Z = 100(1-A/2) percentile from the normal distribution, which is > readily available in many softwares and tables. > > Now calculate B = 2r + Z*Z, C = Z*SQRT(Z*Z + 4rq) and D= 2(n + Z*Z) > > The confidence interval for the population proportion is then > > (B - C)/D to (B + C)/D > > The examples they give are for 1 event in a sample of 29, (p = 0.03448) > for which the 95% CI evaluates to 0.006 to 0.172, and > > zero events in a sample of 20, clearly a proportion of 0.0 giving a 95% > CI of 0 to 0.161 > > In the book they give other related methods, such as confidence > intervals for differences in proportions for two samples, for both the > paired case and unpaired case. > > -- > Robin Edwards ZFC W Serious Statistical Software > REAL Statistics with Graphics for RISC OS machines > Please email [EMAIL PROTECTED] for details of our loan software. >
Thanks a lot - this is VERY helpful, just what I was looking for. Thanks, Peter. -- Serwis Usenet w portalu Gazeta.pl -> http://www.gazeta.pl/usenet/ . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
