Hi All,
I would like to prove the followin situation algebraically:
I have a random sample X1, X2, X3, ...., XN with grand mean M, standard
deviation S and standard error SE_N=S/sqrt(N)
I divide my sample into P partitions and compute the means of each partition
m1, m2, ..., mP. Define M'=mean(m1, m2, ..., mP), the mean of the means,
which is simply the grand mean i.e. M'=M. Let S_P be the standard deviation
of these P partition means and SE_P=S_P/sqrt(P) the standard error (of M').
Clearly As P-> N SE_P -> SE_N in other words
As P-> N S_P/sqrt(P) -> S/sqrt(N) [1]
I would like to demonstrate [1] algebraically and also determine the rate of
convergence
Many thanks in advance for your help
regards,
Richard.
_________________________________________________________________
Express yourself instantly with MSN Messenger! Download today - it's FREE!
http://messenger.msn.click-url.com/go/onm00200471ave/direct/01/
|