[R] Problem with Weighted Variance in Hmisc

[jiho]

On 2007-June-01  , at 01:03 , Tom La Bone wrote:
> The function wtd.var(x,w) in Hmisc calculates the weighted variance  
> of x
> where w are the weights.  It appears to me that wtd.var(x,w) = var 
> (x) if all
> of the weights are equal, but this does not appear to be the case. Can
> someone point out to me where I am going wrong here?  Thanks.

The true formula of weighted variance is this one:
	http://www.itl.nist.gov/div898/software/dataplot/refman2/ch2/ 
weighvar.pdf
But for computation purposes, wtd.var uses another definition which  
considers the weights as repeats instead of true weights. However if  
the weights are normalized (sum to one) to two formulas are equal. If  
you consider weights as real weights instead of repeats, I would  
recommend to use this option.
With normwt=T, your issue is solved:

 > a=1:10
 > b=a
 > b[]=2
 > b
[1] 2 2 2 2 2 2 2 2 2 2
 > wtd.var(a,b)
[1] 8.68421
# all weights equal 2 <=> there are two repeats of each element of a
 > var(c(a,a))
[1] 8.68421
 > wtd.var(a,b,normwt=T)
[1] 9.166667
 > var(a)
[1] 9.166667

Cheers,

JiHO
---
http://jo.irisson.free.fr/