A Sobel test is a method of testing the significance of a mediation effect.
According to Wikipedia:
In mediation, the relationship between the independent variable and the dependent variable is hypothesized to be an indirect effect that exists due to the influence of a third variable (the mediator). As a result when the mediator is included in a regression analysis model with the independent variable, the effect of the independent variable is reduced and the effect of the mediator remains significant.
The Sobel test is basically a specialized t test that provides a method to determine whether the reduction in the effect of the independent variable, after including the mediator in the model, is a significant reduction and therefore whether the mediation effect is statistically significant.
This tutorial explains how to conduct a Sobel test in Excel.
How to Conduct a Sobel Test in Excel
A sobel test uses the following formula to calculate a test statistic:
Sobel test statistic = (a*b) /√(b2*sa2 + a2*sb2)
- a is the raw regression coefficient for the association between the independent variable and the mediator
- sa is the standard error of a
- b is the raw coefficient for the association between the mediator and the dependent variable
- sb is the standard error of b
Note: the standard errors, sa and sb, should never be negative.
In order to get a and sa, run a regression analysis with the independent variable predicting the mediator.
In order to get b and sb, run a regression analysis with the independent variable and the mediator predicting the dependent variable.
Once you have these four numbers, you can conduct the Sobel test. For example, suppose we get the following numbers:
- a = 0.92
- sa = 0.31
- b = 0.77
- sb = 0.21
The screenshot below shows how to perform the Sobel test in Excel using these numbers:
You need to enter the values in cells B1:B4. Then, the results of the test are shown in cells B6:B8 along with the formulas used to get those results in cells C6:C8.
For this particular example, suppose we are conducting a two-sided Sobel test using a significance level of alpha = 0.05. In this case, the two-tailed p-value of the test is 0.021065, which is less than 0.05. This indicates that the mediation effect is statistically significant.
Note: You may use a different alpha level in your own test. Common choices for alpha include 0.01, 0.05, and 0.10.