spurious correlation

spurious correlation A correlation between two variables when there is no causal link between them. A famous spurious correlation often quoted in the literature is that between the number of fire-engines at a fire (X) and the amount of damage done (Y). Once the size of the conflagration (T) is controlled for—that is, large fires cause more damage, and therefore require more fire-engines to extinguish them—the original relationship disappears. Hence the X → Y relationship becomes T → X, T → Y, but X and Y are not causally related, where T — the size of the fire—is an antecedent variable. Note also that it is not really the correlation which is spurious, but rather the implicit causal model: there are indeed more fire-engines at fires where the greatest damage is done, but it is not the fire-engines which cause the damage. Similarly, in certain societies there is a close correlation between the volume of perfume imports, and the rate of marriage. Naturally enough, however, on closer inspection these two phenomena turn out not to be causally related. Rather, both are associated with a prior antecedent variable (in this case economic growth), and simply move up and down in a spurious manner in conjunction with the buoyancy of the local economy.