[R] Why two chisq.test p values differ when the contingency

[(Ted Harding)]

On 15-Jul-03 Shi, Tao wrote:
> Hi, Ted and Dennis:
>  
> Thanks for your speedy replies!  I don't think this happens just
> randomly, rather, I'm thinking it may be due to the way chisq.test
> function handles simulation.  Here shows why: (Ted, I think there is an
> error in your code, "tx" should be t(x)  )

Not so -- I had already transposed them:
> x
     [,1] [,2]
[1,]  149  151
[2,]    1    8
> tx
     [,1] [,2]
[1,]  149    1
[2,]  151    8

Anyway, just to check, a third run (which as it happens follows straight
on from the ones previously reported since I had not used that instance
of R since) amd putting the new results alongside the previous ones:

> c2trx<-chisq.test(t(x), simulate.p.value=T, B=100000)$p.value
> for(i in (1:9)){c2trx<-c(c2trx,chisq.test(t(x), simulate.p.value=T,
B=100000)$p.value)}
> cbind(c2x,c2tx,c2trx)
          c2x    c2tx   c2trx
 [1,] 0.01627 0.01720 0.01628
 [2,] 0.01672 0.01690 0.01686
 [3,] 0.01662 0.01669 0.01706
 [4,] 0.01733 0.01656 0.01705
 [5,] 0.01679 0.01777 0.01633
 [6,] 0.01715 0.01769 0.01782
 [7,] 0.01765 0.01769 0.01688
 [8,] 0.01703 0.01740 0.01683
 [9,] 0.01704 0.01708 0.01689
[10,] 0.01669 0.01655 0.01721

Maybe Peter Dalgaard's suspicion is true, that one case is not being
counted. But this must be R-implementation/version-dependent. In my
case:
> version
         _                
platform i686-pc-linux-gnu
arch     i686             
os       linux-gnu        
system   i686, linux-gnu  
status                    
major    1                
minor    6.1              
year     2002             
month    11               
day      01               
language R                

Ted.


> 
>> x
>      [,1] [,2]
> [1,]  149  151
> [2,]    1    8
>> c2x<-chisq.test(x, simulate.p.value=T, B=100000)$p.value
>> for(i in (1:20)){c2x<-c(c2x,chisq.test(x, simulate.p.value=T,
> +                        B=100000)$p.value)}
>> c2tx<-chisq.test(t(x), simulate.p.value=T, B=100000)$p.value
>> for(i in (1:20)){c2tx<-c(c2tx,chisq.test(t(x), simulate.p.value=T,
> +                         B=100000)$p.value)}
>> cbind(c2x,c2tx)
>           c2x    c2tx
>  [1,] 0.03727 0.01629
>  [2,] 0.03682 0.01662
>  [3,] 0.03671 0.01665
>  [4,] 0.03788 0.01745
>  [5,] 0.03706 0.01646
>  [6,] 0.03715 0.01728
>  [7,] 0.03664 0.01683
>  [8,] 0.03681 0.01720
>  [9,] 0.03742 0.01758
> [10,] 0.03712 0.01685
> [11,] 0.03739 0.01615
> [12,] 0.03811 0.01653
> [13,] 0.03711 0.01673
> [14,] 0.03639 0.01678
> [15,] 0.03714 0.01719
> [16,] 0.03774 0.01780
> [17,] 0.03574 0.01707
> [18,] 0.03661 0.01705
> [19,] 0.03751 0.01711
> [20,] 0.03683 0.01718
> [21,] 0.03678 0.01653
>  
>  
>  
> ...Tao
>  
> ============================================================
> Ted.Harding at nessie.mcc.ac.uk wrote:
> On 15-Jul-03 Tao Shi wrote:
>>>x
>> [,1] [,2]
>> [1,] 149 151
>> [2,] 1 8
>>>t(x)
>> [,1] [,2]
>> [1,] 149 1
>> [2,] 151 8
>>>chisq.test(x, simulate.p.value=T, B=100000)
>> Pearson's Chi-squared test with simulated p-value (based on
>> 1e+05 replicates)
>> data: x
>> X-squared = 5.2001, df = NA, p-value = 0.03774
>> 
>>>chisq.test(t(x), simulate.p.value=T, B=100000)
>> Pearson's Chi-squared test with simulated p-value (based on
>> 1e+05 replicates)
>> data: t(x)
>> X-squared = 5.2001, df = NA, p-value = 0.01642
> 
> Possibly you may just have been unlucky, though the 0.03774 seems
> large:
> 
> c2x<-chisq.test(x, simulate.p.value=T, B=100000)$p.value
> for(i in (1:9)){c2x<-c(c2x,chisq.test(x, simulate.p.value=T,
> B=100000)$p.value)}
> c2tx<-chisq.test(tx, simulate.p.value=T, B=100000)$p.value
> for(i in (1:9)){c2tx<-c(c2tx,chisq.test(tx, simulate.p.value=T,
> B=100000)$p.value)}
> cbind(c2x,c2tx)
> c2x c2tx
> [1,] 0.01627 0.01720
> [2,] 0.01672 0.01690
> [3,] 0.01662 0.01669
> [4,] 0.01733 0.01656
> [5,] 0.01679 0.01777
> [6,] 0.01715 0.01769
> [7,] 0.01765 0.01769
> [8,] 0.01703 0.01740
> [9,] 0.01704 0.01708
> [10,] 0.01669 0.01655
> 
> sd(c2x)
> [1] 0.0003946715
> sd(c2tx)
> [1] 0.0004737099
> 
> Ted.
> 
> 
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> E-Mail: (Ted Harding) 
> Fax-to-email: +44 (0)870 167 1972
> Date: 15-Jul-03 Time: 21:00:04
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E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 167 1972
Date: 16-Jul-03                                       Time: 01:30:59
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