This tool estimates natural indirect effect measures from mediation path coefficients. It supports additive and ratio-style interpretations, computes Sobel-based uncertainty, and summarizes direct, total, and mediated shares in one place.
Calculator Inputs
Use the responsive grid below. Large screens show three columns, smaller screens show two, and mobile shows one.
Example Data Table
This sample illustrates a mediation setup with one-unit exposure contrast.
| Scenario | Path a | Path b | Total effect c | Direct effect c′ | SE(a) | SE(b) | Computed NIE |
|---|---|---|---|---|---|---|---|
| Program → adherence → blood pressure | 0.42 | 0.31 | 0.29 | 0.16 | 0.08 | 0.09 | 0.1302 |
| Training → confidence → productivity | 0.55 | 0.24 | 0.36 | 0.228 | 0.10 | 0.07 | 0.1320 |
| Exposure → biomarker → disease risk | -0.33 | 0.41 | -0.21 | -0.0747 | 0.06 | 0.08 | -0.1353 |
Formula Used
Additive scale: Natural indirect effect (NIE) = a × b × contrast.
Natural direct effect: NDE = total effect − NIE, unless a direct effect is supplied.
Total effect: TE = NIE + NDE.
Sobel standard error: SE(NIE) = |contrast| × √[(b² × SE(a)²) + (a² × SE(b)²)].
Z statistic: z = NIE / SE(NIE).
Two-sided p-value: p = 2 × [1 − Φ(|z|)].
Confidence interval: NIE ± zcritical × SE(NIE).
Ratio scale option: log(NIE ratio) = a × b × contrast, so NIE ratio = exp(a × b × contrast).
Proportion mediated: additive uses NIE / TE, while ratio mode uses log(NIE ratio) / log(TE ratio).
How to Use This Calculator
- Choose the effect scale that matches your mediation model and reporting style.
- Enter the path a coefficient from exposure to mediator.
- Enter the path b coefficient from mediator to outcome after adjusting for exposure.
- Provide the total effect, then optionally enter the direct effect if already estimated elsewhere.
- Add standard errors for path a and path b to compute the Sobel interval and p-value.
- Set the exposure contrast. Keep it at 1 for a standard one-unit effect comparison.
- Optionally rename the exposure, mediator, and outcome labels for cleaner reporting.
- Submit the form. Review NIE, NDE, TE, interval, percent mediated, and interpretation note above the form.
Frequently Asked Questions
1. What does the natural indirect effect measure?
It estimates how much of an exposure’s effect reaches the outcome through the mediator, assuming the underlying mediation and causal identification assumptions are reasonable.
2. When should I use additive mode?
Use additive mode when your coefficients are interpreted on a difference scale, such as many linear regression settings with continuous outcomes.
3. When is ratio mode helpful?
Ratio mode is useful when effects are naturally discussed on a multiplicative scale. It converts the indirect log-effect into an interpretable ratio.
4. Why are standard errors needed?
The calculator uses standard errors for path a and path b in the Sobel approximation, allowing an interval estimate and significance test for the indirect effect.
5. What if I do not know the direct effect?
Leave the direct effect blank. The tool will derive it from the total effect and the estimated indirect effect on the selected scale.
6. Can percent mediated exceed 100%?
Yes. That can occur in inconsistent or competitive mediation, especially when direct and indirect components point in opposite directions or the total effect is small.
7. Is the Sobel method always enough?
Not always. Bootstrap intervals are often preferred in applied research because indirect effect distributions can be skewed, especially in modest samples.
8. Does this prove causality?
No. The calculator summarizes mediation quantities from supplied estimates. Causal interpretation still depends on study design, model validity, and unconfounded pathways.