Raul Miller wrote: > On 6/26/07, Oleg Kobchenko <[EMAIL PROTECTED]> wrote: >> Although in correlation the n-1 cancel out, statistical stddev >> and cov should use sample variance, as the estimated mean is >> used in E(X-E(X))^2 is one less degree of freedom. > > I am rather dubious of any context where that's a significant > issue. >
Actually, you have to rely on this: the sample variance with (n-1) in the denominator is an unbiased estimator of the population variance: with denominator n, it is not. This can be "explained" in terms of degrees of freedom as Oleg suggests: the idea is that if you know x1,...,sn as well as the sample mean m, you have one redundant piece of information. Correct reasoning using degrees of freedom is like voodoo, however. You know that the sum of the squares of the deviation from the sample mean is greater or equal to the sum of the squares of the deviation from the population mean. If you go through the not very enlightening calculation, you find that the discrepancy is accounted for by a factor of n % n-1. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
