Enter standardized path inputs
Use standardized coefficients when possible. Results appear above this form after submission.
Example data table
This example uses the same default values preloaded in the calculator for a quick demonstration.
| Predictor | a Path to Self-Efficacy | Direct Path to Exam Score | b Path from Self-Efficacy | Indirect Effect | Total Effect |
|---|---|---|---|---|---|
| Study Hours | 0.42 | 0.18 | 0.47 | 0.1974 | 0.3774 |
| Attendance | 0.31 | 0.22 | 0.47 | 0.1457 | 0.3657 |
| Sample size: 220 | Predictor correlation: 0.28 | Mediator R²: 0.3218 | Outcome R²: 0.4983 | |||||
Formula used
1) Direct, indirect, and total effects
Direct effect: c′
Indirect effect: a × b
Total effect: c′ + (a × b)
2) Sobel-style standard error for the indirect effect
SEindirect = √[(b² × SEa²) + (a² × SEb²)]
3) Z test and confidence interval
Z statistic: Estimate ÷ SE
Confidence interval: Estimate ± Zcritical × SE
4) Approximate explained variance and residual path
For the mediator model: R² ≈ β′Rβ, using predictor correlation.
Residual path = √(1 − R²)
These calculations are practical approximations for standardized path models with one mediator and two correlated predictors. Use full SEM software for latent variables, several mediators, missing data handling, or global fit indices.
How to use this calculator
Step 1: Enter labels for both predictors, the mediator, and the outcome.
Step 2: Enter standardized path coefficients for a1, a2, b, c1′, and c2′.
Step 3: Add standard errors and the correlation between both predictors.
Step 4: Choose a confidence level and submit the form.
Step 5: Review direct, indirect, total, residual, and R² results, then export them as CSV or PDF.
FAQs
1) What does this path analysis calculator estimate?
It estimates direct effects, indirect effects through one mediator, total effects, approximate explained variance, residual paths, z statistics, p values, and confidence intervals.
2) Should I use standardized or unstandardized coefficients?
Use standardized coefficients for the variance and residual formulas shown here. Unstandardized coefficients can still produce effect sizes, but the R² approximations become less meaningful.
3) How is the indirect effect calculated?
The indirect effect is the product of the path from predictor to mediator and the path from mediator to outcome. In symbols, it is a × b.
4) How are confidence intervals created?
The calculator uses a normal-approximation interval: estimate ± critical value × standard error. Indirect-effect standard errors follow a Sobel-style formula.
5) Why might the displayed R² be capped?
Some combinations of user-entered standardized paths are mathematically inconsistent and imply R² below 0 or above 1. The calculator warns you and caps the displayed value.
6) Can indirect effects be negative?
Yes. A negative indirect effect appears when one path is positive and the other is negative, or when both have signs that reverse the mediated direction.
7) Does a significant path prove causality?
No. Statistical significance alone does not establish causality. Sound design, temporal ordering, measurement quality, and theoretical justification remain essential.
8) When should I switch to full SEM software?
Use SEM software when you need latent constructs, several mediators, bootstrapped indirect effects, missing-data methods, multi-group models, or formal global fit indices.