[R] Question about biasing in sd()???

[Peter Dalgaard]

"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