Aldi,
Your concept of sample is different from mine.
I would expect with replacement to be equivalent for a for loop of sampling
without replacement.
samples <- 1:400
for (i in 1:400) samples[i] <- sample(c(0,1,2),1 ,prob=c(0.02 ,0.93 ,0.05 ))
Sampling without replacement:
first : sample(c(0,1,2),1 ,prob=c(0.02 ,0.93 ,0.05 ))
second: depending on first (suppose 2 was selected)
sample(c(0,1),1 ,prob=c(0.02 ,0.93)/.95)
third: whatever is remaining with probability 1.
n.b. the second is equivalent to sample(c(0,1),1 ,prob=c(0.02 ,0.93)), since
sample normalized the probabilities itself.
Concerning your result:
observed <- c(0.0200, 0.9225, 0.0575 )*400
expected <- c(0.02 ,0.93 ,0.05 )*400
stat <- sum((observed-expected)^2/expected)
pchisq(stat,2,lower=FALSE)
[1] 0.788915
Seems ok to me.
Cheers,
Kees
On Saturday 30 December 2006 16:55, Aldi Kraja wrote:
> Partial Summary and discussion:
> =====================
> Thank you to Chao Gai, Chuck Cleland, and Jim Lemon for their suggestion
> to use replace=T in R.
> There is a problem though (see below)
>
> In the Splus7, sample is defined as
> -------------
> sample(x, size = n, replace = F, prob = NULL, n = NULL, ...) where
> replace=F
> In Splus7
>
> xlrmN1 <- sample(c(0,1,2),400 ,prob=c(0.02 ,0.93 ,0.05 ))
>
> and the
>
> table(xlrmN1)/400
> 0 1 2
> 0.02 0.93 0.05
> show that "sample" is working exactly as expected based on the prob vector.
>
> When "sample" is used in Splus7 with replacement we see the following
>
> result:
> > xlrmN1 <- sample(c(0,1,2),400 ,replace=T,prob=c(0.02 ,0.93 ,0.05 ))
> > table(xlrmN1)/400
>
> 0 1 2
> 0.0125 0.925 0.0625
> which I think is working again as expected.
>
> In the R, sample is defined as
> ---------
>
> sample(x, size, replace = FALSE, prob = NULL)
>
> So the above statement with replace=F did not work (reported error)
> but with replace=T produced,
>
> > table(xlrmN1)/400
>
> xlrmN1
> 0 1 2
> 0.0200 0.9225 0.0575
>
> which is not exactly the sample with the probabilities provided
> (0.02,0.93,0.05)
>
> Now let's return to the concept of replace=F and replace=T.
> When I ask "sample" to select a sample of 400 from a vector of 3 with NO
> replacement, I would think the following a). create a very large sample
> from 0, 1, and 2. b). From this large sample, based on the prob vector
> select without replacement. c). As result I expect the probability of
> selected sample to be exactly the same with the prob vector (As in Splus7)
>
> When I ask "sample" to select a sample of 400 from a vector of 3 with
> replacement, I would think the following a). create a very large sample
> from 0, 1, and 2. b). From this large sample, based on the prob vector
> select with replacement, which means some of the previous selected 0, 1, 2
> can be selected again. c). As result I expect the probability of selected
> sample to be NOT exactly the same with the prob vector (As in Splus7 and
> R).
>
> So there are two conclusions: "sample" in R is not working correct, OR I am
> missing some precision as a rounding error to produce
>
> prob=c(0.02 ,0.93 ,0.05 ).
> Am I misunderstanding the "sample" function in R?
>
> Any suggestions are appreciated.
> TIA,
>
> Aldi
>
> Aldi Kraja wrote:
> >Hi,
> >In Splus7 this statement
> >xlrmN1 <- sample(c(0,1,2),400 ,prob=c(0.02 ,0.93 ,0.05 ))
> >worked fine, but in R the interpreter reports that the length of the
> >vector to chose c(0,1,2) is shorter than the size of many times I want
> >to be selected from the vector c(0,1,2).
> >Any good reason?
> >See below the error.
> >
> > > xlrmN1 <- sample(c(0,1,2),400 ,prob=c(0.02 ,0.93 ,0.05 ))
> >
> >Error in sample(length(x), size, replace, prob) :
> > cannot take a sample larger than the population
> > when 'replace = FALSE'
> >Execution halted
> >
> >TIA,
> >
> >Aldi
> >
> >--
>
> --
>
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