Extremely sharp thoughts on how we are wired at a very deep level to relate correlation and causation. This kind of identification of our heuristics and biases is essential to figuring out how to design societies in which people have a chance of making good judgments: Judea Pearl and Dana Mackenzie: Simpson's Paradox: "Any claim to resolve a paradox... should explain why people find the paradox surprising or unbelievable....When the paradox does occur, and we have to make a choice between two plausible yet contradictory statements, it should tell us which statement is correct.... A paradox... should entail a conflict between two deeply held convictions...
...Suppose that the choice is... between two properties, A and B. If the Democrat wins, the businessman has a 5 percent chance of making $ 1 on Property A and an 8 percent chance of making $ 1 on Property B. So B is preferred to A. If the Republican wins, he has a 30 percent chance of making $ 1 on Property A and a 40 percent chance of making $ 1 on Property B.... If the businessman’s decision to buy can change the election’s outcome... then buying Property A may be in his best interest. The harm of electing the wrong president may outweigh whatever financial gain he might extract from the deal....
To make the sure-thing principle valid, we must insist that the businessman’s decision will not affect the outcome of the election.... The missing ingredient... is a causal assumption. A correct version... would read as follows: an action that increases the probability of a certain outcome assuming either that Event C occurred or that Event C did not occur will also increase its probability if we don’t know whether C occurred… provided that the action does not change the probability of C.... Our strong intuitive belief that a BBG drug is impossible suggests that humans (as well as machines programmed to emulate human thought) use something like the do-calculus to guide their intuition....
In the study, women clearly had a preference for taking Drug D and men preferred not to. Thus Gender is a confounder of Drug and Heart Attack. For an unbiased estimate of the effect of Drug on Heart Attack, we must adjust for the confounder. We can do that by looking at the data for men and women separately, then taking the average.... Drug D isn’t BBG, it’s BBB: bad for women, bad for women, and bad for people.
I don’t want you to get the impression from this example that aggregating the data is always wrong or that partitioning the data is always right. It depends.... Let’s begin with the assumption that blood pressure is known to be a possible cause of heart attack, and Drug B is supposed to reduce blood pressure.... The numbers are the same... the conclusion is exactly the opposite.... Drug B succeeded in lowering the patients’ blood pressure....It moved people from the higher-risk category into the lower-risk category.... The aggregated part... gives us the correct result....
The causal diagram will tell us what procedure we need to use. However, for statisticians who are trained in “conventional” (i.e., model-blind) methodology and avoid using causal lenses, it is deeply paradoxical that the correct conclusion in one case would be incorrect in another, even though the data look exactly the same...
#noted #2019-10-10
