On Thu, 30 Nov 2000 11:35:50 GMT, [EMAIL PROTECTED] wrote:
> who knows an answer to the following question?
> Let's assume that I take a sample of e.g. 100 people. I ask them a
> question and, e.g. 50% say "yes". I construct a 90%-confidence interval
> and get a standard error of 11.6. Fine.
>
> However, this assumes that the population size is unlimited.
> If the population was 100, then I would not have any standard error.
> However, what if the population size is 200? How do I construct a
> confidence interval then?
>
> Anybody with an idea?
This particular example has numbers that makes it easy. But I will
try to point to the principles involved, too.
You want to know the variance of C=A+B where
A= Yeses among 100 known responses, and
B= Yeses among 100 unknown responses, assumed to be wholly similar.
I hope you are familiar with computing "variances" and the general
formula that holds for uncorrelated variables,
Var(C) = Var(A) + Var(B)
- but Var(A)= 0 because it is the observed and FIXED count, and
Var(B)=
< the variance for 100 random cases, which happens to be known >.
If you want to compute the Finite Population variance estimate, you
need to frame your statistic like C, in a way that lets you combine
the fixed elements with the still-random elements.
So if you observed a SD of 11.6 Yeses for N=100, you will expect the
SD, in terms of Yeses, to be 11.6 for the next 100.
No matter how big your Population, your SD is the same 11.6 if there
are 100 responses (random ones) that are still unknown.
You may note that this fits the formula given in another post.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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