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Reza,

If you are just asking why n-1 in the formula commonly found in stat books for computing the sample variance s^2, it is so that we have an unbiased estimate of the population variance – look at a good calculus based probability and stat book.

Other estimation methods (e.g., maximum likelihood) divide by n instead of n-1.

Oh, while the n-1 does make the sample variance s^2 an unbiased estimate of the population variance sigma^2, taking the square root and getting the sample standard deviation s does not result in an unbiased estimated of the population standard deviation sigma. Another reason some prefer m.l.e.

Best,

Bill

--

William V Harper, Mathematical Sciences

Otterbein College, Towers Hall 139, 1 Otterbein College

Westerville OH 43081-2006 USA

Office phone: 614-823-1417 Office Fax 614-823-3201

Faculty page: http://www.otterbein.edu/home/fac/WLLVHRPR

For the best in geostatistics: http://geoecosse.hypermart.net/

**From:**Reza Nazarian [mailto:rnazarian@...]

**Sent:**Thursday, August 25, 2005 3:23 PM

**To:**ai-geostats@...

**Subject:**[ai-geostats] Why degree of freedom is n-1Dear Experts

Sorry may be the question is so basic .After searching my statistics books to find an answer with no great success, could you please explain me why we consider degree of freedom as**n-1**in calculating variance. Thanks for your kind advises.

Very Best Regards

Reza Nazarian

Schlumberger Information Solutions

SONILS Oil Services Centre, Porto de Luanda , Angola

(Via UK : +44 (0)207 576 6306

* rnazarian@...

__http://www.sis.slb.com__ - View SourceDear Reza

I was away from my office for quite a while. After surfing my folder, I

came across your enquiry. I found it helpful to share the following

thoughts with you and other colleagues over the list.

I prefer to approach your question from another angle.

At first, one has to acknowledge that almost all measurements are

corrupted by noise in one way or another. Furthermore, standard deviation is a

measure uncertainty in measurement. Now, keeping These points in mind, look

at the relation for calculating the standard deviation or for that matter

variance when you have only ONE measurement. If you use

the relation with n in the denominator, then you would get 0 for standard

deviation implying your single measurement is exact and not corrupted by

noise which is not true. On the other hand, relation with n-1 in the

denominator would give you 0/0 which is indeterminate more compatible with

preliminary propositions mentioned above.

Another useful question might be the origin of that equation which has

something to do with Normal probability distribution. The first chapter of

"Nonlinear parameter estimation by Bard (1974)" might be useful to refer

to as he was resorting to Entropy to derive Normal distribution and its

associated parameters.

Hope this helps.

Thanks

Abedini

On Thu, 25 Aug 2005, Reza Nazarian wrote:

> Dear Experts

> Sorry may be the question is so basic .After searching my statistics books to

> find an answer with no great success, could you please explain me why we

> consider degree of freedom as n-1 in calculating variance. Thanks for your

> kind advises.

>

>

> Very Best Regards

> Reza Nazarian

> Schlumberger Information Solutions

> SONILS Oil Services Centre, Porto de Luanda, Angola

>

> (Via UK: +44 (0)207 576 6306

> * rnazarian@...

> http://www.sis.slb.com

>