[R] Different value between R variance and definition of variance
Daniel Nordlund
res90sx5 at verizon.net
Wed Nov 28 17:19:45 CET 2007
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf
> Of Tine
> Sent: Wednesday, November 28, 2007 12:57 AM
> To: r-help at r-project.org
> Subject: [R] Different value between R variance and definition of variance
>
> Hi!
>
> Let us define random variable:
> > x = seq(0,1,length=100)
>
> If we calculate variance following definition E[(x-E(x))^2] we get:
> > mean( (x - mean(x))^2 ) # == mean(x^2) - mean(x)^2
> 0.08501684
>
> And if we use internal R function var:
> > var(x)
> 0.08587559
>
> Can anyone tells me why the difference?
>
I haven't seen a response, so I will chime in. R calculates an unbiased estimate of the population variance from which your x is assumed to be a simple random sample of size n (in your case n=100). See any basic book on statistics. So, using your formula, R "in effect" calculates
mean((x-mean(x)^2) * n/(n-1)
Hope this is helpful,
Dan
Daniel Nordlund
Bothell, WA USA
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