If the correlation was significant enough (however you define it), does it necessarily show that there is some underlying cause even if it's not direct causation?
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1$\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$– Community BotJun 3 at 16:51
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$\begingroup$ I think David Hume would say that you can't have certain knowledge of causal relationships based on empirical observation (we can't observe causation - only correlation/sequence) but Kant would say that our knowledge is based on observation and theory (Adrian's "mechanism" - +1), so we can't say "necessarily" because it is contingent on agreement about theory and it's assumptions. Caveat lector: I'm (evidently) not a philosopher, just interested where it impinges on statistics and science. $\endgroup$– Dikran MarsupialJun 3 at 17:59
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1$\begingroup$ Lack of correlation does not mean lack of causation. $\endgroup$– AlexisJun 3 at 18:05
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2$\begingroup$ Also: See my answer to Who first coined the phrase "correlation does not imply causation"? $\endgroup$– AlexisJun 3 at 18:07
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$\begingroup$ I'd suggest that many processes tend to change (e.g. increase) over time. To see correlation, there may be no connection whatever other than two processes each existing in time. To attribute time as the cause of each rather stretches the notion of cause. $\endgroup$– Glen_bJun 4 at 1:39
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It is not "necessarily". The usual "post hoc ergo propter hoc" fallacy is the fallacy that says correlation always implies causation, or even that you can infer causality. This is still a fallacy. However, if you add another condition to the correlation - namely, that of mechanism - then you get Reichenbach’s common cause principle: "No correlation without causation."
As an example, the rooster crowing causing the sunrise is a "post hoc" because there's no plausible mechanism for a lone rooster crowing to cause the sunrise - although, interestingly enough, there could be causation the other way: does the sunrise cause the rooster to crow? Perhaps.
We've been conditioned to avoid post hoc so strongly that I think the Reichenbach common cause principle needs trumpeting. The Reichenbach common cause principle says that if there's a mechanism, you should look for causality somewhere: the principle doesn't say which direction the causality is, and it also doesn't rule out a third common cause (confounding variable).
Another way of saying it is
Correlation doesn’t imply causation, but it does waggle its eyebrows suggestively and gesture furtively while mouthing ‘look over there’. - Randall Munroe.
answered Jun 3 at 16:43
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$\begingroup$ Thanks, but isn't that saying there necessarily is a causation, directly, indirectly or in the other direction somehow? $\endgroup$– cspJun 3 at 16:53
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1$\begingroup$ Essentially, yes: if there is a suspected mechanism, then correlation usually (not always) implies causation. $\endgroup$ Jun 3 at 17:08
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$\begingroup$ Got it. And when you say "NOT implies causation," you mean in cases where it's either indirect or the opposite, right? $\endgroup$– cspJun 3 at 17:21
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$\begingroup$ No, I mean that when correlation does not imply causation, there is no causal path to or from one variable to the other. The Reichenbach principle says there is either a direct arrow one way, a direct arrow the other, or a third variable (or set of variables) with arrows to or from the two starting variables: there is causation somewhere. It says that pure serendipity (coincidence) is unlikely. $\endgroup$ Jun 3 at 17:45
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$\begingroup$ Right. I meant 3rd variable when I said indrect. I suppose the existence of pure serendipities is unknowable, unless you mean they are just rare when you said unlikely. $\endgroup$– cspJun 3 at 17:48