Calculator inputs
Choose a mode, enter assumptions, and calculate the required sample.
Formula used
Population proportion estimate
Finite population correction
Dropout adjustment
One-sample power approximation
Two-proportion comparison
How to use the calculator
- Select the calculation mode matching your study goal.
- Choose percentage or decimal probability inputs.
- Enter the expected proportions and precision assumptions.
- Add power, significance, or group allocation when required.
- Apply population, clustering, and dropout adjustments when relevant.
- Calculate and review every intermediate sample size.
- Export the result using copy, CSV, PDF, or print.
Example data
| Scenario | Expected inputs | Useful mode | Planning purpose |
|---|---|---|---|
| Customer survey | 95% confidence, 5% margin, p = 50% | Estimate one proportion | Estimate a population percentage. |
| Single-arm response study | p₀ = 40%, p₁ = 55%, 80% power | One-sample binomial test | Detect improvement above a benchmark. |
| Two-group trial | 50% versus 62%, equal allocation | Compare two proportions | Compare treatment and control success. |
| Small expected prevalence | p = 8%, exact 95% interval | Confidence interval precision | Plan conservative exact interval precision. |
Interpretation and limitations
Confidence controls interval reliability across repeated samples. Power controls the chance of detecting a real effect. They answer different study design questions.
One-sided tests target changes in one chosen direction. Two-sided tests allow changes in either direction. Direction should be chosen before reviewing outcomes.
Finite population correction matters for large sampling fractions. Design effects increase samples for clustered observations. Dropout adjustments protect final analysable sample counts.
Normal methods can perform poorly with rare outcomes. Wilson intervals often improve interval behaviour. Exact intervals are conservative but computationally heavier.
Frequently asked questions
Why does p = 0.50 give the largest sample?
Binomial variance peaks when success and failure are equally likely. That choice produces the most conservative normal sample estimate. It protects planning when prevalence remains unknown.
Should I use confidence level or statistical power?
Use confidence for estimation and interval precision. Use power for testing a specific alternative effect. Some studies require both planning approaches.
When should finite population correction be used?
Use it when sampling without replacement from a known population. It matters most when sampling fractions become large. Leave population size blank otherwise.
What does design effect mean?
Design effect compares complex sampling variance against simple random sampling. Values above one increase the required sample. Clustered designs commonly need this adjustment.
How is dropout adjustment calculated?
The usable sample is divided by one minus dropout. This inflates recruitment before data collection begins. Dropout must remain below one hundred percent.
Which confidence interval method should I choose?
Wald is simple but can be inaccurate near boundaries. Wilson usually offers better practical coverage. Exact intervals are conservative for small samples.
What is an unequal allocation ratio?
It sets treatment participants relative to control participants. A ratio of two doubles treatment recruitment. Unequal allocation can increase total requirements.
What is a minimum detectable effect?
It is the smallest planned difference worth detecting. Smaller effects require larger samples for equal power. Choose effects with practical importance.
Why does the calculator always round upward?
Fractional participants cannot be recruited or analysed. Rounding downward would reduce planned precision or power. Upward rounding preserves the design target.