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Correlation is not causation

Today’s xkcd: (thanks Viktor!)
Correlation

“Correlation doesn’t imply causation, but it does waggle its eyebrows suggestively and gesture furtively while mouthing ‘look over there’.”

2 Comments

  1. J Delong says:

    That cartoon would be way funnier with a box plot… or a violin plot. :)

  2. Botez says:

    The Concise Oxford Dictionary defines correlation as "mutual relation between two or more things" and causation as "causing or producing an effect". Correlation and causation can be given precise mathematical definitions, but most people do not know mathematics, so settle for the dictionary definitions. It should be pretty clear even with these that correlation is not causation.

    One of the worst afflictions of the British chattering classes, especially those in the media (including the BBC), is to assume that correlation means causation. This particularly arises when dubious surveys (or "scientific" studies) are carried out by dubious organisations with a particular story to spin. As long as the conclusion confirms some prejudice of the commentator then the survey is taken as proof that some "common sense" (usually "conservative") view has been upheld (and some horrid "liberal, 1960s" view has been trashed). Note that the circumstances under which the surveys are done is never discussed, and it is likely that these by themselves invalidate any conclusions. (It is often said that you can get any answer you want out of a survey.) But for the sake of the argument assume the surveys (or studies) have been done properly.

    Some of the most common examples of the confusion between correlation and causation are to do with family life (many others are to do with health). Consider the following statements:

    (1) "Children raised by single parents do less well at school (and later in life)." The conclusion is supposed to be that parents should become and stay married.

    (2) "Children where the mother stays at home do better at school (and later in life)." The conclusion is supposed to be that mothers should stay at home. (Or occasionally, but rarely, that mothers and fathers should stay at home, but usually this kind of survey is just a crude attack on working mothers so fathers are never mentioned.)

    (3) "People who are married are happier than people who are not." The conclusion is supposed to be that everybody should be married (and in particular the government should force non-married people to subsidise married people via the tax system; note that normally other words are substituted for "happy" when the tax argument is made, but it amounts to the same thing).

    (4) "People who are married are more likely to divorce than people who are not." (Well, obviously married people are the only people who will ever divorce.) The conclusion is supposed to be that married people should pay more tax than non-married people because divorce (which occurs in a third of marriages) is costly to the government (because of the courts) and so should be paid for by the people who cause the expense.

    Actually, (4) is the only point which would never be discussed in the media, because it does not confirm the prejudices of the chattering classes, most of whom are married and most of whom assume they are more moral citizens as a result. And as it happens (4) has the only conclusion which has any merit (although whether people should be forced to pay more tax for undertaking dubious activities like marriage or rock climbing is not generally accepted, with smoking being the prime example of having to pay lots of tax in these circumstances).

    Here are two more statements, unrelated to family life, which are analogous to statements (1) – (3), and which will perhaps point out the silliness of the various conclusions above:

    (5) "People who own red cars are twice as likely to have an accident as people who own blue cars." The conclusion is supposed to be that people who own red cars should re-paint their cars blue.

    (6) "Men who have beards are happier than men who do not." The conclusion is supposed to be that all men should grow beards.

    The basic situation in all the examples is that there are two groups of people, with one group having a "desirable" property and the other group not (this is the correlation). The conclusion is supposed to be that if only people in the second group could be forced to join the first group then all would be well (this is the causation). Unfortunately there is no proof that it is membership of the group which is causing the particular observed behaviour, it could be many other things. Indeed it could even be that the causation is the other way around, so that having the desired property naturally causes someone to be in the first group, so artificially being forced into this group does no good.

    It's possible, of course, that in one or more of the cases the stated conclusion is true, but the survey (or study) does not prove this one way or the other. Causations are much harder (and more expensive) to prove than correlations.

    In (1) the more significant correlation is with poverty. People who are poor have worse educations and people who are single are generally poorer (which is a reason for married, or partnered, people to pay more, not less tax). To the extent that forcing someone into marriage might raise the household income it's possible that marriage by itself might improve the education of these children, but that would have to be offset by the obvious and serious negative consequences of such a policy.

    In (2) it is obvious that in the best of all possible worlds children should be given constant care and attention by their parents. However this is not a cost-free alternative. If the mother does not work then the household will lose substantial income and that is also not good for the children (or parents). Many parents decide that working is better than not working, and parents can perhaps be trusted more than pseudo-scientists posing pseudo-surveys.

    In (3) it is quite possible that happy people are very likely to get married and unhappy people not. It is not the act of marriage itself which makes people happy. The emotional state of people who are likely to get married in the first place is perhaps more settled than that of the rest. If being happy is worthy of a tax break then perhaps happy people should be given one.

    In (5) it is much more likely that people who are more aggressive prefer to buy red cars rather than blue cars, and just painting the car blue is unlikely to calm them down (but you never know, it might help, however the survey does not address this question).

    In (6) we have an example almost exactly the same as (3), and nobody would treat the conclusion seriously. But no doubt on a quiet news day this kind of silly story could be given prominence in the national media.