Correlation Does Not Imply Causation

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Researchers are often interested in a statistical relationship between two variables because they think that one of the variables causes the other. That is, the statistical relationship reflects a causal relationship. In these situations, the variable that is thought to be the cause is called the independent variable (often referred to as X for short), and the variable that is thought to be the effect is called the dependent variable (often referred to as Y). For example, the statistical relationship between whether or not a depressed person receives psychotherapy and the number of depressive symptoms he or she has reflects the fact that the psychotherapy (the independent variable) causes the reduction in symptoms (the dependent variable). Understanding causal relationships is important in part because it allows us to change people’s behavior in predictable ways. If we know that psychotherapy causes a reduction in depressive symptoms—and we want people to have fewer depressive symptoms—then we can use psychotherapy to achieve this goal.

But not all statistical relationships reflect causal relationships. This is what psychologists mean when they say, “Correlation does not imply causation.” An obvious example comes from a study in Taiwan showing a positive relationship between the number of electrical appliances that people use and the extent to which they use birth control (Stanovich, 2010). 1 It seems clear, however, that this does not mean that owning electrical appliances causes people to use birth control, and it would not make sense to try to increase the use of birth control by giving people toasters and hair dryers.

There are two reasons that correlation does not imply causation. The first is called the directionality problem. Two variables, X and Y, can be statistically related because X causes Y or because Y causes X. Consider, for example, a study showing that whether or not people exercise is statistically related to how happy they are—such that people who exercise are happier on average than people who do not. This statistical relationship is consistent with the idea that exercising causes happiness, but it is also consistent with the idea that happiness causes exercise. Perhaps being happy gives people more energy or leads them to seek opportunities to socialize with others by going to the gym.

The second reason that correlation does not imply causation is called the third-variable problem. Two variables, X and Y, can be statistically related not because Xcauses Y, or because Y causes X, but because some third variable, Z, causes both Xand Y. For example, the fact that people with more electrical appliances are more likely to use birth control probably reflects the fact that having more education or income causes people to own more appliances and causes them to use birth control. Similarly, the statistical relationship between exercise and happiness could mean that some third variable, such as physical health, causes both of the others. Being physically healthy could cause people to exercise and cause them to be happier.

As we will see later in the book, there are various ways that researchers address the directionality and third-variable problems. The most effective, however, is to conduct an experiment. An experiment is a study in which the researcher manipulates the independent variable. For example, instead of simply measuring how much people exercise, a researcher could bring people into a laboratory and randomly assign half of them to run on a treadmill for 15 minutes and the rest to sit on a couch for 15 minutes. Although this seems like a minor addition to the research design, it is extremely important. Now if the exercisers end up in more positive moods than those who did not exercise, it cannot be because their moods affected how much they exercised (because it was the researcher who determined how much they exercised). Likewise, it cannot be because some third variable (e.g., physical health) affected both how much they exercised and what mood they were in (because, again, it was the researcher who determined how much they exercised). Thus experiments eliminate the directionality and third-variable problems and allow researchers to draw firm conclusions about causal relationships. We will have much more to say about experimental and nonexperimental research later in the book.