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chisq.test with simulate.p.value=TRUE (PR#13292)

4 messages · constant at unb.br, Berwin A Turlach, Ben Bolker

Original
constant at unb.br
# 
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:
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
X-squared = 138.2898, df = NA, p-value = 1e-04
X-squared = 138.2898, df = NA, p-value = 1e-05
X-squared = 138.2898, df = NA, p-value = 1e-06
...

Also tested the same R version under Windows XP and got the same results.
1 day later
Berwin A Turlach
# 
G'day Reginaldo, 

On Sun, 16 Nov 2008 01:00:09 +0100 (CET)
constant at unb.br wrote:

            

      
      
      
    

        
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.

            

      
      
      
    

        
Cheers,

	Berwin

=========================== Full address =============================
Berwin A Turlach                            Tel.: +65 6516 4416 (secr)
Dept of Statistics and Applied Probability        +65 6516 6650 (self)
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      Ben Bolker
    

    

      
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<constant <at> unb.br> writes:

            

      
      
      
    

        
Could you explain why this is wrong?
The data are extremely unlikely under the null hypothesis
(the standard chisq.test() gives p<2.2e-16), so the result
of the simulation protocol is always 1/(B+1); that is, as
is standard with these protocols, the observed value is added
to the ensemble of simulations.
  Why is the p value "obviously incorrect"?

  cheers
   Ben Bolker

  
  


  


      

    

    
1 day later

    

      
      

        


  

        

      Ben Bolker
    

    

      
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<constant <at> unb.br> writes:

            

      
      
      
    

        
Tried to answer this the other day but the answer must
have gotten lost.  The standard analytical chi-squared test
here gives p<2.2e-16 (i.e. very very small).  The values given
above, up to limited display of significant digits, are
precisely 1/(B+1); that is, the simulated chi-squared values
are never less than the observed chi-squared statistic (the
observed value itself is included in the ensemble, so the
p-value is given as 1/(B+1) rather that <1/B; you can read
about the reasons for this elsewhere [?]).  Bottom line:
why do you think these results are "obviously incorrect"?

  Ben Bolker