# Whats on the causal path?

I have an experiment that perturbs variable x and causes a change in variable z. There is a concurrent change in variable y. How can I determine whether variable y is on the causal path between x and z or if it is an irrelevant epiphenomenon?

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while it is difficult/impossible to "prove" causation, look into the subject of statistical mediation, which seems to be exactly what you're describing. This has been studied in many social sciences with the seminal paper by Baron and Kenny in the 1980s with many incremental advances since then by many statisticians in the field of causal inference. –  Macro Jul 1 '11 at 23:46

Experimental design rather than statistics alone will give you a solid answer. You may well have already thought about this and ruled it out as a possibility, but can you design an experiment that tests whether Z changes as a function of Y when X is held constant? Further, perhaps you could build in trials that test the extent to which Z changes as a function of X when Y is held constant. Isolating predictors in this way is your best bet of capturing the causal relationships.

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But if Z changes as a function of Y by only a tiny amount this might not account fully for the effect of X. –  alwaysean Jul 3 '11 at 20:52
I've edited my answer. –  rolando2 Jul 4 '11 at 1:16
Thanks for the answers but I need a quantitative solution. –  alwaysean Jul 5 '11 at 17:12

I think you're looking for an instrumental variable test, which will allow you to assess whether $y$ mediates the correlation between $x$ and $z$. The section on "interpretation as two-stage least squares" provides a nice intuition for this procedure.

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Thank you - I will look into the instrumental variable test. And thanks everyone for very helpful comments. –  alwaysean Jul 12 '11 at 21:41

You might try comparing...

-the corr. of x with z while controlling for y

-the corr. of y with z while controlling for x

It won't give you a definitive answer, since as @Macro said statistics are limited in that way, but it could give you clues.

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