```Date: Thu, 14 Sep 2000 14:03:22 -0400 Reply-To: Mark.K.Moran@CENSUS.GOV Sender: "SAS(r) Discussion" Comments: To: z From: Mark.K.Moran@CENSUS.GOV Subject: Re: Why offset in confidence interval for proportions? Comments: To: SAS-L@LISTSERV.VT.EDU Content-type: text/plain; charset=us-ascii Mr./Ms. Zuckier, You are talking about the Joint Commission on the Accreditation of Healthcare Organizations? Most Joint Commission events reporting that I've heard of (keep in mind that I have only heard of a *small part* of what they do) are for *rare* events--adverse outcomes, sentinel events, deaths etc. These events would not be distributed Gaussian or even Z, but they would have some skewed distribution. I think that accounts for the off-centering of the 99% CI. More than that, I am not sure about the exact formula. Recommend you ask someone with a PhD. Mark z on 09/14/2000 11:37:26 AM Please respond to z To: SAS-L@LISTSERV.VT.EDU cc: (bcc: Mark K Moran/CSD/HQ/BOC) Subject: Why offset in confidence interval for proportions? Hi. This is more a stats question than a SAS one, but.... I'm trying to wade through the JCAHO ORYX reporting requirements. Their formulae for upper and lower limits for a 99% confidence interval for a proportion are U=((p+(Z^2)/(2n))+Z(root))/(1+(Z^2)/n) L=((p+(Z^2)/(2n))-Z(root))/(1+(Z^2)/n) where root=((z^2)/(4(n^2))+p(1-p)/n)^.5 Z=2.576 n=Number of patients p=observed proportion I can't exactly see where this comes from (I would have come up with p(+or-)Z(p(1-p)/n)^.5 myself), and more to the point, this gives me a confidence interval whose center is offset from p by the (Z^2)/2n term. Waiting for the JCAHO to clarify is a slow process, in the meantime, can anyone explain the theory behind this calculation? Thanks. Sent via Deja.com http://www.deja.com/ Before you buy. ```

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