Having N samples, and then n degrees of freedom.
One degree of freedom is used (or taken) by the mean calculation.
Then when you calculate the variance or the standard deviation, you only have left n-1 degrees of freedom.
Regards,
Federico
At 8/25/2005 Thursday 05:06 PM, you wrote:
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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
--
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Otterbein College, Towers Hall 139, 1 Otterbein College
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From: Reza Nazarian [mailto:[EMAIL PROTECTED]]
Sent: Thursday, August 25, 2005 3:23 PM
To: [email protected]
Subject: [ai-geostats] Why degree of freedom is n-1
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
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