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Reply #67: True when population size is much larger than sample size. [View All]

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thanatonautos Donating Member (282 posts) Send PM | Profile | Ignore Sun Jan-16-05 04:00 AM
Response to Reply #59
67. True when population size is much larger than sample size.
This is just nitpicking, but anyway.

If n=1,000, and the polling universe is N=1,000,
then clearly the margin of error is zero, since
all entries in the list have been sampled.

The intuitive belief is actually therefore correct:
when the sample size approaches the size of the
polling universe.

Nevertheless, your approximation for the margin of
error is extremely accurate for the cases you list,
namely n=1000, or n=10,000, with N=10^6, N=10^7, N=10^8.

When n approaches a significant fraction of N, however,
there are finite population corrections to consider.

A conservative estimate of the standard error in
a sample percentage, sampling without replacement
from a list of zeros and ones, for a sample of size n
from a list of size N is that the standard error in
the sample is no greater than:

sigma = f * 50%/(n^1/2), with f = ((N - n)/(N - 1))^(1/2)

For your cases, we have:

(n=1000, N=10^6) f=0.99950037
(n=1000, N=10^7) f=0.99995005
(n=1000, N=10^8) f=0.999995

(n=10000, N=10^6) f=0.9949873
(n=10000, N=10^7) f=0.9994999
(n=10000, N=10^8) f=0.99995

So finite population size corrections to your estimate
of the mean sample error are not very large at all in
any of the cases you mention: the largest being 0.25% for
the case n=10000, N=10^6.

(These are only upper bounds, one can certainly do better
by using the sample itself to estimate the standard
deviation of the whole list.)

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