Date: Sep 5, 2011 3:50 AM
Author: Steven D'Aprano
Subject: Re: Which sample variance should I choose?
On Thu, 1 Sep 2011 06:30 pm Steven D'Aprano wrote:

> On Thu, 1 Sep 2011 04:34 am Paul wrote:

>

>> If you know the population mean, then

>> s2_1 = ?(x - ยต)^2 / n

>> is unbiased.

>>

>> If you don't know the population mean, then

>> s2_2 = ?(x - m)^2 / (n-1)

>> is unbiased, while

>> s2_3 = ?(x - m)^2 / n

>> is biased but nevertheless more accurate than s2_2.

>

> Thanks Paul, that's exactly the sort of thing I'm looking for.

>

> Not that I don't believe you :) but if you also have a reference

> (especially one that's online) that would be really helpful.

For the record, in case anyone else is interested, I've found a reference:

Press, W. H., Teukolsky, S.A., Vetterling, W.T., & Flannery, B.P.

(1992, 2nd Ed.). Numerical Recipes. Cambridge, MA: Cambridge University

Press.

quoted here:

http://www.visualstatistics.net/scaling/True and Unbiased Variance/True and Unbiased Variance.htm

--

Steven