We saw in the last chapter how Pearson’s correlation coefficient measures how close the points on a scatter-plot are to a straight line. When considering English hospitals conducting children’s heart surgery in the 1990s, and plotting the number of cases against their survival, the high correlation showed that bigger hospitals were associated with lower mortality. But we could not conclude that bigger hospitals caused the lower mortality.

This cautious attitude has a long pedigree. When Karl Pearson’s newly developed correlation coefficient was being discussed in the journal Nature in 1900, a commentator warned that ‘correlation does not imply causation’. In the succeeding century this phrase has been a mantra repeatedly uttered by statisticians when confronted by claims based on simply observing that two things tend to vary together. There is even a website that automatically generates idiotic associations, such as the delightful correlation of 0.96 between the annual per-capita consumption of mozzarella cheese in the US between 2000 and 2009, and the number of civil engineering doctorates awarded in each of those years.

There seems to be a deep human need to explain things that happen in terms of simple cause-effect relationships  -  I am sure we could all construct a good story about all those new engineers gorging on pizzas. There is even a word for the tendency to construct reasons for a connection between what are actually unrelated events  -  apophenia (the tendency to perceive a connection or meaningful pattern between unrelated or random things (such as objects or ideas))  -  with the most extreme case being when simple misfortune or bad luck is blamed on others’ ill-will or even witchcraft.

Unfortunately, or perhaps fortunately, the world is a bit more complicated than simple witchcraft. And the first complication comes in trying to work out what we mean by ‘cause’.

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What Is ‘Causation’ Anyway?

Causation is a deeply contested subject, which is perhaps surprising as it seems rather simple in real life: we do something, and that leads to something else. I jammed my thumb in the car door, and now it hurts.

But how do we know that my thumb would not have hurt anyway? Perhaps we can think of what is known as a counter-factual. If I hadn’t jammed my thumb in the door, then my thumb would not hurt. But this will always be an assumption, requiring the rewriting of history, since we can never really know for certain what I might have felt (although in this case I might be fairly confident that my thumb would not suddenly start hurting of its own accord).

This gets even trickier when we allow for the unavoidable variability that underlies everything interesting in real life. For example, the medical community now agrees that smoking cigarettes causes lung cancer, but it took decades for doctors to come to this conclusion. Why did it take so long? Because most people who smoke do not get lung cancer. And some people who do not smoke do get lung cancer. All we can say is that you are more likely to get lung cancer if you smoke than if you do not smoke, which is one reason why it took so long for laws to be enacted to restrict smoking.

So our ‘statistical’ idea of causation is not strictly deterministic. When we say that X causes Y, we do not mean that every time X occurs, then Y will too. Or that Y will only occur if X occurs. We simply mean that if we intervene and force X to occur, then Y tends to happen more often. So we can never say that X caused Y in a specific case, only that X increases the proportion of times that Y happens. This has two vital consequences for what we have to do if we want to know what causes what. First, in order to infer causation with real confidence, we ideally need to intervene and perform experiments. Second, since this is a statistical or stochastic world, we need to intervene more than once in order to amass evidence.
 

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