Formula Used
Indirect effect: ab = a × b
Direct effect: c′
Total effect: c = c′ + ab, unless a total effect is entered.
Proportion mediated: (ab ÷ c) × 100
Sobel standard error: SEab = √(b²SEa² + a²SEb²)
Sobel z: z = ab ÷ SEab
Simulated interval: The page draws many normal estimates for a and b. It multiplies each pair and reports percentile bounds.
How to Use This Calculator
- Enter a path coefficient for the effect of X on the mediator.
- Enter b path coefficient for the adjusted effect of the mediator on Y.
- Add c′ for the direct effect after the mediator is controlled.
- Add standard errors from your regression, SEM, or path model.
- Choose confidence level, simulation runs, and decimal places.
- Press calculate and review results above the form.
- Use the chart, CSV, and PDF options for reporting.
Example Data Table
| Scenario | a Path | SEa | b Path | SEb | c′ | SEc′ | Expected Meaning |
|---|---|---|---|---|---|---|---|
| Learning study | 0.42 | 0.08 | 0.31 | 0.07 | 0.18 | 0.06 | Confidence explains part of the effect. |
| Marketing study | 0.55 | 0.10 | 0.22 | 0.05 | 0.09 | 0.04 | Trust may mediate campaign impact. |
| Health study | -0.30 | 0.09 | 0.40 | 0.08 | -0.05 | 0.05 | Behavior change may reduce risk. |
About This Mediation Calculator
What It Measures
Mediation analysis studies how one variable affects another through a third variable. This calculator focuses on the main paths used in common mediation models. The a path connects the predictor to the mediator. The b path connects the mediator to the outcome. The c′ path shows the remaining direct effect.
Why It Is Useful
A direct result may look simple. Yet the process behind it can be more complex. Mediation helps explain that process. It shows whether a middle variable carries part of the effect. This is useful in education, health, marketing, psychology, and business studies.
Simulation Based Interval
The indirect effect is often not normally distributed. A simple standard error may miss that shape. This page uses a parametric simulation. It draws many possible a and b values from their standard errors. Each draw creates a new indirect effect. The final interval uses percentiles from those simulated effects.
Reading the Output
The indirect effect tells you how much influence passes through the mediator. The direct effect tells you what remains after accounting for the mediator. The total effect combines both parts. The mediated share converts the indirect pathway into a percentage. This makes the output easier to explain.
Best Practice
Use coefficients from a well planned model. Check assumptions before reporting results. Add theory, design details, and sample information. Do not rely only on the p value. Review the interval, effect size, and direction together. Use more simulation runs for final reporting.
Reporting Tip
Report the a path, b path, indirect effect, confidence interval, and direct effect. Mention the confidence level and number of simulation runs. Keep interpretation clear. Explain what the mediator means in real terms. Good reporting connects statistics with the actual research question.
FAQs
1. What is a mediation effect?
A mediation effect shows how one variable influences an outcome through a middle variable. It helps explain the path or process behind a relationship.
2. What is the indirect effect?
The indirect effect is the a path multiplied by the b path. It estimates how much effect travels through the mediator.
3. What does c′ mean?
c′ is the direct effect. It shows the remaining effect of the predictor on the outcome after the mediator is included.
4. Why use simulated intervals?
The indirect effect can have a skewed distribution. Simulated intervals can better show uncertainty than a simple normal interval.
5. What is the Sobel test?
The Sobel test checks whether the indirect effect differs from zero using an approximate standard error and z score.
6. What does proportion mediated mean?
It is the indirect effect divided by the total effect. It shows the percentage of the total effect carried by the mediator.
7. Can I use standardized coefficients?
Yes. You can use standardized coefficients if all entered paths and standard errors are on the same standardized scale.
8. Is this a replacement for full statistical software?
No. It is a reporting and checking tool. Use full statistical software for model fitting, diagnostics, and complex study designs.