Enter the effect of the independent variable on the mediator, the effect of the mediator on the dependent variable, controlling for the independent variable, and the standard errors of both into the calculator to determine the Sobel Test statistic.

Sobel Test Formula

The following formula is used to calculate the Sobel Test. 

S = (a*b - (SEa*SEb)) / sqrt((b^2 * SEa^2) + SEb^2)

Variables:

  • S is the Sobel Test statistic
  • a is the effect of the independent variable on the mediator (also known as the ‘a path’)
  • b is the effect of the mediator on the dependent variable, controlling for the independent variable (also known as the ‘b path’)
  • SEa is the standard error of
  • aSEb is the standard error of b

To calculate the Sobel Test statistic, multiply the effect of the independent variable on the mediator (a) by the effect of the mediator on the dependent variable, controlling for the independent variable (b). Subtract the product of the standard errors of a and b from this result. Divide this by the square root of the sum of the square of b times the square of the standard error of a and the square of the standard error of b.

What is a Sobel Test?

A Sobel Test is a statistical test used to determine the significance of a mediation effect in a model. It is used to check if the relationship between an independent variable and a dependent variable is significantly reduced or eliminated when a mediator variable is introduced. The test essentially measures the indirect effect of the independent variable on the dependent variable through the mediator. It is named after American statistician Michael E. Sobel who developed the test.

How to Calculate Sobel Test?

The following steps outline how to calculate the Sobel Test using the given formula:

  1. First, determine the value of a (effect of the independent variable on the mediator).
  2. Next, determine the value of b (effect of the mediator on the dependent variable, controlling for the independent variable).
  3. Next, determine the value of SEa (standard error of a).
  4. Next, determine the value of SEb (standard error of b).
  5. Using the formula S = (a*b – (SEa*SEb)) / sqrt((b^2 * SEa^2) + SEb^2), substitute the values of a, b, SEa, and SEb into the formula.
  6. Finally, calculate the Sobel Test statistic (S).

Example Problem:

Use the following variables as an example problem to test your knowledge:

a = 0.5

b = 0.8

SEa = 0.2

SEb = 0.3