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Topic: Re: Standard error of variance
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Jack Tomsky

Posts: 1,834
Registered: 12/18/04
Re: Standard error of variance
Posted: Sep 10, 2013 10:57 PM
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For a normal distribution, using the results in http://web.eecs.umich.edu/~fessler/papers/files/tr/stderr.pdf, suppose the sample standard deviation if defined by s = sqrt(s^2).

Then the exact standard error of s is

SE(s) = sigma*sqrt(V)/sqrt(N-1),

where V = 2*[{(N-1)/2} - {Gamma(N/2)/Gamma((N-1)/2)}^2]
sigma is the population sigma and Gamma is the gamma function.

For N large, SE(s) is approximately

SE(s) ~~ sigma/sqrt(2(N-1))

Note that the standard error of s is proportional to sigma.



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