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.
“Lots of Candy Could Lead to Violence”
Although researchers in psychology know that correlation does not imply causation, many journalists do not. One website about correlation and causation, http://jonathan.mueller.faculty.noctrl.edu/100/correlation_or_causation.htm, links to dozens of media reports about real biomedical and psychological research. Many of the headlines suggest that a causal relationship has been demonstrated, when a careful reading of the articles shows that it has not because of the directionality and third-variable problems.
One article is about a study showing that children who ate candy every day were more likely than other children to be arrested for a violent offense later in life. But could candy really “lead to” violence, as the headline suggests? What alternative explanations can you think of for this statistical relationship? How could the headline be rewritten so that it is not misleading?
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.
KEY TAKEAWAYS
- Research questions in psychology are about variables and relationships between variables.
- Two basic forms of statistical relationship are differences between group means and correlations between quantitative variables, each of which can be described using a few simple statistical techniques.
- Correlation does not imply causation. A statistical relationship between two variables, X and Y, does not necessarily mean that X causes Y. It is also possible that Y causes X, or that a third variable, Z, causes both Xand Y.
EXERCISE
- Practice: List 10 variables that might be of interest to a researcher in psychology. For each, specify whether it is quantitative or categorical.
- Practice: Imagine that you categorize people as either introverts (quieter, shyer, more inward looking) or extroverts (louder, more outgoing, more outward looking). Sketch a bar graph showing a hypothetical statistical relationship between this variable and the number of words people speak per day.
- Practice: Now imagine that you measure people’s levels of extroversion as a quantitative variable, with values ranging from 0 (extreme introversion) to 30 (extreme extroversion). Sketch a scatterplot showing a hypothetical statistical relationship between this variable and the number of words people speak per day.
- Practice: For each of the following statistical relationships, decide whether the directionality problem is present and think of at least one plausible third variable:
- People who eat more lobster tend to live longer.
- People who exercise more tend to weigh less.
- College students who drink more alcohol tend to have poorer grades.
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