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 testis 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) /√(b^{2}*s_{a}^{2} + a^{2}*s_{b}^{2})

where:

is the raw regression coefficient for the association between the independent variable and the mediator**a**is the standard error of**s**_{a}*a*is the raw coefficient for the association between the mediator and the dependent variable**b**is the standard error of**s**_{b}*b*

*Note: the standard errors, s_{a} and s_{b}, should never be negative.*

In order to get * a* and

**s**, run a regression analysis with the independent variable predicting the mediator.

_{a}In order to get * b* and

**s**, run a regression analysis with the independent variable and the mediator predicting the dependent variable.

_{b}Once you have these four numbers, you can conduct the Sobel test. For example, suppose we get the following numbers:

= 0.92**a**= 0.31**s**_{a}= 0.77**b**= 0.21**s**_{b}

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.