[R] Can I use "mcnemar.test" for 3*3 tables (or is there a bug in the command?)

[David Freedman]

There is a function mh_test in the coin package.  

library(coin)
mh_test(tt)

The documentation states, "The null hypothesis of independence of row and
column totals is tested. The corresponding test for binary factors x and y
is known as McNemar test. For larger tables, Stuart’s W0 statistic (Stuart,
1955, Agresti, 2002, page 422, also known as Stuart-Maxwell test) is
computed."

hth, david freedman


Tal Galili wrote:
> 
> Hello all,
> 
> I wish to perform a mcnemar test for a 3 by 3 matrix.
> By running the slandered R command I am getting a result but I am not sure
> I
> am getting the correct one.
> Here is an example code:
> 
> (tt <-  as.table(t(matrix(c(1,4,1    ,
>                             0,5,5,
>                             3,1,5), ncol = 3))))
> mcnemar.test(tt, correct=T)
> #And I get:
>         McNemar's Chi-squared test
> data:  tt
> McNemar's chi-squared = 7.6667, df = 3, p-value = *0.05343*
> 
> 
> Now I was wondering if the test I just performed is the correct one.
>>From looking at the Wikipedia article on mcnemar (
> http://en.wikipedia.org/wiki/McNemar's_test), it is said that:
> "The Stuart-Maxwell
> test<http://ourworld.compuserve.com/homepages/jsuebersax/mcnemar.htm>
> is
> different generalization of the McNemar test, used for testing marginal
> homogeneity in a square table with more than two rows/columns"
> 
>>From searching for a Stuart-Maxwell
> test<http://ourworld.compuserve.com/homepages/jsuebersax/mcnemar.htm>
> in
> google, I found an algorithm here:
> http://www.m-hikari.com/ams/ams-password-2009/ams-password9-12-2009/abbasiAMS9-12-2009.pdf
> 
>>From running this algorithm I am getting a different P value, here is the
> (somewhat ugly) code I produced for this:
> get.d <- function(xx)
> {
>   length1 <- dim(xx)[1]
>   ret1 <- margin.table(xx,1) - margin.table(xx,2)
>   return(ret1)
> }
> 
> get.s <- function(xx)
> {
>   the.s <- xx
>   for( i in 1:dim(xx)[1])
>   {
>     for(j in 1:dim(xx)[2])
>     {
>       if(i == j)
>       {
>         the.s[i,j] <- margin.table(xx,1)[i] + margin.table(xx,2)[i] -
> 2*xx[i,i]
>       } else {
>         the.s[i,j] <- -(xx[i,j] + xx[j,i])
>       }
>     }
>   }
>   return(the.s)
> }
> 
> chi.statistic <- t(get.d(tt)[-3]) %*% solve(get.s(tt)[-3,-3])  %*%
> get.d(tt)[-3]
> paste("the P value:", pchisq(chi.statistic, 2))
> 
> #and the result was:
>  "the P value: 0.268384371053358"
> 
> 
> 
> So to summarize my questions:
> 1) can I use "mcnemar.test" for 3*3 (or more) tables ?
> 2) if so, what test is being performed (
> Stuart-Maxwell<http://ourworld.compuserve.com/homepages/jsuebersax/mcnemar.htm>)
> ?
> 3) Do you have a recommended link to an explanation of the algorithm
> employed?
> 
> 
> Thanks,
> Tal
> 
> 
> 
> 
> 
> -- 
> ----------------------------------------------
> 
> 
> My contact information:
> Tal Galili
> Phone number: 972-50-3373767
> FaceBook: Tal Galili
> My Blogs:
> http://www.r-statistics.com/
> http://www.talgalili.com
> http://www.biostatistics.co.il
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
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> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 
> 

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