Advanced Mediation Calculator
Example Data Table
| Scenario | Path a | Path b | Total c | Direct c′ | SE a | SE b | Expected Indirect |
|---|---|---|---|---|---|---|---|
| Training improves productivity through confidence | 0.45 | 0.38 | 0.52 | 0.35 | 0.11 | 0.10 | 0.1710 |
| Study time improves score through preparation | 0.62 | 0.41 | 0.74 | 0.49 | 0.14 | 0.12 | 0.2542 |
| Ad exposure affects sales through interest | 0.31 | 0.56 | 0.44 | 0.27 | 0.09 | 0.15 | 0.1736 |
Formula Used
The calculator uses common mediation analysis formulas based on path coefficients.
Indirect effect: ab = a × b
Total effect by parts: c = c′ + ab
Indirect effect by difference: ab = c − c′
Sobel standard error: SEab = √(b²SEa² + a²SEb²)
Sobel z score: z = ab / SEab
Percent mediated: (ab / c) × 100
Standardized indirect effect: ab × SDx / SDy
How to Use This Calculator
Enter the path a coefficient from the model where X predicts the mediator. Enter path b from the model where the mediator predicts Y while X is controlled. Add the total effect c and direct effect c′. Then enter standard errors for paths a and b.
Choose a confidence level. Add standard deviations when you want standardized effects. Press the calculate button. The result section will appear below the header and above the form. Use the CSV or PDF button to save the output.
Mediation Analysis Guide
What Mediation Means
Mediation analysis explains how one variable affects another variable through a third variable. The first variable is often called X. The outcome is called Y. The mediator is called M. A useful mediation model does more than show that X and Y are related. It also shows a possible pathway between them.
Why the Indirect Effect Matters
The indirect effect is the core value in mediation. It is found by multiplying path a by path b. Path a shows how X changes the mediator. Path b shows how the mediator changes Y after controlling for X. When this product is large, the mediator may carry an important part of the effect.
Direct and Total Effects
The total effect is the overall link between X and Y. The direct effect is the remaining link after the mediator is added. If the direct effect becomes smaller, mediation may be present. If it changes direction, the pattern may be competitive. This is common when different mechanisms work against each other.
Using Significance Tests
The Sobel test checks whether the indirect effect differs from zero. It uses the path coefficients and their standard errors. A small p value suggests that the mediation pathway is unlikely to be random. However, the Sobel test assumes a near normal indirect effect. That assumption may be weak in small samples.
Reading the Percent Mediated
The percent mediated compares the indirect effect with the total effect. It can help explain practical meaning. A high percentage suggests that much of the relationship flows through the mediator. A low percentage suggests that other pathways may explain more. This value should be interpreted carefully when the total effect is small.
Practical Advice
Use clean regression estimates. Keep variables measured in clear units. Check model assumptions before reporting results. Compare the product method with the difference method. Large differences may suggest rounding, model mismatch, or omitted variables. Treat the calculator as an analysis aid, not as final proof of causation.
Frequently Asked Questions
1. What is a mediation calculation?
It estimates whether a mediator helps explain how an independent variable affects an outcome variable. The main result is the indirect effect, calculated from paths a and b.
2. What is path a?
Path a is the effect of the independent variable on the mediator. It usually comes from a regression model where the mediator is the dependent variable.
3. What is path b?
Path b is the effect of the mediator on the outcome while controlling the independent variable. It shows whether the mediator predicts the final outcome.
4. What is the indirect effect?
The indirect effect is path a multiplied by path b. It estimates how much of the relationship passes through the mediator.
5. What does percent mediated mean?
Percent mediated shows the indirect effect as a percentage of the total effect. It helps describe how much influence flows through the mediator.
6. What is the Sobel test?
The Sobel test checks whether the indirect effect is statistically different from zero. It uses coefficients and standard errors for paths a and b.
7. Can this prove causation?
No. Mediation analysis supports a proposed mechanism, but causation needs strong design, timing, theory, and control of confounding variables.
8. Why are standardized effects useful?
Standardized effects make results easier to compare across measures. They adjust the effect using standard deviations of the predictor and outcome.