I was once critiqued for using a "wrong" test because the test I chose didn't actually prove causation. I admit that I'm not a statistician. My education is very incomplete. What statistical tests actually PROVE causation? I thought there was no way to use statistics to prove causation. I invite correction if this is erroneous.
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3You may be interested in the questions tagged [tag:causality], including https://stats.stackexchange.com/questions/534/under-what-conditions-does-correlation-imply-causation and https://stats.stackexchange.com/questions/2245/statistics-and-causal-inference – mkt Aug 17 '20 at 13:52
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1So, if one is looking at a sample drawn from a population that one has not manipulated, the only inference that can be made is association, not causation. Thus, whether or not one has demonstrated causation has nothing to do with the specific test chosen but with entirely non-statistical elements. – Bryan Aug 17 '20 at 13:59
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2There is no mathematical proof of causation, but there are frameworks for "showing" or "demonstrating" causality. One, of course, is the Randomized Controlled Trial. The other is the new Causal Revolution. Both are well worth your time investigating. – Adrian Keister Aug 17 '20 at 14:46
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2@AdrianKeister has an excellent point. *Causation* is a belief—i.e. a narrative about how the world works—as with all narratives, we can only provide *evidence* for (of varying quality), not *proof* of (in a sense akin to mathematical derivation, or 100% certainty). Even Einstein's general relativity, or the second law of thermodynamics, both of which have amassed *humongous* bodies of supporting evidence behind them, rely on assumptions like (no facetiousness intended), "am I hallucinating a history of supporting evidence?" or "are we privy to only a select part of universal experience?" etc. – Alexis Aug 17 '20 at 17:59