Spurious correlations that have had important effects upon history

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Separating the Wheat and the Chaff: Spurious Correlations

Researchers commonly encounter behaviors that seem to be related to one another in some way. In the case of the number of miles a car is driven and its gas consumption, there is an obvious and genuine connection. But simply because two behaviors share a significant statistical correlation does not always prove that there is a real relationship between the two variables.

With complex systems, it may be difficult to determine if a statistical correlation is genuine or completely coincidental and spurious. While the continental drift of the West Coast of North America may be highly correlated with the growth of the federal deficit in recent decades, it is unlikely that there is a meaningful connection between the two. Apparently, there is also a strong negative correlation between the number of PhDs and the number of mules in a state. As one commentator remarked, “Are the PhDs created when mules die?” Similarly, a positive correlation exists between ice cream sales and deaths by drowning. The same researcher humorously asked if “people buy more ice cream when they hear of a drowning?” Even when a connection exists, it may be trivial or misleading. In the end, correlation is worthless without interpretation, and that interpretation should be as well-grounded as possible. Consider the following examples:

• My favorite spurious correlation is between shoe size and the ability to solve mathematical equations (or any other task requiring schooling). The students usually express a lot of puzzlement over that one, until you point out that children’s feet tend to grow as they go through school. (Wuensch, p. 3)

• One . . . [example of a spurious con-nection] is the strong positive correlation between places of worship in a locale and the number of bars in the same vicinity. The explanation is obvious: Religion drives people to drink. (Beins, p. 3)

In most research problems, however, the spurious nature of the correlation may not be immediately clear, requiring additional information and careful interpretation to establish the real nature of the connection between the variables. Indeed, important issues may be riding on correctly evaluating and understanding the correlation.

[A] story I sometimes use is based on a Nova television show from a few years back. Chinese medical researchers had found a correlation between incidence of human esophageal cancer and the incidence of tumors in chickens. Were the chickens the source of the human cancers? Were the humans giving the chickens their tumors? What they eventually found was that regional preferences for a fermented cabbage dish and minerals in the soil in which the cabbage was grown gave both the humans, who ate the cabbage, and the chickens, who ate the scraps, their tumors. (Street, p. 3)