Translating from causal to statistical models

The official language of statistics is the probability calculus, based on the notion of a probability distribution. For instance, if you conduct an analysis of variance (ANOVA) then the key piece of information is the probability of observing a particular value of Fisher's F statistic in a random sample of data, given a particular hypothesis or model. To obtain this crucial piece of information, you (or your computer) must know the probability density function of the F statistic. Certain other (mathematical) languages are tolerated within statistics but, in the end, one must link one's ideas to a probability distribution in order to be understood. If we wish to study causal relationships using statistics, it is necessary that we translate, without error, from the language of causality to the only language that statistics can understand: probability theory.

Such a rigorous translation device did not exist until very recently (Pearl 1988). It is no wonder that statisticians have virtually banished the word ‘cause’ from statistics; such a word has no equivalent in their language. Within the world of statistics the scientific notion of causality has, until recently, been a stranger in a strange land. Posing causal questions in the language of the probability calculus is like a unilingual Englishman asking for directions to the Louvre from a Frenchman who can't speak English. The Frenchman might understand that directions are being requested, and the Englishman might see fingers pointing in particular directions, but it is not at all certain that works of art will be found. Imperfect translations between the language of causality and the language of probability theory are equally disorienting.

Mistakes in translation come in all kinds. The most dangerous ones are the subtle errors in which a slight change in inflection or context of a word can change the meaning in disastrous ways. Because the French word demande both sounds like the English word ‘demand’ and has roughly the same meaning (it simply means ‘to ask for’, without any connotation of obligation), I have seen French-speaking people come up to a shop assistant and, while speaking English, ‘demand service’. They think that they are politely asking for help, while the assistant thinks they are issuing an ultimatum.