On Apr 14, 3:05 am, Richard Ulrich <Rich.Ulr...@comcast.net> wrote:
On Fri, 11 Apr 2008 07:55:31 -0700 (PDT), Beorne <matteo...@gmail.com
wrote:
Having a total population of n we check for abnormalities ('yes' or
'no') on a sample of size s (< n).
We found that x of the s samples are abnormal ('yes')
What is the formulae that connects the precision of the x/s estimate
of probability p of abnormalities to the sample/population ratio s/n ?
Are you looking for the formula for the "Finite Population"
correction for the standard deviation? You can Google
for that, I'm pretty sure. It assumes that the measured
fraction is exact (zero variance), and that the residual has
the mean and variance of what has been measured so far.
That is how I would figure it, since it works out in general,
for various models.
The safer thing is somewhat cruder -- Take the standard
deviation of the sample, and the confidence interval,
and inflate it to the full N. This is also the proper measure
when general inference is being implied, to other populations
or to the future. The FPC is used on election eve when
predicting the rest of the vote (also, taking into account
which districts are not-in).
--
Rich
Ulrichhttp://www.pitt.edu/~wpilib/index.html
Yes, i assume it is a finite population correction. The other thing I
noted is that the p +- 1.96 * Sqrt( p*(1-p)/s ) formulae assumes
binomuial distribution can be simplified as normal distribution, ut in
my case that n*p is almost zero so this approximation is untrue.
I tought this formulae would be very easy to find, since is the basic
formulae to justify sampling size in defect control process, but I
have some problem finding it and its theoretic framework.
Thanks
