Calculator
Example Data Table
| Scenario | Test | Effect | Alpha | Power | Approximate sample |
|---|---|---|---|---|---|
| Balanced trial | Two means | d = 0.50 | 0.05 | 0.80 | 128 total |
| Association study | Correlation | r = 0.30 | 0.05 | 0.80 | 85 total |
| Three groups | ANOVA | f = 0.25 | 0.05 | 0.80 | Planning estimate |
Formula Used
The calculator uses planning approximations based on the normal critical value, target power value, and selected effect size.
Basic one sample form: n = ((Z alpha + Z power) / effect)^2.
Two group form: n1 = (1 + 1 / ratio) * (Z alpha + Z power)^2 / effect^2.
Correlation form: n = ((Z alpha + Z power) / Fisher z(r))^2 + 3.
Regression form: N = (Z alpha + Z power)^2 / f squared + predictors + 2.
Attrition adjustment: recruitment sample = analytic sample / (1 - attrition rate).
How To Use This Calculator
- Select whether you need sample size, achieved power, or detectable effect.
- Choose the test family that matches the planned analysis.
- Enter alpha, power, tail choice, and effect details.
- Add allocation ratio, attrition, groups, or predictors when needed.
- Press calculate and review the result above the form.
- Download CSV or PDF for your planning record.
Why Power Planning Matters
A power analysis turns a research idea into a practical sampling plan. It links four values: effect size, significance level, statistical power, and sample size. When one value changes, the others shift. This calculator helps you test those tradeoffs before data collection begins.
Good planning reduces wasted effort. A study with too few observations may miss a real effect. A study with too many observations may spend more time and money than needed. A balanced plan protects budgets, participants, and conclusions.
What This Calculator Estimates
The tool supports common planning cases used in G style workflows. You can estimate sample size, achieved power, or a detectable effect. It covers one mean, two means, paired designs, proportions, correlation, analysis of variance, regression, and chi square style tests.
The formulas use normal approximations and standard effect size definitions. They are best for planning, comparison, and early design checks. Very small samples, rare events, complex mixed models, or exact noncentral tests may need specialist software.
How To Choose Inputs
Start with the research question. Pick the test family that matches the planned analysis. Enter alpha, target power, tails, and effect size. Use a smaller effect when evidence is uncertain. This creates a safer plan.
Attrition should be added before recruitment starts. For example, ten percent attrition means more people must be invited than the final analyzable count. Allocation ratio matters when one group is harder to recruit.
Reading The Results
The output gives required sample size, group counts, adjusted recruitment need, and key assumptions. It also shows an interpretation label for common effect measures. Use the CSV or PDF buttons to save the calculation record.
Power analysis is not a guarantee. It is a planning estimate. Results still depend on measurement quality, model fit, missing data, and honest reporting. Update the calculation when assumptions change.
Practical Quality Checks
Always document where each input came from. Pilot work, prior papers, clinical judgment, and policy targets can all justify an effect. Do not choose a larger effect only to reduce sample size. That weakens the design. Run several scenarios. Compare conservative, expected, and optimistic effects. Share those scenarios with reviewers before the actual study begins and protocol approval starts safely now.
FAQs
What is a power analysis sample size calculator?
It estimates the sample needed to detect an expected effect. It uses alpha, power, test type, and effect size assumptions.
Can it replace dedicated statistical software?
No. It is a planning tool. Use specialist software for exact noncentral tests, regulated protocols, or complex designs.
What power value should I use?
Many studies use 0.80 or 0.90. Higher power needs a larger sample but lowers the chance of missing real effects.
What is effect size?
Effect size is the expected signal strength. Examples include Cohen d, Cohen f, Cohen h, f squared, w, and correlation r.
Why does attrition increase recruitment size?
Attrition means some participants may not remain analyzable. The calculator adds extra recruitment to protect the final target sample.
What does allocation ratio mean?
It is the size of group two divided by group one. A ratio of one means equal group sizes.
Why are results approximate?
The calculator uses normal approximation formulas. Exact results can vary with distributions, corrections, noncentral tests, and model details.
Can I export my result?
Yes. Use CSV for spreadsheets. Use PDF for a simple report that stores assumptions and results.