## 31 Correlation is not Causation

In the Midwest, especially in the region around Kansas City, there are 50 to 60 thunderstorms in the course of an average year. Since a typical year has 365 days, then simply by random chance it is expected that 60/365 or about 1/6 of all well pumps that fail from age and normal wear will fail on a day in which there has been a thunderstorm.

This same correlation, however, also applies to other singular events such as stopped clocks, blown tires, and weddings. In other words, random chance also dictates that there is a similar 1/6 probability in an average year that a clock will stop working, a tire will blow out, or a wedding will be held on a day in which a thunderstorm occurs. Of course when these other events occur on the same day as a thunderstorm, no one seriously believes they have actually been caused by the thunderstorm. It is generally acknowledged that they are just coincidences.

However, when an electrical appliance, such as a well pump, fails on a day in which a thunderstorm occurs, there is a tendency to presume that lightning must have had something to do with the failure, that is, that there is a cause-and-effect relationship between the two events. The rationale often applied in such cases is, "it worked fine until that storm occurred." Of course, this argument ignores the role that coincidence plays in the two events, or the obvious fact that the appliance had endured many such thunderstorms before and had not failed.

The probability that a well pump will fail for any reason after a thunderstorm increases as the length of time between the thunderstorm and the date the well pump failed increases. For example, by applying some basic proba-

Plate 3.1 ARC-over from circulating panel lid, which was grounded.

bility rules, specifically Bayes' theorem, to the weather statistics already cited, it is found that when a well pump has failed due to age and wear, there is a 30% chance that there was a thunderstorm in the immediate area two days or less prior to the discovery of the failure.

Similarly, by again applying Bayes' theorem, it is found that there is a 50% chance that there will be thunderstorm in the area four days or less immediately prior to a well pump failure. In other words, when a well pump fails, there is a significant probability that a thunderstorm has occurred a few days prior to the failure simply by random chance.

Thus, the mere fact that a well pump has failed a day or so after a thunderstorm has occurred is not evidence that a thunderstorm caused the failure. In fact, it is arguable whether it has any significance at all. Random chance alone indicates that it is likely that well pumps will fail a few days directly after a thunderstorm, no matter what has caused the failure.

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