R help - Nov 2007 - 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?

Hi!


maybe because sample variance has N-1 at the denominator (say degrees of
freedom)?

so

all.equal((sum(x^2) - 100*mean(x)^2)/99, var(x)) ## TRUE 

but

(sum(x^2) - 100*mean(x)^2)/100 # == your value


Stef

On Wed, Nov 28, 2007 at 09:56:58AM +0100, Tine wrote:
<Tine>Hi!
<Tine>
<Tine>Let us define random variable:
<Tine> > x = seq(0,1,length=100)
<Tine>
<Tine>If we calculate variance following definition E[(x-E(x))^2] we get:
<Tine> > mean( (x - mean(x))^2 ) # == mean(x^2) - mean(x)^2
<Tine>0.08501684
<Tine>
<Tine>And if we use internal R function var:
<Tine> > var(x)
<Tine>0.08587559
<Tine>
<Tine>Can anyone tells me why the difference?
<Tine>
<Tine>______________________________________________
<Tine>R-help a r-project.org mailing list
<Tine>https://stat.ethz.ch/mailman/listinfo/r-help
<Tine>PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
<Tine>and provide commented, minimal, self-contained, reproducible code.

> -----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