## Re: [ai-geostats] Why degree of freedom is n-1

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• Dear 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
Message 1 of 7 , Sep 17, 2005
Dear 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