Sobel Test

The Sobel test is used to determine whether a variable carries (or mediates) the effect of an independent variable to the dependent variable—the outcome of interest. A significant test statistic offers evidence that an independent variable has an indirect effect (i.e., an effect that is mediated in whole or in part through another variable) on the dependent variable. This is done by testing the hypothesis that there is no statistical difference between the total effect (i.e., the effect of a specified independent variable on the dependent variable) and the direct effect (i.e., the effect of that same independent variable on the dependent variable) after taking into account the influence of a potential mediator.

Mediation effects of this nature abound in communication research. For instance, some of the earliest work on media effects, much of which was inspired by the apparent success of Axis propaganda efforts during World War II, sought to connect messages from the mass media with attitudes and behaviors at the level of the individual. Instead of uncovering large, direct effects in line with what they had anticipated, however, researchers instead found that the impact of the mass media was almost wholly mediated through opinion leaders and other social channels of communication. The Sobel test, and other similar methods, is used in exploring such relationships and is essential to determinations of whether the effect of an independent variable on a dependent variable is carried at least in part by one or more mediating variables.

This entry offers an overview of mediational analysis and provides a motivating example. It goes on to detail the conduct of the Sobel test, its constituent components, and the formula that is used in its calculation. It also discusses the assumptions behind the Sobel test, its limitations, and briefly introduces some alternative tests and methods for demonstrating the presence of a significant mediation effect.