[Rd] chisq.test with simulate.p.value=TRUE (PR#13292)
Berwin A Turlach
berwin at maths.uwa.edu.au
Mon Nov 17 09:23:03 CET 2008
G'day Reginaldo,
On Sun, 16 Nov 2008 01:00:09 +0100 (CET)
constant at unb.br wrote:
> Full_Name: Reginaldo Constantino
> Version: 2.8.0
> OS: Ubuntu Hardy (32 bit, kernel 2.6.24)
> Submission from: (NULL) (189.61.88.2)
>
>
> For many tables, chisq.test with simulate.p.value=TRUE gives a p
> value that is obviously incorrect and inversely proportional to the
> number of replicates:
Why is this Monte-Carlo p-value obviously incorrect?
In your example, did you look at the observed ChiSquare statistics?
Any idea how likely it is to observe a value that is at least as
extreme as the one observed?
Essentially, you are doing B Monte-Carlo simulations and in none of
these simulations do you obtain a statistic that is at least as extreme
as the one that you have observed. So your Monte-Carlo p-value ends up
to be 1/(B+1).
I do not see any problem or bug here.
> > data(HairEyeColor)
> > x <- margin.table(HairEyeColor, c(1, 2))
> > chisq.test(x,simulate.p.value=TRUE,B=2000)
> Pearson's Chi-squared test with simulated p-value (based on
> 2000 replicates)
> data: x
> X-squared = 138.2898, df = NA, p-value = 0.0004998
>
> > chisq.test(x,simulate.p.value=TRUE,B=10000)
> X-squared = 138.2898, df = NA, p-value = 1e-04
>
> > chisq.test(x,simulate.p.value=TRUE,B=100000)
> X-squared = 138.2898, df = NA, p-value = 1e-05
>
> > chisq.test(x,simulate.p.value=TRUE,B=1000000)
> X-squared = 138.2898, df = NA, p-value = 1e-06
> ...
>
> Also tested the same R version under Windows XP and got the same
> results.
Cheers,
Berwin
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