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This question is somehow similar to Does causation imply correlation?, but what I would like to know is there any sense in applying a causal inference methods when we have a low correlation level. I'm very interested in a several particular cases, for the one of them the correlation coefficient equals 0.40, the scatter plot is attached. enter image description here

Will the results of causal inference be meaningful, or the variable contains too much noise?

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Boddha
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Statements on how "meaningfull" something is, necessarily involves a subjective assessment. So, it depends: A not very precise estimate for a very relevant topic for which there is no more precise measure yet, is probably very meaningful, as long as it is interpreted with the right degree of caution.

Moreover, what is a high and low correlation depends on the context. For example: for a survey in the social sciences I would consider a correlation of .4 as suspiciously high; not impossible, but something I would check very very closely before believing it.

Maarten Buis
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  • Well, the subject is physical properties, so the correlation .4 is considered low. The point is can one apply causal inference methods (like PC algorithm) in this case? – Boddha Dec 16 '15 at 11:14
  • The first part of my answer answers that question. Is that unclear? If yes, can you tell me what is unclear, so I can try to clarrify it? – Maarten Buis Dec 16 '15 at 14:40
  • For me unclear is the practical use of your answer. Also I do not see any connection of your answer with methods of causal inference. Would be very grateful if you explained me. – Boddha Dec 17 '15 at 10:49
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    You asked "Will the results of causal inference be meaningful, or the variable contains too much noise?" and the answer is "you can do anything you like, as long as you interpret the results correctly, and whether that is meaningfull is your subjective opinion". So, go for it, look at the results, be careful, and decide whether you think that is meaningful or not. I did not comment on particular methods as those tend to depend on many many details that you can not give us. – Maarten Buis Dec 17 '15 at 10:59