[Numpy-discussion] non-standard standard deviation

Bruce Southey bsouthey@gmail....
Sun Dec 6 20:12:58 CST 2009


On Sun, Dec 6, 2009 at 11:36 AM, Sturla Molden <sturla@molden.no> wrote:
> Colin J. Williams skrev:
>> When one has a smallish sample size, what give the best estimate of the
>> variance?
> What do you mean by "best estimate"?
>
> Unbiased? Smallest standard error?
>
>
>> In the widely used Analysis of Variance (ANOVA), the degrees of freedom
>> are reduced for each mean estimated,
> That is for statistical tests, not to compute estimators.
>
>
>
>
>
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Ignoring the estimation method, there is no correct answer unless you
impose various conditions like minimum-variance unbiased estimator
(http://en.wikipedia.org/wiki/Minimum_variance_unbiased) where usually
N-1 wins.

Anyhow, this is way off topic since it is totally in the realm of math stats.

Law of large numbers
(http://en.wikipedia.org/wiki/Law_of_large_numbers) just address that
the average not the variance so it is not directly applicable.

Bruce


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