Mediation Analysis Calculator

Mediation analysis tests whether a third variable (the mediator) explains the relationship between an independent variable (X) and a dependent variable (Y). Use it when you have a theoretical reason to believe X influences M, and M in turn influences Y — for example, whether stress (X) affects health outcomes (Y) through sleep quality (M).

The Sobel test evaluates whether the indirect effect of X on Y through M (calculated as a × b) is statistically different from zero. It computes a z-statistic by dividing the indirect effect by its standard error, then derives a two-tailed p-value. A significant result (typically p < 0.05) indicates meaningful mediation.

Path coefficient a is the unstandardized regression coefficient from the independent variable (X) to the mediator (M). Path coefficient b is the unstandardized regression coefficient from the mediator (M) to the dependent variable (Y), controlling for X. Both come from standard ordinary least squares regression analyses.

All three test the same indirect effect but differ slightly in their standard error formula. The Sobel test omits the term (SEa² × SEb²), the Aroian test includes it, and Goodman's (1959) test subtracts it. The Aroian/Goodman (1960) version is considered the most conservative and is generally recommended for small samples.

No — the Sobel test assumes a normal distribution of the indirect effect, which only holds well in large samples (typically n > 200). For smaller samples, bootstrapping methods (such as those available in Hayes' PROCESS macro) are strongly preferred because they impose no distributional assumptions and tend to be more accurate.

A non-significant result (p > α) means there is insufficient evidence that the mediator significantly transmits the effect of X to Y. However, this does not necessarily mean no mediation exists — the test may simply lack power, particularly in small samples. Consider using bootstrapping or increasing your sample size.

Full mediation occurs when the direct effect of X on Y becomes non-significant after controlling for the mediator M, while the indirect effect (a × b) remains significant. Partial mediation means both the direct and indirect effects are significant, indicating M explains some but not all of the X→Y relationship.

Run two separate regression analyses. First, regress M on X to get coefficient a and its standard error SEa. Second, regress Y on both X and M to get coefficient b and its standard error SEb. Most statistical software (SPSS, R, Python, Stata) reports these standard errors automatically in the regression output table.