[R] Question about biasing in sd()???
Peter Dalgaard
p.dalgaard at biostat.ku.dk
Wed Mar 9 15:04:51 CET 2005
"Roy Werkman" <roy.werkman at asml.com> writes:
> Hi,
>
> Can anyone help me with the following. I have been using R for Monte
> Carlo simulations and got some results I couldn't explain. Therefor I
> performed following short test:
>
> --------------
> mean.sds <- NULL
> sample.sizes <- 3:30
>
> for(N in sample.sizes){
> dum <- NULL
> for(I in 1:5000){
> x <- rnorm(N,0,1)
> dum <- c(dum,sd(x))
> }
> mean.sds<- c(mean.sds,mean(dum))
> }
> plot(sample.sizes,mean.sds)
> --------------
>
> My question is why don't I get 1 as a result from my sd() for small
> sample sizes? According to the help, sd() is unbiased, which anyway
> would not explain the small offset... Is it something in rnorm()?
According to *what* help? In ?sd, it isn't there and it wouldn't be
true if it was there. Please don't spread rumors like that.
The _variance_, var(x) is unbiased, and sd(x) is the square root of
that. It is not possible for a concave function of an unbiased
estimator to be unbiased (unless you're talking median unbiasedness
which is clearly not the case). This is first-year math-stat theory.
--
O__ ---- Peter Dalgaard Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics 2200 Cph. N
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
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