Xiao --
> My question is why isn't there a N variable in our equation for
> SD(p^)?
Basically, because it makes the formula longer and doesn't change the result very
much. The actual formula is:
SD(p^) = root{[(p^(1-p^))/n]*(1 - n/N)}.
When n is "sufficiently small" it is typically ignored.
Hope this helps!
-- Chris
Chris Olsen
George Washington High School
2205 Forest Drive SE
Cedar Rapids, IA
(319)-398-2161
> -----Original Message-----
> From: Xiao Li [mailto:[EMAIL PROTECTED]
> Sent: Friday, January 30, 2004 8:39 PM
> To: [EMAIL PROTECTED]
> Subject: [edstat] Why does sample proportion SD have no N?
>
>
> Let N be the population size. Let p denote the proportion of this
> population with a certain characteristic (ie. has diabetes, divorced,
> homosexual, etc.) Let's say we are trying to estimate p using a
> sample of size n. So we collect our sample and calculate p^ to be the
> proportion of elements in our sample with our characteristic of
> interest. Then we calculate the standard of deviation of p^ (also
> known as the standard error) because it gives us an idea of how close
> our sample proportion is to the real proportion.
>
> Now, my statistics textbook says the standard of deviation is given by
> SD(p^) = root[(p^(1-p^))/n] when sampling with replacement or when
> the sample size is significantly smaller than the population size.
>
> My question is why isn't there a N variable in our equation for
> SD(p^)? According to this formula, if we are trying to figure out the
> proportion of people with diabetes in Berkeley, California with sample
> size n, we would get the same standard of error as if we are trying to
> figure out the proportion of people with diabetes in the world with
> sample size n. (In the former, the N is a lot smaller than in the
> later).
> .
> .
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