expected correlation / transitivity ?

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laurie on 1 Jun 2012
i have an "experimental correlation" between A and B (coefficient c1), and a "control correlation" between A and B' (coefficient c2).
the problem is, B' is correlated with A' with coefficient c3 and A' is correlated with A with coefficient c4.
so, is there a relation between c2, c3 and c4 ?
thank you laurie
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the cyclist
the cyclist on 2 Jun 2012
This is not a MATLAB question. You might have a better chance of having it answered on a math or statistics forum.

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Accepted Answer

Tom Lane
Tom Lane on 2 Jun 2012
It seems like you are saying [1 c4 c2; c4 1 c3; c2 c3 1] is the correlation matrix of A,A',B'. This is a valid correlation for some combinations of (c2,c3,c4) but not others. You could use MATLAB to investigate which combinations are valid, by determining which lead to a matrix whose smallest eigenvalue is non-negative. For example, you could set c4 equal to some value and draw a contour plot of the smallest eigenvalue. That will show you the legal combinations of c2 and c3.
  1 Comment
laurie on 6 Jun 2012
thanks. i gave up trying to solve this though ! math really isnt my strong suit. maybe someone else will be able to fully appreciate your answer ;-)

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