On Sun, 30 Sep 2001, John Jackson wrote:
> Here is my solution using figures which are self-explanatory:
>
> Sample Size Determination
>
> pi = 50% central area 0.99
> confid level= 99% 2 tail area 0.5
> sampling error 2% 1 tail area 0.025
> z =2.58
> n1 4,146.82 Excel function for determining central interval
> NORMSINV($B$10+(1-$B$10)/2)
> n 4,147
>
> The algebraic formula for n was:
>
> n = pi(1-pi)*(z/e)^2
>
>
> It is simply amazing to me that you can do a random sample of 4,147
> people out of 50 million and get a valid answer.
It is not clear what part of this you find "amazing".
(Would you otherwise expect an INvalid answer, in some sense?)
Thme hard part, of course, is taking the random sample in the first
place. The equation you used, I believe, assumes a "simple random
sample", sometimes known in the trade as a SRS; but it seems to me
VERY unlikely that any real sampling among the ballots cast in a
national election would be done that way. I'd expect it to involve
stratifying on (e.g.) states, and possibly clustering within states;
both of which would affect the precision of the estimate, and therefore
the minimum sample size desired.
As to what may be your concern, that 4,000 looks like a small
part of 50 million, the precision of an estimate depends principally
on the amount of information available -- that is, on the size of the
sample; not on the proportion that amount bears to the total amount
of information that may be of interest. Rather like a hologram, in
some respects; and very like the resolving power of an optical
instrument (e.g., a telescope), which is a function of the amount of
information the instrument can receive (the area of the primary lens
or reflector), not on how far away the object in view may be nor what
its absolute magnitude may be.
> What is the reason for taking multiple samples of the same n -
> to achieve more accuracy?
I, for one, don't understand the point of this question at all.
Multiple samples? Who takes them, or advocates taking them?
< snip, the rest >
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Donald F. Burrill [EMAIL PROTECTED]
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