[R] correlation comparison one more time

[Bill.Venables at csiro.au]

Hypothesis tests are normally set up to test a null hypothesis within a broader class of alternatives, which includes the null as a special case.  Roughly speaking the logic is

"We assume that the outer class includes the truth. We have a simple special case of this we call the null hypothesis that in some sense represents 'no effect'. Does the data provide cogent evidence that the special case is not adequate?"

A standard way to address this question is, for example, to maximise the likelihood under null and alternative and to use the difference in log likelihood as the basis of a test statistic known as the likelihood ratio.

The way you have set up your hypotheses does not match this paradigm.  Your hypothesis is, in essence, that the squared correlation between A and D is larger than any other squared correlation involving two different variables, which include A or D.

It is clear enough what you are asking, but since it doesn't match the standard paradigm it is unlilely that any standard procedure will be available to address it.  It is unclear, for example, how you might go about setting up a likelihood ratio test. 

I think the answer to your question is "no", not off the shelf at least, and you probably need to think about the problem in the null and alternative hypothesis framework to make progress.

Bill Venables
CSIRO Laboratories
PO Box 120, Cleveland, 4163
AUSTRALIA
Office Phone (email preferred): +61 7 3826 7251
Fax (if absolutely necessary):  +61 7 3826 7304
Mobile:                                      (I don't have one!)
Home Phone:                             +61 7 3286 7700
mailto:Bill.Venables at csiro.au
http://www.cmis.csiro.au/bill.venables/ 

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of rafael
Sent: Sunday, 17 June 2007 8:20 PM
To: r-help at stat.math.ethz.ch
Subject: [R] correlation comparison one more time

I would like ask again,
because I cant find the answer

I have such problem:

My data containing 4 variables (A,B,C,D) and are completed from 4 samples.
Each of matrix is such:
        A   B   C   D
A     1   ab   ac   ad
B     ab  1    bc   bd  
C     ac   bc   1   cd
D     ad   bd   cd   1

My hypothesis are that

ad is the strongest correlation for A and for D (sign doesn't matter)
bc is the strongest correlation for B and for C (sign doesn't matter)

across samples.

Is it possible test these hypothesis?

Any help would be appreciated

Rafał Bartczuk
bartczuk at kul.lublin.pl

______________________________________________
R-help at stat.math.ethz.ch 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.