Some time ago I had already written about the “number of the day”. Today’s number, displayed in the metro station on my way to university was: “Probability that a male (cigarette) smoker lives in China: 31%”.
I basically have had the same strange feeling I had back then — the statement somehow sounds wrong. Maybe it is because as a psychologist/statistician I am so much used to reading probability statements where people explicitly or implicitly assume a causal relationship. For example, a statement like “the probability that the child of a person with schizophrenia will suffer from the same condition is 10%” (e.g. here) is usually understood as saying that genes have some causal relationship with developing schizophrenia.
Now, I don’t want to go into a discussion of causality (haven’t I said that before?), by far not having read enough (e.g. Pearl’s book is gathering up dust on the shelf, lying there unread for more than two years now). It just sounds strange, doesn’t it? In the statement about smoking and living in China, it does not seem too unlikely that living in China (compared to living, say, somewhere like Singapore) somehow increases your chances of becoming a smoker — but I think it’s not the other way round: Being a smoker surely won’t increase your chances of moving to China like in the counterfactual statement: “If he weren’t a smoker, he would not have moved to China”.
Well. The real catch is that probabilistic statements do not entail statements about causation, no matter how much we are used to it (I think I am speaking for many psychologists on that account). But maybe this mix-up is not only due to too many attempts to find out about probabilistic causation in the soft sciences. When I visited introductory courses on motivation and social psychology, I always liked the Heider and Michotte experiments on causal attribution: people seem to be biased into perceiving causality even where there is none.