Re: Sampling question
- From: Bruce Weaver <bweaver@xxxxxxxxxxxx>
- Date: Thu, 12 Jul 2007 21:20:34 -0400
sci.stat.math wrote:
A simple question for experts but I'm a novice so excuse my
ignorance...Suppose I have a huge population of recordings of certain
values for each individual (eg: ratio of height/weight of individuals,
body fat % etc) and from that I would like to take a sample that
represents the population. My questions:
Should sampling be with or without replacement?
How do I determine what is a good size of the sample to have a good
enough estimate of the population? is there a specific formula or
test?
Thanks
When you sample from a "huge" population, there is very little practical difference between sampling with and without replacement (assuming the sample is small relative to the population). Let N be the size of the huge population, n the size of the sample, and p the probability of any element being drawn. When you sample randomly *with* replacement, p = 1/N on each draw. If you sample randomly *without* replacement, p = 1/N on the first draw, 1/(N-1) on the second draw, 1/(N-2) on the 3rd draw, and so on until 1/(N-n+1) for the last draw. Of course, those probabilities are for elements not yet drawn; once an element has been drawn, its probability of being drawn again becomes 0. The point is that if N is huge, 1/(N-n+1) does not differ substantially from 1/N.
--
Bruce Weaver
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir
"When all else fails, RTFM."
.
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