Calculator Form
Example Data Table
| Case | Path a | SE a | Path b | SE b | Total c | Direct c prime | Expected indirect |
|---|---|---|---|---|---|---|---|
| Study time through confidence | 0.62 | 0.14 | 0.48 | 0.12 | 0.58 | 0.28 | 0.2976 |
| Training through skill gain | 0.75 | 0.18 | 0.36 | 0.10 | 0.50 | 0.23 | 0.2700 |
| Stress through sleep quality | -0.40 | 0.11 | 0.52 | 0.15 | -0.35 | -0.14 | -0.2080 |
Formula Used
Indirect effect: a × b
Computed total effect: c prime + a × b
Sobel standard error: square root of b²SEa² + a²SEb²
Sobel z score: indirect effect divided by Sobel standard error
Proportion mediated: indirect effect divided by total effect, then multiplied by 100
Path a estimates the predictor to mediator relation. Path b estimates the mediator to outcome relation while controlling the predictor. Path c is the total effect. Path c prime is the remaining direct effect after adding the mediator.
How to Use This Calculator
- Enter labels for the predictor, mediator, and outcome.
- Add path a and its standard error from your model.
- Add path b and its standard error from your model.
- Enter the total effect c and direct effect c prime.
- Choose the confidence level and decimal precision.
- Press the calculate button.
- Review the result shown above the form.
- Use the CSV or PDF button to save the output.
About the Mediation Calculator
Purpose
A mediation calculator helps study how one variable explains the link between another predictor and an outcome. It is common in psychology, education, health research, business studies, and social science. The predictor is usually called X. The mediator is called M. The final outcome is called Y. The tool uses path coefficients to estimate direct and indirect influence.
Inputs
This page accepts the main paths used in a simple mediation model. Path a measures how X predicts M. Path b measures how M predicts Y while X is controlled. Path c is the total effect of X on Y. Path c prime is the direct effect after the mediator is included. The indirect effect is found by multiplying a and b.
Testing
The calculator also estimates the Sobel standard error. This value is useful when standard errors for a and b are known. A z score and approximate p value are then reported. The confidence interval gives a quick range for the indirect effect. It should not replace a full statistical model, yet it is helpful for learning and reporting checks.
Interpretation
Advanced use needs careful interpretation. Mediation does not prove causation by itself. Good design, timing, theory, and measurement quality still matter. A strong indirect effect only says the mediator statistically carries part of the association. It does not show that the pathway is truly causal without stronger evidence.
Comparison
Researchers often compare the direct effect and indirect effect. When the indirect effect is large, the mediator may explain much of the original relationship. When the direct effect remains large, other mechanisms may still be active. The proportion mediated can help summarize this balance. It is reported only when the total effect is not zero.
Best Practice
This calculator is best for coefficient based work. You can copy values from regression output, path analysis output, or classroom examples. Use the same scale and model family for all paths. Keep more decimal places while entering values. Rounded inputs can change small indirect effects. Save the exported table for notes, peer review, or audit records. Always report your original model, sample size, assumptions, and software method with calculator results.
For detailed reports, confirm calculator results with bootstrapped intervals. Product terms can skew in small study samples too.
FAQs
1. What is mediation analysis?
Mediation analysis studies whether a mediator explains part of the relationship between a predictor and an outcome. It separates the indirect effect from the remaining direct effect.
2. What is the indirect effect?
The indirect effect is the product of path a and path b. It estimates how much influence moves through the mediator.
3. What is path a?
Path a is the coefficient for the predictor’s effect on the mediator. It is usually taken from a regression or path model.
4. What is path b?
Path b is the mediator’s effect on the outcome while the predictor is controlled. It helps estimate the mediated pathway.
5. What is the Sobel test?
The Sobel test checks whether the indirect effect differs from zero. It uses path coefficients and their standard errors.
6. Can this calculator prove causation?
No. Mediation results support a statistical pathway. Causal claims need strong design, theory, timing, and control of alternative explanations.
7. Why is proportion mediated unavailable sometimes?
Proportion mediated needs a nonzero total effect. If the total effect is zero, the percentage would be undefined.
8. Should I use bootstrapping too?
Yes, when possible. Bootstrapped confidence intervals are often preferred because indirect effects can be skewed, especially in smaller samples.