>"u -> x1, e -> x2 ? I know you said it somewhere, but I can't find it."
u -> x2.
> Even if the true regressions were the same in both groups, 'u' would > look more useful as a predictor (and, if the sample sizes were equal, > would be "more signficiant") in the Study group than in the Control > group because its SD is higher. A fair comparison would require the > SDs to be (close to) the same in both groups.
That's what I thought, ignorantly and naively, so I'm glad you confirmed my intuition.
One of my old mentors, Ray Dougherty (still at NYU), once explained to me why the early TV technicians broadcast the particular pictures that they chose to broadcast after station sign-off. It's because those pictures contained close to the exact amount and kind of information they need to calibrate their equipment. It's somewhat of the same thing here (I think) - there's less "information" in the "u" control group signal, because there's less variation.
I will bet that if I gave you enough of the right kind of data, you would be able to show that the distribution of "u" in the control group closely approximates some kind of well-known "random" distribtion. (I know I'm not saying this correctly, but I think you'll know what I'm trying to say ...)
Anyway, I will do the same numbers for "e" (->x1) at some point in the near future, just for comparison. But note that the choice of u betwewen 1.01 and 1.36 in the control group and 1.01 and 4.00 in the study group restricts the values that e can assume in each. If we had started with "e", then the values of "e" would restrict the values that "u" can assume.