Donald, I totally agree w/your point about the stratification of the sample. My facts were set up merely for simplicity's sake notwithstanding their clear artificiality.
The only instances of multiple samples I have seen are in textbooks to prove the CLT; that w/increasing numbers of sample means, the distribution (of sample means) becomes normal even if the population isn't. Statistics is a relatively new area study for me and I never would have intuitively thought that a sample of a few thousand could reveal such meaningful results. But I understand your point completely. I suppose like you say that when you factor in stratification and clustering, it isn't such a no brainer as in my example. Thank you again for enlightening me. "Donald Burrill" <[EMAIL PROTECTED]> wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... > 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 > > > ------------------------------------------------------------------------ > Donald F. Burrill [EMAIL PROTECTED] > 184 Nashua Road, Bedford, NH 03110 603-471-7128 > > > > ================================================================= > Instructions for joining and leaving this list and remarks about > the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ > ================================================================= ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
