I've recently had an experience with the whole "correlation does not imply causation", which is certainly true as far as a true/false proposition is concerned, but which also seems to be used too often to dismiss. What I wanted to ask refers to correlation as evidence, that is how reliable is correlation as a measure of proximity to a causal source. I've read the interesting related CrossValidated questions which I'll tease out the related snippets below...
- Under what conditions does correlation imply causation?
- Statistics and causal inference?
- If 'correlation doesn't imply causation', then if I find a statistically significant correlation, how can I prove the causality?
- Online resources for philosophy of causation for causal inference
Wikipedia Article: Correlation does not imply causation: Use of correlation as scientific evidence
However, sometimes people commit the opposite fallacy – dismissing correlation entirely, as if it does not suggest causation at all... This would dismiss a large swath of important scientific evidence
Answer to #3 by Peter
A very likely reason for 2 variables being correlated is that their changes are linked to a third variable. Other likely reasons are chance (if you test enough non-correlated variables for correlation, some will show correlation), or very complex mechanisms that involve multiple steps.
Answer to #1 by Yaroslav Bulatov
under what conditions can you reliably extract causal relations from data? ... infer the direction of causality from observations of pairs of variables where one variable was known to cause another
Answer to #2 by Gaetan Lion
It just confirms that certain events occur before others and that those events appear to have a consistent directional relationship. This seems to entail true causality but it is not always the case.
Answer to #4 by Graeme Walsh quoting Russell
that inductions do not make their conclusions probable unless certain conditions are fulfilled The main logical function that the assumptions have to fulfill is that of conferring a high probability on the conclusions and inductions that satisfy certain conditions.
All of these questions happen to fall upon the actual conclusion of some causal source from some correlated information, but I'm interested in the intermediate state where discovery is still taking place and conclusions are not yet drawn. Perhaps even to simplify the situation a bit let's say a valid statistically significant correlation is discovered but there is no direct causal link between the two correlates.
Please excuse any ambiguity and lack of articulateness in the following question since this is difficult to articulate what exactly I mean by "close", and "proximate". Basically if one happens to have discovered a correlation like mentioned above what is the likelihood that it occurs from absolute unrelated pure chance? Can two randomly chosen independent variables randomly correlate without there being an intermediary albeit unknown variable that influences each? It's hard for me to imagine that a true and persistent correlation would not at the least imply that an investigator is "close" to the source of causality. Put another way given the two variables that correlate there must at least be a third (or a chain to a third) nearby that I can at least be confident that I'm looking in the right direction as far as measuring the "right" things.
This question may be hard to apply in practical situations due to the fact that investigators don't really focus upon random facts or measurements but are entering and exploring a body of knowledge and phenomena that already binds relations to things they happen to be manipulating. Although I read somewhere in the above links that data miners are doing just such blind correlation discoveries, probably in the hopes of being proximate to a cause where proximate is good enough. In a nutshell should correlation be viewed more optimistically as hope for discovery of a cause than to pessimistically assume it demonstrates a suspicious relation or even invalid evidence.