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2208Re: [ai-geostats] Why degree of freedom is n-1

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  • M.J. Abedini
    Sep 17, 2005
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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 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.


      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
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