But doesn't a similar argument hold for non-error sources of variance that are "orthogonal" to the group difference? (Sorry, I know this is vague; I'm writing to the list in case any Actual Scientists can spare a moment to help me make my intuition more precise.) Like, suppose performance on some particular cognitive task can be modeled as the sum of the general intelligence factor (zero or negligible sex difference[^jensen]), and a special ability factor that does show sex differences. Then, even with zero _measurement_ error, _d_ would underestimate the difference between women and men _of the same general intelligence_.
But doesn't a similar argument hold for non-error sources of variance that are "orthogonal" to the group difference? (Sorry, I know this is vague; I'm writing to the list in case any Actual Scientists can spare a moment to help me make my intuition more precise.) Like, suppose performance on some particular cognitive task can be modeled as the sum of the general intelligence factor (zero or negligible sex difference[^jensen]), and a special ability factor that does show sex differences. Then, even with zero _measurement_ error, _d_ would underestimate the difference between women and men _of the same general intelligence_.