Numbers don’t lie and other myths

Letter to the Editor

John CrockerPaulton, Bristol, U.K.

To the editor:

While I agree with your statement in the February issue of OR/MS Today (Inside Story: “Numbers don’t lie,” page 4) regarding the use that O.R. people make of statistics, I have noticed an increasing number of articles (from other sources) where your three opening statements could very well apply.

One of the most popular races held in the United Kingdom every year is the Grand National. Typically there is a field of 40 starters and they are required to do two circuits of the Aintree (near Liverpool) course comprising of a number of very high or wide fences. To give you an idea of the severity of the course, only 17 of 40 starters made it to the finish line this year.

My colleague found an article in which the author claimed to be able to predict the winner. Nothing new about that, but this one was allegedly written by a mathematician. His analysis of the past 176 races brought him to the conclusion that the winning horse would have a name comprising one word and it would be either eight or 10 letters long starting with one of four letters. He cited four criteria and he gave marks (1-4) for each. The horse with the highest score (13/16) would, he claimed, be this year’s winner. It came in 13th. The one he placed second failed to complete the course after falling at the 12th fence. His third-place pick did, somewhat remarkably, come in third. However, five out of the first six horses all had names comprising two words, not one.

I strongly suspect that if the author had not claimed to be a mathematician no one would have even considered taking it seriously.

Another article claims that people who suffer from hair loss are likely to also suffer from migraines. Apparently this conclusion was reached by reviewing published research. I am willing to concede that the probability of suffering from migraine given you also suffer from hair-loss is marginally higher than if you don’t, or even that the probability of suffering from hair-loss given you also suffer from migraine is also marginally higher, but this is long way from claiming that one is the cause of the other. There must be millions of bald Americans (and not just the eagles) who have never had a migraine headache. Equally, one can imagine of the all the people who suffer from migraines, the vast majority have not lost their hair.

If you look hard enough for a correlation, there is a very good chance you will find one, but just because data from two variables show a correlation does not mean that there is a causal relationship. Humans are extremely loath to accept that a coincidence is anything more than a random chance. Complementary medicine and most religions depend on us believing that coincidences cannot be random, unconnected events. If I trip over, I will probably think nothing of it. But if I trip over and it happens to be Friday the 13th, or that I have just walked under a ladder or that I have just seen a lone magpie or any of a million such superstitions then I am likely to link these two events and hence further substantiate the superstition. If I am particularly superstitious, then after tripping over, I am likely to go back through my memory to try to relate it to one of the above events (even though it may have happened several days ago). There is no time limit with the possible exception of Friday the 13th.

There is an extremely good reason for insisting that drug trials are done double-blind. It is all too easy to ignore such concerns when trawling the Internet or using an analytics tool. I would not be at all surprised if by entering the right keywords one could find a correlation between migraine and Republican voters and, surprise, surprise, by changing the keywords, a similar correlation between migraine and Democrat voters.

Dr. John Crocker is a Fellow of the OR Society (United Kingdom) and editor of Inside OR.