OBJECTIVE To understand real-life examples in which two variables are mathematically correlated but changes in one variable do not necessarily cause changes in the other.
If two variables are correlated, it does not necessarily mean that a change in one variable causes a change in the other. For example, the mathematician John Allen Paulos points out that shoe size is strongly correlated to mathematics scores among school children. Does this mean that we should stretch children's feet to improve their mathematical ability? Certainly not—both shoe size and math skills increase independently with age. We refer to "age" here as the hidden variable; increasing age is the real reason that shoe size and mathematical ability increase simultaneously. Here are some more examples of the hidden variable phenomenon.
Do churches cause murder? In the 1980s several studies used census data to show that the more churches a city has, the more murders occur in the city each year. With tongue in cheek, the authors claimed to have proved that the presence of churches increases the prevalence of murders. While the data were correct, the conconclusion was obviously nonsense. What is the hidden variable here? Larger cities tend to have more of everything, including both churches and murders, so the hidden variable is population size.
Vladislav Gurfinkel/Shutterstock.com 2009
Jack Dagley/Shutterstock.com 2009
Do video games cause violent behavior? Some studies have shown that playing violent video games and aggressive behavior are strongly correlated. While it is certainly possible that violent video games might cause desensitization to actual aggressive behavior, could there be a hidden variable here as well? Some people are innately more violent than others, quicker to lose their temper or lash out. Perhaps these inborn tendencies cause both an interest in violent video games and a tendency toward real-life violence. More research is needed to settle these questions.
It is important not to jump to conclusions. Correlation and causation are not the same thing. Correlation is a useful tool for bringing important cause-and-effect relationships to light, but to prove causation, we must explain the mechanism by which one variable affects the other. For example, the link between smoking and lung cancer was observed as a correlation long before medical science determined how the toxins in tobacco smoke actually cause lung cancer.
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Just because not every correlation is evidence of causation doesn't mean that we should be too skeptical about studies that use correlation to link two variables. But sometimes people get the direction of causation wrong; instead of concluding correctly that A causes B, they conclude wrongly that B causes A. Here are some examples of this type of thinking.