[R] Can I use "mcnemar.test" for 3*3 tables (or is there a bug in the command?)
Charles C. Berry
cberry at tajo.ucsd.edu
Sun Jul 19 21:26:18 CEST 2009
On Sun, 19 Jul 2009, Tal Galili wrote:
> Hello David,Thank you for your answer.
>
> Do you know then what does the "mcnemar.test" do in the case of a 3*3 table
> ?
print(mcnemar.test)
will show you what it does.
> Because the results for the simple example I gave are rather different (P
> value of 0.053 VS 0.73)
The test mcnemar.test() constructs is one of symmetry, which is equivalent
to marginal homogenity in hierarchical log-linear models as I recall from
Bishop, Fienberg, and Holland's 1975 opus on count data.
Stuart-Maxwell uses the dispersion matrix of marginal difference.
These are two different tests. I suspect that Stuart-Maxwell is less
susceptible to continuity issues in very sparse tables, which may account
for the difference you see here.
>
> In case the mcnemar can't really handle a 3*3 matrix (or more), shouldn't
> there be an error massage for this case? (if so, who should I turn to, in
> order to report this?)
Well, the code is pretty straightforward and
mcnemar.test(matrix(1:16,4))
returns 11.5495 which is correct.
It looks like there is nothing to report. 3,1,5), ncol = 3))))
Chuck
>
> Thanks again,
> Tal
>
>
>
>
>
> On Sun, Jul 19, 2009 at 3:47 PM, David Freedman <3.14david at gmail.com> wrote:
>
>>
>> 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]]
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>>
>>
>> --
>> View this message in context:
>> http://www.nabble.com/Can-I-use-%22mcnemar.test%22-for-3*3-tables-%28or-is-there-a-bug-in-the-command-%29-tp24556414p24556693.html
>> Sent from the R help mailing list archive at Nabble.com.
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
>
>
> --
> ----------------------------------------------
>
>
> 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]]
>
>
Charles C. Berry (858) 534-2098
Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901
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