# RE: [R] Question about biasing in sd()???

From: Liaw, Andy <andy_liaw_at_merck.com>
Date: Thu 10 Mar 2005 - 00:55:01 EST

Where in the help file of sd() do you see the claim that it produces unbiased estimate? Try the following:

sample.sizes <- 3:30
reps <- 5000
set.seed(1)
mean.vars <- sapply(sample.sizes,

```                    function(n) mean(sd(matrix(rnorm(n*reps), nc=reps))^2))
```
plot(sample.sizes,mean.vars)

I.e., the sample variance, or sd()^2, is unbiased for the true variance. If U is an unbiased estimator of a parameter theta, f(U) is _not_ necessarily unbiased for f(theta). It would be if f() is linear.

Andy

> From: Roy Werkman
>
> 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()?
>
> Thanx,
> Roy
>
>
> --
> The information contained in this communication and any\ >...{{dropped}}

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