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Simpson's Paradox/Cartwright: E.g. Exercise prevents cancer even in smokers. - It may be that the risk reduction through exercise is greater than the cause by smoking. Paradox: that exercise seems to cause cancer - i.e. in the case, when smoking and exercising are highly enough correlated in the population. - Solution: form subgroups - In the whole group smoking seems no more harmful - but important argument: in both subgroups: athletes and non-athletes - E.g. Salmon: a cause does not necessarily increase the probability of its effect.
Causally homogeneous: if all or no one work out, exercise cannot be correlated with cancer.
Better: law "uranium causes radioactivity", then no matter whether polonium present.
If the third factor is causally irrelevant to E, then there is no reason to keep it fixed, and fixing it even provides a false evaluation of causes and strategies. - E.g. The university seemed to reject women more often. - Solution: division into departments. - Women applied more in subjects with higher rejection rate. (E.g. medicine) - Problem: the partition variable is arbitrary: in roller skating more women would have been rejected. ((s) if the actually Rejected in that subject had been looked at).
How the laws of physics lie Oxford New York 1983