Sobel Test Calculator

1. Run your mediation regression: First, run two regression models in SPSS, AMOS, or any statistical software. Model 1: regress the mediator (M) on the independent variable (X) to get coefficient a and its standard error. Model 2: regress the dependent variable (Y) on both X and M to get coefficient b and its standard error.

2. Enter Path A values: The unstandardized coefficient (a) from the regression of M on X, and its standard error (Sa). These values come from the "Coefficients" table in SPSS output.

3. Enter Path B values: The unstandardized coefficient (b) from the regression of Y on M (controlling for X), and its standard error (Sb).

4. Click Calculate: The calculator computes the z-value and p-value for three variants of the test. If the p-value is below 0.05, the indirect effect is statistically significant, meaning the mediator carries the influence of X on Y.

5. Use the APA citation: Copy the generated citation directly into your thesis methodology or results chapter. The citation follows APA 7th edition format.

The Sobel test (Sobel, 1982) is the most widely used method for testing the significance of an indirect effect in mediation analysis. In a simple mediation model, the independent variable (X) influences the dependent variable (Y) through a mediator (M). The indirect effect is the product of path a (X to M) and path b (M to Y).

The Three Test Variants

Sobel (1982) is the standard test and the most widely cited. It tests whether the indirect effect (ab) is significantly different from zero using the formula: z = ab / sqrt(b²s⊂a² + a²s⊂b²).

Aroian (1947) is a more conservative version that includes the often-omitted s⊂a²s⊂b² term in the standard error calculation. Many methodologists recommend the Aroian test over the standard Sobel test because it provides a more accurate estimate.

Goodman (1960) is the least conservative variant that subtracts the s⊂a²s⊂b² term. It is included for completeness but is rarely recommended as the primary test.

When to Use the Sobel Test

Use the Sobel test when you have a simple mediation model (X → M → Y) and want to test whether the indirect effect is statistically significant. The test assumes that the sampling distribution of the indirect effect is normal, which is reasonable for large samples (N > 100). For smaller samples, consider using bootstrapping via the PROCESS macro.

Important Notes

The Sobel test uses unstandardized coefficients and their standard errors, not standardized (beta) values. Make sure you are reading the correct column from your regression output. In SPSS, use the "B" column under "Unstandardized Coefficients," not the "Beta" column.