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Question about biasing in sd()???
2 messages · Roy Werkman, 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