From: Clint Bowman <clint_at_ecy.wa.gov>

Date: Tue 13 Jul 2004 - 04:24:39 EST

Date: Tue 13 Jul 2004 - 04:24:39 EST

It seems to me that a transformation is in order since [0,1] can't
possibly contain a normal distribution without cutting off both tails.

On Mon, 12 Jul 2004, Rolf Turner wrote:

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> Darren Shaw wrote:

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**> > this may be a simple question - but i would appreciate any thoughts
**> >
**> > does anyone know how you would get one lower and one upper confidence
**> > interval for a set of data that consists of proportions. i.e. taking a
**> > usual confidence interval for normal data would result in the lower
**> > confidence interval being negative - which is not possible given the data
**> > (which is constrained between 0 and 1)
**> >
**> > i can see how you calculate a upper and lower confidence interval for a
**> > single proportion, but not for a set of proportions
**>
**>
**> (1) Your question appears to be a bit ``off topic''. I.e. it is
**> really about statistical methodology, rather than about how to
**> implement methodology in R.
**>
**> (2) You need to make the scenario clearer. What do your data
**> actually consist of? What are you assuming?
**>
**> The only reasonable scenario that springs to mind (perhaps this is
**> merely indicative of poverty of imagination on my part) is that you
**> have a number of ***independent*** samples, each yielding a sample
**> proportion, and each coming from the same population (or at least
**> from populations having the same population proportion ``p''. I.e.
**> you have p.hat_1, ..., p.hat_n and from these you wish to calculate a
**> confidence interval for p.
**>
**> You need to know the sample ***sizes*** for each sample. If you
**> don't, you're screwed. Full stop. There is absolutely nothing
**> sensible you can do. If you ***do*** know the sample sizes (say k_1,
**> ..., k_n) then the problem is trivial.
**>
**> You have p.hat_j = x_j/k_j for j = 1, ..., n.
**>
**> Let x = x_1 + ... + x_n and k = k_1 + ... + k_n.
**>
**> Form p.hat = x/k. (I.e. you ***really*** just have one big
**> happy sample.) Then calculate the confidence interval for p
**> in the usual way:
**>
**> p.hat +/- (z-value) * sqrt(p.hat * (1 - p.hat)/k)
**>
**> If this is not the scenario with which you need to cope, then
**> you'll have to explain what that scenario actually is.
**>
**> cheers,
**>
**> Rolf Turner
**> rolf@math.unb.ca
**>
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**>
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-- Clint Bowman INTERNET: clint@ecy.wa.gov Air Quality Modeler INTERNET: clint@math.utah.edu Department of Ecology VOICE: (360) 407-6815 PO Box 47600 FAX: (360) 407-7534 Olympia, WA 98504-7600 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.htmlReceived on Tue Jul 13 04:47:51 2004

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