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Topic: Which sample variance should I choose?
Replies: 7   Last Post: Sep 5, 2011 3:50 AM

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 Steven D'Aprano Posts: 21 Registered: 3/22/11
Re: Which sample variance should I choose?
Posted: Sep 5, 2011 3:50 AM

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 - µ)^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

Date Subject Author
8/31/11 Steven D'Aprano
8/31/11 leoldv
8/31/11 Richard Ulrich
8/31/11 Paige Miller
8/31/11 Steven D'Aprano
8/31/11 paulvonhippel at yahoo
9/1/11 Steven D'Aprano
9/5/11 Steven D'Aprano