The Epistemology behind Covariate Adjustment

It is often asserted that to control for the effects of confounders, one should include the confounding variables of concern in a statistical model as a covariate. Conversely, it is also asserted that control can only be concluded by design, where the results from an analysis can only be interpreted as evidence of an effect because the design controlled for the cause. To suggest otherwise is said to be a fallacy of cum hoc ergo propter hoc. Obviously, these two assertions create a conundrum: How can the effect of confounder be controlled for with analysis instead of by design without committing cum hoc ergo propter hoc? The present manuscript answers this conundrum.