How to answer the question about transitive correlation?

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Date: Fri, 22 Apr 2011 11:42:59 +0800
From: mailzhuyao at gmail.com
To: r-help at r-project.org
Subject: [R] How to answer the question about transitive correlation?

Hi, everyone. I know it may be a basic statistical question. But I can't
find a good answer.

I have a question raised by one of the reviewers.
Factor A expression was strongly correlated with B expression (chi-square)
in this series. Prior reports by the same authors showed that B expression
strongly correlated with survival (Log-rank). Please provide an explanation
why then were the results not transitive.

The only explanation that would have any value would require you post the
data and let everyone look at it and any R output would be a benefit too. 
So you compared A and B with one test, 
B vs C with another, cutoff the result at some arbitrary criterion, and
then wonder why some unspeficied test and criterion applied to A vs C
doesn't vote in the majority with the same answer? Changing acceptance levels
or applying a "correction" after careful shoppping can always "fix" that
logical inconsistency LOL. Its not hard to plot 3 normal curves on same graph
and see one example of how their overlaps can relate.

I'm not sure what to think but perhaps you could look at stuff like this,

http://en.wikipedia.org/wiki/Path_analysis_%28statistics%29