Quantitative Results

Moderation and mediation are fundamental statistical concepts in the social sciences. Through these analyses, we can better understand why certain variables may be related to each other (mediation) and under what conditions certain variables are related to each other (moderation). For more explanation on the conceptual differences between moderation and mediation, see our previous blog on the topic.

Statistical approaches to moderation and mediation have evolved over the years, as computer programming has become more ubiquitous, and statistical software packages have become more robust and diverse in their capabilities. One of the most notable changes in mediation techniques is the shift from Baron and Kenny’s (1986) classic approach to more formal testing of indirect effects. In Baron and Kenny’s approach, evidence of mediation is established through a series of regressions. In the first regression, the independent variable predicts the mediator; in the second, the independent variable predicts the dependent variable; and in the third, the independent variable and mediator both predict the dependent variable. There is evidence for mediation if the relationship between the independent variable and the dependent variable is significantly weakened after adding the mediator to the regression.

As Preacher and Hayes (2004) noted, there are limitations in the Baron and Kenny approach to mediation that can be alleviated by formally testing indirect effects. In simple mediation, the indirect effect is the difference in the relationship between the independent variable (X) and dependent variable (Y) before and after controlling for the mediator. For example, if X predicts Y with a regression coefficient of 0.5 before controlling for the mediator, and this regression coefficient is reduced to 0.2 after controlling for the mediator, the indirect effect would be computed by subtracting 0.2 from 0.5, giving us a value of 0.3. We can then perform statistical tests to determine if the indirect effect is significantly different from zero, which would provide evidence for mediation. To perform such a test, Preacher and Hayes (2004) suggested generating confidence intervals for the indirect effect using bootstrapping; if the confidence interval for the indirect effect does not contain zero, we can conclude that the effect is significant. For example, if we generated a 95% confidence interval for our indirect effect and found the lower and upper bounds to be 0.15 and 0.45 respectively, we could conclude that the indirect effect is significantly greater than zero.

Statistics scholars and software developers have since created tools for performing these kinds of calculations. Among the most well-known tools is the Hayes PROCESS macro, which may be used to perform many types of moderation and mediation analyses in the SPSS, SAS, and R software packages. More information about how to use PROCESS is detailed in Hayes (2017). Intellectus Statistics also offers options for mediation and moderation analyses, including estimation of indirect effects.

**References**

Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. *Journal of Personality and Social Psychology, 51*, 1173-1182.

Hayes, A. F. (2017). *Introduction to mediation, moderation, and conditional process analysis: A regression-based approach*. Guilford publications.

Preacher, K. J., & Hayes, A. F. (2004). SPSS and SAS procedures for estimating indirect effects in simple mediation models. *Behavior Research Methods, Instruments, & Computers*, *36*(4), 717-731.

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