Indirect Effect Mediation Calculator

Enter path estimates and errors with confidence choices. Check indirect, direct, total, and mediated shares. Export practical mediation reports in clear reusable formats today.

Calculator Inputs

Formula Used

The indirect effect is calculated as a × b. Path a estimates the predictor to mediator relationship. Path b estimates the mediator to outcome relationship while controlling the predictor.

The total effect is c = c' + ab. If only c is entered, the calculator estimates c' as c - ab. If only c' is entered, the calculator estimates c as c' + ab.

Sobel standard error is √(b²SEa² + a²SEb²). Aroian adds SEa²SEb². Goodman subtracts SEa²SEb². The z value equals indirect effect divided by its standard error.

The Monte Carlo interval draws many likely a and b values. It multiplies each draw. The lower and upper percentiles create an interval for the indirect path.

How To Use This Calculator

  1. Enter the path a coefficient from the mediator model.
  2. Enter the path b coefficient from the outcome model.
  3. Add standard errors for both paths.
  4. Enter total effect c, direct effect c', or both.
  5. Adjust confidence level, draws, seed, and decimals as needed.
  6. Press calculate to show results below the header and above the form.
  7. Use CSV or PDF buttons to export the current calculation.

Example Data Table

Scenario a b c' c ab Interpretation
Work stress through sleep quality 0.35 0.42 0.403 0.550 0.147 Positive indirect pathway
Training through confidence 0.28 0.31 0.180 0.267 0.087 Partial mediation pattern
Price through satisfaction -0.22 0.40 -0.110 -0.198 -0.088 Negative mediated pathway

Understanding Indirect Effect Mediation

Mediation analysis studies how one variable explains a relationship. It separates a total effect into direct and indirect parts. The indirect effect passes through a mediator. The direct effect stays after the mediator is considered. This calculator helps you inspect that pathway with common estimates used in research reports.

Why This Calculator Helps

Many studies report path a and path b. Path a links the predictor to the mediator. Path b links the mediator to the outcome while controlling the predictor. Multiplying both paths gives the indirect effect. A positive value suggests the mediator carries the relationship in one direction. A negative value suggests an opposite mediated pathway.

Advanced Measures Included

The tool reports Sobel, Aroian, and Goodman standard error methods. These tests use different variance adjustments. The Aroian method is often more conservative because it adds the product of both standard errors. The Goodman method subtracts that product term. The calculator also creates a Monte Carlo interval. It simulates many possible a and b values from their standard errors.

Interpreting Results

A z score shows how far the indirect effect is from zero. The p value gives a familiar significance check. A confidence interval that excludes zero supports a mediated effect. The proportion mediated shows how much of the total effect is represented by the indirect path. This number can be unstable when the total effect is small.

Best Practice

Use this page as a planning and reporting aid. It does not replace a full statistical model. Good mediation analysis still needs valid data, clear theory, reliable measures, and correct model assumptions. Always report sample size, path estimates, standard errors, intervals, and the method used. For final publications, compare these values with results from your primary statistics software.

Practical Use

Researchers can test pilot data, verify textbook examples, or prepare classroom demonstrations. Analysts can compare several models quickly. Students can learn how each formula reacts to changing path estimates. The result table also supports copying, exporting, and checking values without rebuilding a spreadsheet.

Notes

Select coefficients from the same mediation model whenever possible. Matched estimates reduce confusion. Use raw paths, or standardized paths across different scales. Clear records make mediation reporting easier and more defensible.

FAQs

What is an indirect effect?

An indirect effect is the part of a predictor outcome relationship that passes through a mediator. It equals path a multiplied by path b.

What is path a?

Path a is the coefficient linking the predictor to the mediator. It usually comes from a model where the mediator is the dependent variable.

What is path b?

Path b is the coefficient linking the mediator to the outcome while controlling the predictor. It is used with path a to estimate mediation.

What does the Sobel test show?

The Sobel test gives a z score and p value for the indirect effect. It uses a normal approximation and path standard errors.

Why include Aroian and Goodman methods?

They adjust the indirect effect standard error differently. Aroian is more conservative. Goodman can be smaller when estimates are stable.

What does proportion mediated mean?

It shows the indirect effect as a percentage of the total effect. Interpret it carefully when the total effect is close to zero.

Should I enter c or c'?

You may enter either value. If one is missing, the calculator estimates it using the relationship between total, direct, and indirect effects.

Can this replace statistical software?

No. It is best for checking formulas, planning, teaching, and reporting support. Final research should use the original model output.

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