On Jul 19, 2009, at 6:09 PM, Tal Galili wrote:
Hello Charles,
Thank you for the detail reply.
I am still left with the leading question which is: which test
should I use
when analyzing the 3 by 3 matrix I have? The mcnemar.test or the
mh_test?
Is the one necessarily better then the other?
Please define "better".
(for example for
sparser matrices ?)
That does not help.
What about:
mh_test(as.table(matrix(1:16,4)))
It returns a very significant result:
chi-squared = 11.4098, df = 3, p-value = 0.009704
Where as "mcnemar.test(matrix(1:16,4))", didn't:
McNemar's chi-squared = 11.5495, df = 6, p-value = 0.0728
So which one is "right" ?
And now ... define "right".
(from the looks of it, the mh_test is doing much better)
Perhaps from the perspective of a statistically naive reviewer.
Should the strategy be to try and use both methods, and start
digging when
one doesn't sit well with the other?
I am reminded of Jim Holtam's tag line: "What problem are you trying
to solve?"
Thanks,
Tal
On Sun, Jul 19, 2009 at 10:26 PM, Charles C. Berry <cbe...@tajo.ucsd.edu
>wrote:
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, StuartÂ’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:
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Phone number: 972-50-3373767
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My Blogs:
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Charles C. Berry (858) 534-2098
Dept of Family/Preventive
Medicine
E mailto:cbe...@tajo.ucsd.edu UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego
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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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and provide commented, minimal, self-contained, reproducible code.
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Heritage Laboratories
West Hartford, CT
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