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Test on Difference in Mean Correlations
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R
Sep 5, 2012, 10:08:47 PM9/5/12
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Hello:
Is there a way to perform a formal statistical test on whether two
mean correlations [calculated from data from the same sample] are
significantly different from each other:
H0: mean[corr(1,2), (corr 3,4)] = mean[corr(5,6), (corr 7,8)]
I realize that since correlations are not additive, in order to
calculate the mean correlations one would likely use the Fisher's z
transformation or perhaps use squared correlations, but I'm stuck
after this point.
I realize this is a peculiar question--just curious if hypothetically
this would be possible, and if so, how to do it.
Thanks!
Is there a way to perform a formal statistical test on whether two
mean correlations [calculated from data from the same sample] are
significantly different from each other:
H0: mean[corr(1,2), (corr 3,4)] = mean[corr(5,6), (corr 7,8)]
I realize that since correlations are not additive, in order to
calculate the mean correlations one would likely use the Fisher's z
transformation or perhaps use squared correlations, but I'm stuck
after this point.
I realize this is a peculiar question--just curious if hypothetically
this would be possible, and if so, how to do it.
Thanks!
David Jones
Sep 6, 2012, 11:31:25 AM9/6/12
to
"R" <br7...@yahoo.com> wrote in message
news:9068bf69-7cbf-4dc3...@e6g2000yqg.googlegroups.com...
It is of course possible to do this if you are prepared to work in the
context of a fully-formed statistical model, where the maximum likelihood
approach can, theoretically at least, be manipulated into doing what you
want. It might just be possible to work-out what a test statistic would be
in the case of a multivariate normal distribution and to see if this is
"obviously" reasonable for less well-specified applications. It might be
worth looking separately at both a full likelihood ratio test and a Lagrange
multiplier test as the algebra would be different, but I don't think it
would actually be possible to solve the problem algebraically in ether
case... leaving just the possibility of a numerical optimization solution
for any given multidimensional model.
news:9068bf69-7cbf-4dc3...@e6g2000yqg.googlegroups.com...
context of a fully-formed statistical model, where the maximum likelihood
approach can, theoretically at least, be manipulated into doing what you
want. It might just be possible to work-out what a test statistic would be
in the case of a multivariate normal distribution and to see if this is
"obviously" reasonable for less well-specified applications. It might be
worth looking separately at both a full likelihood ratio test and a Lagrange
multiplier test as the algebra would be different, but I don't think it
would actually be possible to solve the problem algebraically in ether
case... leaving just the possibility of a numerical optimization solution
for any given multidimensional model.
Rich Ulrich
Sep 7, 2012, 2:40:14 AM9/7/12
to
I think it is there. The test will also use the rest of the
correlation matrix, elements 1-4 vs 5-8.
I will bring up the point that comparing correlations is
pretty lame for most purposes, whether it is within one
sample (different variables) or between two samples (same
variables). Within one sample, you are either assuming or
implicitly testing such stuff as equal reliability and equivalent
variability (compared to some larger universe) for those items.
*** Googlin on <Steiger, correlation testing>
Tests for Comparing Elements of a Correlation Matrix
www.statpower.net/Steiger%20Biblio/Steiger80.pdf
File Format: PDF/Adobe Acrobat - Quick View
by JH Steiger - 1980 - Cited by 1418 - Related articles
Tests for Comparing Elements of a Correlation Matrix. James H.
Steiger.
--
Rich Ulrich
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