Quantitative design tool
How big a sample do you
How big a sample do you
actually need?
A Monte Carlo power analysis for direct, mediation, and moderation models. Simulate thousands of studies, watch the power curve build, and get the exact sample size — with a pre-registration justification you can paste straight into your method section.
Runs in your browser
Solves exact N
Free · no login
Model & design
Power curve
Run the simulation to generate a pre-registration-ready sample-size justification.
Power table
| N | Effect (β̂) | Power | 95% MC interval | Verdict |
|---|---|---|---|---|
| No simulation has been run yet. | ||||
How this works & what's assumed
For each sample size the tool generates standardized data from your hypothesised model, fits it with ordinary least squares, and tests the effect of interest with a two-tailed t-test (exact t distribution, df = n − k). Power is the share of replications in which that test is significant at α. Variables are standardized so coefficients are interpreted as standardized betas. Mediation uses the joint-significance test of the a (X→M) and b (M→Y, controlling for X) paths — a test with power close to bootstrapping. Moderation estimates the X×W interaction in the full model that includes both main effects. Because every estimate is simulated, power carries Monte Carlo error (shown as the 95% interval); raise the replications to tighten it.