From tlumley at u.washington.edu  Mon Dec  5 22:18:06 2005
From: tlumley at u.washington.edu (Thomas Lumley)
Date: Mon, 5 Dec 2005 13:18:06 -0800 (PST)
Subject: [Rd] [R] computing the variance
In-Reply-To: <x2fyp7mj9f.fsf@turmalin.kubism.ku.dk>
References: <4393FFEC.3040008@bii-sg.org>
	<4394071F.5080509@statistik.uni-dortmund.de>
	<17300.33408.391936.240032@stat.math.ethz.ch>
	<x2fyp7mj9f.fsf@turmalin.kubism.ku.dk>
Message-ID: <Pine.LNX.4.64.0512051316470.14262@homer24.u.washington.edu>

>
> 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



[Rd] [R] computing the variance
Thomas Lumley