Sue, Phil, et al., The essential part of Sue's concern is that, given that she observed 50% of the total population, the typical standard error for the estimated proportion is too large. If you observe that much of the population, you should be more "confident" in your estimate of the proportion. Indeed, you're half way to not needing an estimate at all. The continuity correction that Phil mentioned is relevant to confidence intervals for any estimated proportion, but does not address Sue's primary concern.
The standard error (SE) for the proportion is -- sqrt((prop*(1-prop))/ssize) -- where ssize is sample size (here, 50) and prop is the estimated proportion (here, 0.4). SE = 0.069 The correction to SE that Sue is looking for is accomplished by multiplying the standard error by the finite population correction (FPC), which reduces the standard error: FPC is -- sqrt((popsize-ssize)/(popsize-1)) -- where popsize is the population size (here, 100). FPC = 0.71 The corrected standard error is SE*FPC = 0.049. You can then get an approximate confidence interval for whatever "confidence" you want by multiplying the corrected standard error by the associated Z value. For a typical 95% interval, Z=1.96 and the interval is (0.30, 0.50). Using a simple continuity correction (adding -- 0.5/ssize -- to the upper limit and substracting -- 0.5/ssize -- from the lower limit) widens it a touch: (0.29, 0.51). [This isn't exact, but the continuity correction does little here.] Using prop.test(20, 50, conf.level=0.95) from R in its "raw" form, which includes the continuity correction but is uncorrected for the FPC, gives (0.27, 0.55). I didn't notice a quick way to adjust for the FPC within prop.test(), but I suspect someone has done it. Bottom line: you gain a bit with the FPC, as you'd expect. At 08:55 AM 12/17/2007 -0500, Phil Novack-Gottshall wrote: >Dear Suzanne and interested others, > >The latest best practice I've run across is the >Wilson method using Yates' continuity >correction. It is formally described and advocated in the following articles: > >Newcombe R.G. (1998) Two-Sided Confidence >Intervals for the Single Proportion: Comparison >of Seven Methods. Statistics in Medicine 17, 857872. > >Newcombe R.G. (1998) Interval Estimation for the >Difference Between Independent Proportions: >Comparison of Eleven Methods. Statistics in Medicine 17, 873890. > >If you use the stats language R, it's implemented >using prop.test (which also allows two-sample >testing of equal proportions). There's also a >web interface at: http://faculty.vassar.edu/lowry/prop1.html > >Good luck, >Phil > >At 10:37 PM 12/16/2007, Suzanne Griffin wrote: > >Can anyone tell me how to compute CI's for a > >proportion when the sample is fron from a finite > >population? For example,?the population size is > >100, I sample 50 individuals, and the event of > >interest occurs in 20 cases. I want to put > >confidence intervals around that 0.40. > > > >I would appreciate any guidance. > > > >Sue > > > >Suzanne Griffin > >Wildlife Biology Program > >College of Forestry and Conservation > >University of Montana > >Missoula, MT 59812 > > > >~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > Phil >Novack-Gottshall >[EMAIL PROTECTED] > > Assistant Professor > Department of Geosciences > University of West Georgia > Carrollton, GA 30118-3100 > Phone: 678-839-4061 > Fax: 678-839-4071 > http://www.westga.edu/~pnovackg >~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Dave Hewitt VIMS, Gloucester Point, VA
