Researchers face the third-variable problem in nonexperimental research when some uncontrolled third variable may be responsible for the relationship between the two variables of interest. For example, a finding that people who exercise more have lower anxiety levels could be due to a third variable such as income. High income may cause both exercise and low anxiety (see Chapter 4). When properly designed and executed, the problem does not exist in experimental research, because all extraneous variables are controlled either by keeping the variables constant or by using randomization.
Page 260A technique called partial correlation provides a way of statistically controlling third variables. A partial correlation is a correlation between the two variables of interest, with the influence of the third variable removed from, or “partialed out of,” the original correlation. This provides an indication of what the correlation between the primary variables would be if the third variable were held constant. This is not the same as actually keeping the variable constant, but it is a useful approximation.
Suppose a researcher is interested in a measure of number of bedrooms per person as an index of household crowding—a high number indicates that more space is available for each person in the household. After obtaining this information, the researcher gives a cognitive test to children living in these households. The correlation between bedrooms per person and test scores is .50. Thus, children in more spacious houses score higher on the test. The researcher suspects that a third variable may be operating. Social class could influence both housing and performance on this type of test. If social class is measured, it can be included in a partial correlation calculation that looks at the relationship between bedrooms per person and test scores with social class held constant. To calculate a partial correlation, you need to have scores on the two primary variables of interest and the third variable that you want to examine.
When a partial correlation is calculated, you can compare the partial correlation with the original correlation to see if the third variable did have an effect. Is our original correlation of .50 substantially reduced when social class is held constant? Figure 12.11 shows two different partial correlations. In both, there is a .50 correlation between bedrooms per person and test score. The first partial correlation between bedrooms per person and test scores drops to .09 when social class is held constant because social class is so highly correlated with the primary variables. However, the partial correlation in the second example remains high at .49 because the correlations with social class are relatively small. Thus, the outcome of the partial correlation depends on the magnitude of the correlations between the third variable and the two variables of primary interest.
Two partial correlations between bedrooms per person and performance