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 <3.14da...@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
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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
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