(N-n)/(N-1) is also called the fpc (finite population correction). This is useful in some forensic, administrative, and evaluation contexts where the research question is strictly limited to the pop in the urn. In many research contexts the research question is NOT strictly limited to "this urn".
Hope this helps. Art [EMAIL PROTECTED] Social Research Consultants University Park, MD USA (301) 864-5570 Jason Owen wrote: > Suppose an urn contains N balls that are green and red. You want > to estimate p = proportion of green balls. You could: > > 1) Sample n balls with replacement and calculate > phat1 = sample proportion of green balls. > > 2) Sample n balls without replacement and calculate > phat2 = sample proportion of green balls. > > But, comparing the variances of the estimators: > > Var(phat1) = p(1-p)/n > Var(phat2) = p(1-p)/n * (N-n)/(N-1) > > Thus, it is always the case that sampling without replacement > leads to an estimator with a smaller variance. This may surprise > some folks. > > Jason . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
