From: Frank E Harrell Jr <f.harrell_at_vanderbilt.edu>

Date: Fri, 01 Jun 2007 07:11:50 -0500

*>
*

> 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
*

Date: Fri, 01 Jun 2007 07:11:50 -0500

jiho wrote:

> 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:

The issue is what is being assumed for N in the denominator of the variance formula, since the unbiased estimator subtracts one. Using normwt=TRUE means you are in effect assuming N is the number of elements in the data vector, ignoring the weights.

Frank Harrell

*> ---
*

> http://jo.irisson.free.fr/

*>
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-- Frank E Harrell Jr Professor and Chair School of Medicine Department of Biostatistics Vanderbilt University ______________________________________________ R-help_at_stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.Received on Fri 01 Jun 2007 - 12:26:00 GMT

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