Calculator Inputs
Choose a design, set assumptions, run virtual studies, and estimate statistical power.
Formula Used
Monte Carlo power: Power = rejected simulations / total simulations
Monte Carlo standard error: SE = sqrt(Power × (1 − Power) / simulations)
Simulation interval: Power ± 1.96 × SE
Mean test statistic: t = (estimate − null value) / standard error
For a two sample Welch test, the standard error is sqrt(s1²/n1 + s2²/n2). For a one proportion test, the z statistic uses sqrt(p0(1-p0)/n).
How To Use This Calculator
- Select the study design that matches your planned analysis.
- Enter alpha, tail direction, target power, and sample sizes.
- Choose raw or standardized effect input for mean tests.
- Add realistic standard deviations or proportion values.
- Increase simulation runs for a steadier final estimate.
- Press Run Simulation and review the result above the form.
Example Data Table
| Scenario | Design | n1 | n2 | Effect | SD | Alpha | Runs |
|---|---|---|---|---|---|---|---|
| Balanced trial | Two sample mean | 40 | 40 | 0.50 | 1.00 | 0.05 | 5,000 |
| Small pilot | One sample mean | 25 | — | 0.40 | 1.10 | 0.05 | 8,000 |
| Binary outcome | One proportion | 120 | — | 0.08 | — | 0.05 | 10,000 |
Monte Carlo Power Planning Guide
Monte Carlo Power Simulation
Power measures the chance that a study detects a real effect. A Monte Carlo approach estimates that chance by repeating many virtual studies. Each virtual study follows the assumptions you enter. It draws random outcomes, runs the chosen test, and records whether the null hypothesis is rejected. The final power equals the rejected studies divided by total simulated studies. This method is useful when closed form formulas feel too limited. It also helps when sample sizes are uneven, effects are small, or standard deviations differ.
Why Simulation Helps
Traditional power equations are fast. They also depend on strict assumptions. Simulation lets you see how those assumptions affect decisions. You can change the alpha level, tail direction, sample size, allocation, variation, and effect. You can then compare the power estimate with your target. A higher number of simulations gives a steadier result. Yet it also needs more processing time. The Monte Carlo standard error shows how much random noise remains in the estimate. A narrow interval means the simulated estimate is more stable.
Planning Reliable Tests
Good planning starts with a clear research question. Decide the smallest effect that matters in practice. Then choose a test that matches the design. A one sample mean test checks one group against a reference value. A paired mean test studies differences within matched observations. A two sample mean test compares two independent groups. A one proportion test studies a binary success rate. Enter realistic standard deviations or probabilities. Unrealistic inputs can make power look better than the real study will deliver.
Reading The Result
The calculator reports estimated power, rejection counts, Monte Carlo error, and a confidence interval for the simulation estimate. The target status tells whether the planned design reaches your chosen goal. If power is low, increase sample size, reduce noise, use a stronger design, or accept a larger detectable effect. Avoid changing alpha only to force a better number. A large alpha raises false positives. A balanced design often improves power, but cost and recruitment limits still matter.
Best Practice Tips
Run several simulations with different seeds. Similar results build confidence. Increase the simulation count before making a final decision. Save the settings with your study notes. This makes the planning process repeatable. Check sensitivity across optimistic and conservative assumptions. Use the conservative plan when budget allows. Monte Carlo power is an estimate, not a guarantee. Real data may contain skew, missing values, clustering, or bias. Still, simulation gives a practical way to test design choices before collecting data. It turns abstract power planning into a visible decision process. Use it with expert judgment, sound design, and clear reporting.
Document every assumption before sharing results. Include sample size, alpha, tail choice, effect definition, variation, seed, and simulation count. This record helps reviewers repeat the calculation and understand the limits behind each planning decision clearly in practice today.
FAQs
What does Monte Carlo power mean?
It means estimated statistical power from repeated random trials. The calculator simulates many studies under your assumed true effect. Power is the percentage of studies that reject the null hypothesis.
When should I use simulation instead of a formula?
Use simulation when your design has unequal groups, unusual inputs, practical constraints, or assumptions that are hard to handle with a simple closed form equation.
How many simulations should I run?
More simulations reduce random noise. Start with 5,000 for exploration. Use 10,000 or more before final planning. Watch the Monte Carlo standard error.
What is the random seed?
The seed starts the random number generator. Using the same seed and inputs gives repeatable results. Change it to test simulation stability.
What is a good target power?
Many studies use 0.80 or 0.90 as a planning target. The right target depends on risk, cost, ethics, and the decision importance.
Can this calculator handle two sample tests?
Yes. It supports independent two sample mean tests with Welch unequal variance and pooled equal variance options. Enter both group sizes and deviations.
What does standardized effect mean?
For mean tests, standardized effect is measured in standard deviation units. The calculator converts it into a raw difference before running simulations.
Why does power change slightly between runs?
Monte Carlo simulation uses random sampling. Different seeds create different virtual studies. Larger simulation counts usually make those differences smaller.
Can I use this for proportions?
Yes. Choose one proportion. Enter the null proportion and an effect difference. The true proportion equals the null value plus the effect value.
What if the target is not met?
Increase sample size, improve measurement precision, reduce variation, or reconsider the smallest meaningful effect. Avoid raising alpha without strong justification.
Is the result a guarantee?
No. It is an estimate based on the assumptions entered. Real studies may face missing data, bias, nonnormality, and design changes.