Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the sample size for two proportions calculator works
Normal two-proportion planning combines a pooled null term and separate alternative variances.
Enter the smallest difference worth detecting and realistic baseline rates before data collection.
Worked example
Sample Size for Two Proportions example
Planning for 50% versus 65% at 80% power and 5% two-sided alpha needs roughly 170 observations per equal group.
Normal two-proportion planning combines a pooled null term and separate alternative variances.
Supported inputs
Precision and limits
Model and design
Uses an asymptotic uncorrected test, independent Bernoulli outcomes, stable rates, and fixed allocation.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Enter the smallest difference worth detecting and realistic baseline rates before data collection.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
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