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Correlation does not imply causation, and the Latin names for the classic traps are a useful guide
Two things moving together does not prove that one causes the other. The fallacy cum hoc ergo propter hoc treats any correlation as causation, while post hoc ergo propter hoc assumes that whatever came first must have caused what followed. A third trap is reverse causation, where the arrow points the wrong way. Some correlations hide a common cause that drives both variables, and others are pure coincidence. Statisticians use tools such as the Granger causality test and the Bradford Hill criteria to weigh causal claims, but they still rest on assumptions.
A correlation only shows that two variables move together. A causal link needs evidence that rules out a confounder, a reversed arrow or a coincidence, which is why researchers use controlled studies and specialised tests.
Most arguments about health, policy or trends hinge on this distinction, so knowing the traps helps you ask whether a claim has shown cause or just association.
background
The phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two events or variables solely on the basis of an observed association or correlation between them. The idea that "correlation implies causation" is an example of a questionable-cause logical fallacy, in which two events occurring together are taken to have established a cause-and-effect relationship.
This fallacy is also known by the Latin phrase cum hoc ergo propter hoc ('with this, therefore because of this'). This differs from the fallacy known as post hoc ergo propter hoc ('after this, therefore because of this'), in which an event following another is seen as a necessary consequence of the former event, and from conflation, the errant merging of two events, ideas, databases, etc., into one.
From Wikipedia: Correlation does not imply causation (CC BY-SA 4.0) ↗ · text CC BY-SA 4.0Adapted from Wikipedia, the free encyclopedia · CC BY-SA 4.0
Illustrative photo · Rcragun, CC BY 3.0, via Wikimedia Commons
