Another important use of complex correlational research is to explore possible causal relationships among variables. This might seem surprising given that “correlation does not imply causation.” It is true that correlational research cannot unambiguously establish that one variable causes another. Complex correlational research, however, can often be used to rule out other plausible interpretations.

The primary way of doing this is through the **st****a****t****i****st****i****c****a****l ****co****n****t****rol** of potential third variables. Instead of controlling these variables by random
assignment or by holding them constant as in an experiment, the researcher measures them and includes them in the statistical analysis. Consider some research by Paul Piff and his colleagues,
who hypothesized that being lower in socioeconomic status (SES) causes people to be more generous (Piff, Kraus, Côté, Hayden Cheng, & Keltner, 2011). 1 They measured their participants’ SES and had them play the “dictator game.” They told participants that each would be paired with another participant in a
different room. (In reality, there was no other participant.) Then they gave each participant 10 points (which could later be converted to money) to split with the “partner” in whatever way he
or she decided. Because the participants were the “dictators,” they could even keep all 10 points for themselves if they wanted to.

As these researchers expected, participants who were lower in SES tended to give away more of their points than participants who were higher in SES. This is consistent with the idea that being lower in SES causes people to be more generous. But there are also plausible third variables that could explain this relationship. It could be, for example, that people who are lower in SES tend to be more religious and that it is their greater religiosity that causes them to be more generous. Or it could be that people who are lower in SES tend to come from ethnic groups that emphasize generosity more than other ethnic groups. The researchers dealt with these potential third variables, however, by measuring them and including them in their statistical analyses. They found that neither religiosity nor ethnicity was correlated with generosity and were therefore able to rule them out as third variables. This does not prove that SES causes greater generosity because there could still be other third variables that the researchers did not measure. But by ruling out some of the most plausible third variables, the researchers made a stronger case for SES as the cause of the greater generosity.

Many studies of this type use a statistical technique called **m****ul****t****i****ple ****r****e****g****r****e****ss****i****o****n**. This involves
measuring several independent variables (*X**1**,**X**2**,**X**3**,…**X**i*), all of which are possible causes of a
single dependent variable (*Y*). The result of a multiple regression analysis is an equation that expresses the dependent variable as an additive combination of the independent
variables. This regression equation has the following general form:

*b**1**X**1**+* *b**2**X**2**+* *b**3**X**3**+**… +*
*b**i**X**i**= Y*.

The quantities *b**1**,**b**2*, and so on are regression weights that indicate how large a contribution an independent variable makes, on average, to the
dependent variable. Specifically, they indicate how much the dependent variable changes for each one-unit change in the independent variable.

The advantage of multiple regression is that it can show whether an independent variable makes a contribution to a dependent variable *over**and**above*the contributions
made by other independent variables. As a hypothetical example, imagine that a researcher wants to know how the independent variables of income and health relate to the dependent variable of
happiness. This is tricky because income and health are themselves related to each other. Thus if people with greater incomes tend to be happier, then perhaps this is only because they tend to
be healthier. Likewise, if people who are healthier tend to be happier, perhaps this is only because they tend to make more money. But a multiple regression analysis including both income and
happiness as independent variables would show whether each one makes a contribution to happiness when the other is taken into account. (Research like this, by the way, has shown both income and
health make extremely small contributions to happiness except in the case of severe poverty or illness; Diener, 2000. 2)

The examples discussed in this section only scratch the surface of how researchers use complex correlational research to explore possible causal relationships among variables. It is important to keep in mind, however, that purely correlational approaches cannot unambiguously establish that one variable causes another. The best they can do is show patterns of relationships that are consistent with some causal interpretations and inconsistent with others.

## KEY TAKEAWAYS

- Researchers often use complex correlational research to explore relationships among several variables in the same study.
- Complex correlational research can be used to explore possible causal relationships among variables using techniques such as multiple regression. Such designs can show patterns of relationships that are consistent with some causal interpretations and inconsistent with others, but they cannot unambiguously establish that one variable causes another.

## EXERCISES

- Practice: Make a correlation matrix for a hypothetical study including the variables of depression, anxiety, self-esteem, and happiness. Include the Pearson’s
*r*values that you would expect. - Discussion: Imagine a correlational study that looks at intelligence, the need for cognition, and high school students’ performance in a critical-thinking course. A multiple regression analysis shows that intelligence is not related to performance in the class but that the need for cognition is. Explain what this study has shown in terms of what causes good performance in the critical-thinking course.

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