Mediation Power (Monte-Carlo)

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Mediation (legacy hub)

Independently verified. Every statistic this test reports has been re-derived against an independent reference — never the library the pipeline itself calls — the rendered output was read back in a browser, and the result is locked with a committed regression suite.

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Works out the sample size a mediation study needs to detect its indirect effect a·b — by Monte-Carlo simulation, not a formula.

Mediation power analysis estimates the power to detect an indirect effect a·b at a range of sample sizes. Because the product a·b is not normally distributed, there is no closed-form N; instead it simulates many datasets under the assumed a and b paths (Fritz & MacKinnon 2007) and reports the proportion that reach significance at each n — so you can read off the sample size that hits your target power.

Worked example

How many participants do I need to detect a medium effect?

An a priori power analysis for an independent t-test, medium effect (d = 0.5), α = .05, power = .80.

Result

80 participants per group (160 total) are needed to detect d = 0.5 with 80% power.

How you'd report it (APA)

An a priori power analysis indicated 80 participants per group are required to detect a medium effect (d = 0.5) at 80% power.

When to use it

  • Planning a mediation study
    You have plausible a and b path values (from a pilot or the literature) and need the sample size to detect the indirect effect.
  • Justifying n in a proposal or ethics application
    A Monte-Carlo power curve is the accepted justification for mediation, where G*Power's t/F routines do not apply.
  • Comparing inference methods
    See how required n changes across Sobel, joint-significance and bootstrap tests of a·b.

When NOT to — use instead

  • Powering a simple mean comparison
    For a t-test, ANOVA or correlation, use a closed-form power tool (e.g. G*Power) — it is exact and quicker. This page powers a mediation's indirect effect.
  • You have no a and b to assume
    Monte-Carlo power needs plausible path values; without a pilot or prior estimates the curve rests on guesses.

Hypotheses

H₀: at a given sample size, the study's power to detect the indirect effect a·b equals the target (e.g. .80) — restated, this finds the smallest n reaching that power.
This is a design tool rather than a hypothesis test: it answers 'how many participants do I need?' for a mediation, given assumed a and b, α and the inference method.

Parameter tested: empirical power for the indirect effect a·b at each candidate n, given the a and b paths, α, and the significance method (Sobel, joint-significance, or bootstrap)

Assumptions (and what to do if they fail)

The assumed a and b are realistichigh

Check: Base them on a pilot, a meta-analysis or a defensible minimum effect of interest.

If violated: Optimistic paths understate the required n; the real study ends up underpowered.

The inference method matches the planned analysismedium

Check: Power under Sobel differs from power under bootstrap — use the one you will actually run.

If violated: The n you plan for is calibrated to a test you won't use; Sobel-based n is typically too small for a bootstrap analysis.

Enough simulations for a stable curvelow

Check: More simulated datasets per n give a smoother, more reliable power estimate.

If violated: The power curve is jagged and the chosen n may sit on simulation noise.

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