On 13 Aug 2014, at 20:49 , (Ted Harding) <ted.hard...@wlandres.net> wrote:
> Indeed, this topic has got me wondering how many times I may have > blindly used sd(x) in the past, as if it were going to give me the > standard (sum(x - mean(x))^2)/length(x) result! At the risk of flogging a horse that has been dead for the better part of a century, I don't think there is anything "standard" about an SD with a divisor of N, and the biasedness of the version with N-1 divisor is not really the crucial issue. Rather, the distinction is between - one sample from a known finite distribution - multiple samples from an unknown distribution and in particular between whether the mean is estimated or known. One argument for the N-1 divisor in the normal case is that you can transform data to one observation with unknown mean and N-1 independent observations with mean known to be 0. The variance estimate will be a function of the N-1 variables, and thus there is no reason to let the mere existence of the uninformative Nth variable change the estimator. Of course few people really care about N vs. N-1 but in larger linear models, it becomes N-p and p can be a sizeable fraction of N. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
