When I was a student, the professor of statistics at Imperial College was G. A. Barnard. He warned us that EXTREME CARE must be used when applying statistical methods to human affairs. In particular, the existence of a correlation between two random events, revealed by many trials, does not imply a causal relation. Let me illustrate the truth of Barnard's remark with a story. Suppose "researchers" in a certain state in the US find out, for each year since independence, the number of murders in the state, and also the number of Bibles sold. Suppose that these numbers vary from year to year in an unpredictable way, and so are described by two random variables, X,Y. The sample space is taken to be the integers between 1776 and 2003. From the data we can find the means of X and Y, their covariance, and their correlation coefficient. Suppose we find that the correlation coefficient is 0.8, so that when the murder rate is large, so is the rate of buying Bibles. Can we conclude that (1) a high murder rate in a given year causes people to rush out and buy Bibles? Or, can we suspect that (2) in years when many Bibles were sold, a lot of people read the gory stories in the Old Testament, and decided to follow suit and do some murders of their own? Or, should we (3) reject that the correlation shows any causal relation in either direction? We might look for a common cause for both sets of observations, and might find that both the murder rate and the sales of Bibles are directly proportional to the population, described by a random variable Z, such that X=aZ + R, Y = bZ + S, where a, b are constants and R, S are small random variables. If the latter theory turns out to be true, then someone knowing this explanation of the data would laugh at theories (1) and (2).
We discuss three topics where this mistake is very easy to make.
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© by Ray Streater, 29 Dec 2003.