Procrustean Art of Backtracking: “All Correlations are Not Equal”*

 

In the East, there is the popular old saying, “As the raven flies off the tree, some pears fall down to the ground” (烏飛梨落 in Korean Chinese). The saying is sometimes used as a wakeup call against taking correlation for causality; causality has policy implications, but correlation does not.

             Suppose the leaving raven causes the pears to fall down. One of our counter-measures would be to put up in the air a signboard telling “Ravens, Please Keep Off.” Then, intelligent and rule-abiding ravens in the community would not come and sit on pear trees any more. We are right and everything goes well. This happy ending is thanks to the right causation.

             We are not always fortunate. Even without ravens on the trees, pears may still drop down from time to time. We must suspect that the other time the raven was scared and flew away as pears fell down. Our mistake in the past is a typical case of reverse causation: the falling pears caused the scared raven to fly off.

             Now, we have another policy implication from the new “hypothesis”: to use more fertilizer, to apply some pesticide or something similar, in order to make trees and pears healthier. We will again be happy if the hypothesis turns out to be a theory.

             In still other case, pears do not drop in normal times, but do drop at a whirlwind. Ah ha! There must have been a third cause, that is, the wind: as the wind blew, the pears fell down and the raven flew away almost at the same time. This time, the third cause makes both events happen. Now, we have still different policy implications: to prevent the whirlwind from blowing into the orchard or to grow wind-proof pears.

             Finally, the event can possibly have been a sheer coincidence. If so, we may just forget the correlated events and move forward as usual.

             All in all, we can stay happy only when we get the causality right. Putting a signboard would be waste of money in the other three cases. After all, the correlation coefficient of concurrent events is never zero, while the degree of correlation in itself never proves the kind of causality. The policy implication: we might not take an action of a particular kind just because of a correlation.

 

* The full text copied from somewhere else