In performing case-study research, researchers try to find associations between two or more variables (such as number of pounds and number of inches) used as measures of concepts (such as weight and height). Comparisons of case studies, such as that of Greg with those of others who have suffered damage to the same areas of the brain, have demonstrated that there is an association between damage to particular brain structures and specific physical & mental abnormalities. From the results of these case-study comparisons, researchers can predict that, in the general population, a similar association exists between normal activity in these brain structures and normal mental and physical functioning. Because case-study research, however, involves only a small number of cases and generally includes only people who are abnormal in some way, it is not possible to establish that the predicted association is a common one (that is, that it is true of most individuals, especially of most normal individuals).

One way to establish that there exists a general relationship between variables is to measure those variables in many individuals. A correlational study is a type of study in which two (or more) variables are measured and compared in a large group of individuals. The results of a correlational study allow us to determine whether or not the two variables “go together” — that is, to determine the degree to which they change together, on average. If two variables change together in the same direction, such as is true for height and weight (taller people tend to be heavier, on average, and vice versa), we say that the variables are positively correlated. If two variables change together in the opposite direction, such as alcohol intake and driving ability (the more alcohol one drinks, the less one is able to drive, on average, and vice versa), we say that the variables are negatively correlated. The major strength of correlational studies is that they allow us to quickly discover general relationships among variables (or, at least, more quickly than if we compared a large number of case studies).

Let's look at an example of a correlational study. Deady and Smith (2006) calculated, in 679 women between the ages of 20 and 29 years, correlations between their height and three other variables:

1. maternal personality (importance of having children, desire to have children);
2. reproductive ambition (ideal number of children, ideal age to have first child);
3. career orientation (importance of having a career, career competitiveness.

The researchers found a positive correlation between height and career orientation: on average, the taller a woman was, the stronger was her career orientation. They found a negative correlation between height and maternal personality: on average, the taller a woman was, the less of a maternal personality she had. Finally, they found a negative correlation between height and reproductive ambition: the taller a woman was, the weaker was her reproductive ambition. From these results, can we conclude that height causes women to have less reproductive ambition, a reduced maternal personality, and a greater career orientation? Can we conclude that little girls who, when thinking about what they would like to do when they grow up, express the desire to have many children and seem less interested in having a career, do not grow as tall as do little girls with the opposite goals? What precisely can we conclude from these correlations?

When interpreting the results of correlational studies, it is important to remember two limitations of correlational data:

1. Regardless of the degree to which two variables are correlated, the association will not be observed in all individuals. For instance, there is a correlation between how much nutritious food is eaten during childhood and how tall one is in adulthood. Nevertheless, there are people who ate very well as children but who are very short, and others who had poor nutrition but who are very tall. In a similar way, not all short women want to raise a large family and forgo a career; and not all tall women want to have one child and become CEO of a Fortune-500 company.
2. Regardless of the degree to which two variables are correlated, the association will not tell us the cause of the correlation. For instance, there is a correlation between where students sit in a classroom and their grades: those who sit in front tend to get higher grades than those who sit in back (Perkins & Wieman, 2005). But this does not mean that, if a student is not doing well on tests, the instructor should tell her to sit in front so that she can improve her test grades (see Kalinowski & Taper, 2007). In a similar way, it would not make sense for a mother to give her daughter growth-hormone injections in order to make the daughter grow taller and, hence, become more career-oriented.

When we find a correlation between two variables, such as where students sit in a classroom and course grades, there is no way we can tell from the correlation alone what is causing the two variables to be correlated. Why? Because when two variables, A and B, are correlated, there are three possible explanations for the association:

• Changes in Variable A may be causing changes in Variable B.
• Changes in Variable B may be causing changes in Variable A.
• Changes in Variable C — an unmeasured third variable — may be causing changes in Variable A and in Variable B.

In the correlation between classroom seat location and course grades, it could be that

• sitting in front (Variable A) causes students to get better grades (Variable B),
• getting better grades (Variable B) causes students to sit in front (Variable A), or
• being more motivated (an unmeasured third variable, C) causes students both to sit in front (Variable A) and get better grades (Variable B).

In other words, correlational studies have two major problems that make it impossible to infer anything about the cause of a correlation based on the correlation alone:

• The directionality problem. This refers to the possibility that Variable A is causing changes in Variable B, or that Variable B is causing changes in Variable A.
• The third-variable problem. This refers to the possibility that there is an unmeasured variable, C, that is causing changes in both Variable A and Variable B.

These two problems are illustrated in Figure 1.

Figure 1. The directionality and third-variable problems in correlational studies

Let's examine these two problems by looking at some other examples. There is a correlation between the kind of car one owns and whether or not one has cancer: people who own sports cars are less likely, on average, to have cancer than are people who own other types of car. What is causing this correlation? The directionality problem suggests two possibilities:

• Owning a sports car causes people to be less likely to develop cancer. Perhaps they feel better about themselves and this positive attitude results in less cancer.
• Developing cancer causes people to buy automobiles other than sports cars. Perhaps their cancer treatments cost so much that they cannot afford sports cars.

The third-variable problem suggests another possibility:

• An extraneous variable affects both the kind of car one owns and one’s risk of having cancer. Perhaps people who are older (age being an unmeasured third variable) are less likely to buy sports cars and are more likely to have cancer.

All we can conclude from the negative correlation between whether or not one owns a sports car and whether or not one has been diagnosed with cancer is that the two variables are associated in the general population: as one variables increases, the other variable decreases.

Let's look at another example. It has been found that the existence of gum disease (Variable A) in a pregnant mother is negatively correlated with the birth weight (Variable B) of her baby. In other words, pregnant mothers with gum disease tend to give birth to low-weight babies. What is causing this correlation? The directionality problem suggests two possibilities:

• Gum disease in pregnant mothers causes abnormal fetal development, which leads to lower birth weights. Perhaps the mother's immune system is using too much "energy" to fight off the disease — energy that then is not available to the developing fetus.
• Abnormal fetal development causes gum disease in pregnant mothers. Perhaps the abnormal development is sapping the mother’s strength, thereby leaving her more vulnerable to various diseases.

The third-variable problem suggests another possibility:

• An extraneous variable causes the development of maternal gum disease and abnormal fetal development. Perhaps impoverished pregnant women (poverty being an unmeasured third variable) are less likely to have adequate health care, which leaves both the women and their developing fetuses more vulnerable to disease.

Thus, the major weakness of correlational studies is that the directionality and third-variable problems do not allow researchers to infer cause-and-effect relationships from correlational data. Students often forget this point on tests, so it bears repeating:

We can conclude NOTHING about cause-and-effect between two variables based only on the fact that the two variables are correlated.

Study Questions for Section 3-4

1. How are correlational studies similar to case studies?
2. How do correlational studies differ from case studies?
3. What is an example of a positive correlation not mentioned in the text?
4. What is an example of a negative correlation not mentioned in the text?
5. What is the major strength of correlational studies?
6. What are two limitations of correlational data that affect how we interpret correlations?
7. How would you define the directionality problem in your own words?
8. What is an example of the directionality problem not mentioned in the text?
9. How would you define the third-variable problem in your own words?
10. What is an example of the third-variable problem not mentioned in the text?
11. What is the major weakness of correlational studies?

Go to Quiz 3-4 questions

Go to Readings Section 3-5