Analyze coefficients, direct effects, and indirect strength. Test Sobel significance, standardization, and mediation ratios instantly. Visualize exports, assumptions, formulas, and examples with confidence today.
Use this calculator to estimate the indirect effect in a single mediator model, evaluate practical magnitude, inspect Sobel significance, and generate export-ready summaries.
| Example model | a | b | c | c′ | SE(a) | SE(b) | Indirect effect |
|---|---|---|---|---|---|---|---|
| Stress → Sleep → Performance | 0.45 | 0.38 | 0.41 | 0.24 | 0.08 | 0.07 | 0.171 |
| Training → Confidence → Sales | 0.52 | 0.29 | 0.36 | 0.21 | 0.09 | 0.06 | 0.151 |
| Ad exposure → Recall → Intent | 0.31 | 0.44 | 0.28 | 0.14 | 0.07 | 0.08 | 0.136 |
Indirect effect: a × b
Total effect: c = c′ + a × b when c is not supplied.
Proportion mediated: (a × b) / c
Indirect to direct ratio: (a × b) / c′
Completely standardized indirect effect: (a × b) × (SDx / SDy)
Sobel standard error: √(b² × SEa² + a² × SEb²)
Sobel z: (a × b) / Sobel SE
These formulas are useful for quick summaries, but bootstrap confidence intervals are often preferred in formal mediation analysis because they handle non-normal indirect effects better.
It estimates how much of the predictor’s influence reaches the outcome through the mediator. In a simple model, it equals the product of the a and b paths.
Enter c when your model output reports the total predictor-to-outcome effect directly. If you leave it blank, the calculator reconstructs c from c′ plus the indirect effect.
It is a useful approximation, but many researchers prefer bootstrap intervals because indirect effects can be skewed. Treat Sobel output as a quick screen, not the final word.
It shows the share of the total effect that travels through the mediator. Interpret it carefully when total effects are very small or when direct and indirect effects move in opposite directions.
Inconsistent mediation appears when direct and indirect effects have opposite signs. That means the transmitted pathway and the remaining direct pathway are pushing the outcome in different directions.
It rescales the indirect effect using the standard deviations of the predictor and outcome. This helps compare effect magnitudes across studies measured on different scales.
This page is designed for a single mediator path. For parallel or serial mediation, estimate each indirect pathway separately and use software that supports those full models.
Use the coefficients exactly as reported by your model. Keep all paths from the same estimation scale, and add standard deviations only when you want the standardized effect.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.