Re: [Rd] [R] computing the variance

From: Thomas Lumley <tlumley_at_u.washington.edu>
Date: Mon 05 Dec 2005 - 21:18:06 GMT

>
> Using the biased variance just because it is the MLE (if that is the
> argument) seems confused to me. However, there's another point:
>
>> var(sample(1:3, 100000, replace=TRUE))
> [1] 0.6680556
>
> i.e. if we are considering x as the entire population, then the
> variance when sampling from it is indeed 1/N*E(X-EX)^2, which is why
> some presentations distinguish between the "population" and "sample"
> variances. We might want to support this distinction somehow.
>

We might also consider that the purpose of computing the variance is often to take the square root, and that using 1/(n-1) as the divisor does not give any particular optimality as an estimator of the standard deviation.

         -thomas



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