If intelligence is a cause, it is a within-subjects cause

Borsboom, Mellenbergh, and van Heerden argue that latent variables such as intelligence should be given a between-subjects causal interpretation, but not a within-subjects causal interpretation. That is, while intelligence is a cause of one subject’s doing better than another on an IQ test, there is no non-comparative sense in which intelligence – as standardly measured – is a cause of an individual’s performance. Here I expand upon Pearl’s discussion of Simpson’s paradox to show that there cannot be a cause in a population that is not a cause in at least one of its members and that, consequently, causal variables cannot have an exclusively between-subjects interpretation. The illusion that they can results from not properly distinguishing between causal and non-causal models.