Sobel's Test
As mentioned above, Sobel’s test is calculated to determine if the relationship between the independent variable and dependent variable has been significantly reduced after inclusion of the mediator variable. In other words, this test assesses whether a mediation effect is significant.
File:Sobelteststatistic equation.png
Examines the relationship between the independent variable and the dependent variable compared to the relationship between the independent variable and dependent variable including the mediation factor.
The Sobel test is more accurate than the Baron and Kenny steps explained above, however it does have low statistical power. As such, large sample sizes are required in order to have sufficient power to detect significant effects. This is because the key assumption of Sobel’s test is the assumption of normality. Because Sobel’s test evaluates a given sample on the normal distribution, small sample sizes and skewness of the sampling distribution can be problematic (See Normal Distribution for more details). Thus, the general rule of thumb as suggested by MacKinnon et al., (2002) is that a sample size of 1000 is required to detect a small effect, a sample size of 100 is sufficient in detecting a medium effect, and a sample size of 50 is required to detect a large effect.
Read more about this topic: Mediation (statistics)
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