Rich Ulrich <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
[ snip, previous] > Okay. I think you are asking about describing a small fraction, > and putting a Confidence Limit around it. That part of the > problem, the numeric part, is not too hard. That's it > For a small proportion, we can consider the "counts" to be > numbers that are distributed as Poisson: And in that case, > the square root of the count is very close to being "normal" > with standard error of 1/2. >From my small knowledge, it looks like an application of the Central Limit theorem. The distribution of the sample's means is closing to a "normal" distribution, whatever the distribution of the population is. > Next step: the usual 95% CI is built by taking > the mean, +/- twice the SE -- which would > thus be +/- 1.0 added to the square root of the count. Does SE means Square Error ? > Example: If the Poisson count (something under 20% of > what was sampled) is 25, then the 95% CI on counts > is (16, 36) since that is the range implied by 5.0 +/- 1.0 . > > You write the CI most readily on 'counts' but it translates > directly to fractions. It works as 25 out of 500, or out > of 5000, or whatever. Thanks for this easy method. I can apply it whenever without complicating my mind with big numbers! On my side, I have continued my research with this Central Limit Theorem. I was wondering if your reasoning had the same basis. Here is what I have found : The Central Limit theorem gives us this relation : The standard deviation 's' of the sample (n items) can be linked to the standard deviation 'S' of the population (N items) by the following rule : s = S/square root(n) * square root((N-n)/N-1)) The term (square root((N-n)/N-1))) is enough close to 1 to be dropped if n/N<1/7 AND n>30. In this case, the result would depend on the count (n)! I am then using the "reduced normal law" to set the CI... With my deepest thanks, Louis Tillier. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
