The problem

It is fairly familiar knowledge that we sometimes obtain between quantities varying with the time (time-variables) quite high correlations to which we cannot attach any physical significance whatever, although under the ordinary test the correlation would be held to be certainly ‘significant’. As the occurrence of such ‘nonsensecorrelations’ makes one mistrust the serious arguments that are sometimes put forward on the basis of correlations between time-series – my readers can supply their own examples – it is important to clear up the problem how they arise and in what special cases. Figure 9.1 gives a very good illustration. The full line shows the proportion of Church of England marriages to all marriages for the years 1866–1911 inclusive: the small circles give the standardized mortality per 1,000 persons for the same years. Evidently there is a very high correlation between the two figures for the same year: the correlation coefficient actually works out at +0-9512.

Now I suppose it is possible, given a little ingenuity and goodwill, to rationalize very nearly anything. And I can imagine some enthusiast arguing that the fall in the proportion of Church of England marriages is simply due to the Spread of Scientific Thinking since 1866, and the fall in mortality is also clearly to be ascribed to the Progress of Science; hence both variables are largely or mainly influenced by a common factor and consequently ought to be highly correlated.