Superiority Test Sample Size Calculator

Plan superiority studies with flexible endpoint choices. Enter assumptions, inspect totals, and compare allocation impacts. Export tables, save summaries, and visualize sample trends clearly.

Calculator Form

Endpoint Type

Alpha Sidedness

Alpha

Power

Allocation Ratio (Treatment:Control) Use 1 for equal groups.

Superiority Margin Use 0 for a standard superiority test.

Expected Dropout (%)

Expected Mean Difference (Treatment - Control)

Treatment Standard Deviation

Control Standard Deviation

Treatment Proportion Enter a decimal between 0 and 1.

Control Proportion Enter a decimal between 0 and 1.

Reset Form

Example Data Table

Example	Endpoint	Main Inputs	Interpretation
Case 1	Means	Difference 5, SDs 12 and 12, alpha 0.025, power 0.80	Useful for testing whether treatment mean exceeds control mean.
Case 2	Proportions	Treatment 0.65, control 0.50, alpha 0.025, power 0.90	Useful for comparing response rates or success rates.
Case 3	Means	Difference 3, margin 0, ratio 2, dropout 15%	Useful when treatment enrollment is planned at twice control size.

Formula Used

Core superiority signal: Signal = Expected effect - Superiority margin

Critical values: z_alpha comes from the chosen alpha and sidedness. z_beta comes from the chosen power.

For two independent means:

n_control = ((z_alpha + z_beta)² × (SD_treatment² / ratio + SD_control²)) / Signal²

n_treatment = ratio × n_control

For two independent proportions:

n_control = ((z_alpha + z_beta)² × (p_treatment(1-p_treatment) / ratio + p_control(1-p_control))) / Signal²

n_treatment = ratio × n_control

Dropout adjustment: Adjusted sample = Ceiling(Base sample / (1 - dropout rate))

This page uses a normal approximation. Final protocol planning should always be reviewed with a statistician.

How to Use This Calculator

Choose whether your superiority endpoint is based on means or proportions.
Enter alpha, power, allocation ratio, superiority margin, and expected dropout.
For means, enter the expected treatment minus control difference and both standard deviations.
For proportions, enter treatment and control event rates as decimals.
Submit the form to view base sample sizes, dropout-adjusted totals, the sensitivity table, and the trend graph.

FAQs

1. What does this calculator estimate?

It estimates the number of participants needed to show treatment superiority over control for either means or proportions, using selected alpha, power, ratio, and dropout assumptions.

2. When should I choose one-sided alpha?

One-sided alpha is common for superiority studies when only improvement in one direction matters. Two-sided alpha is more conservative and tests both directions.

3. What margin should I enter?

For standard superiority testing, enter 0. If your protocol defines a different superiority threshold, enter that value and ensure the expected effect stays above it.

4. Why does dropout increase the result?

Expected losses reduce analyzable data. The calculator inflates the base sample so the final completed sample still meets your target power.

5. Can I use unequal allocation?

Yes. Enter any positive treatment-to-control ratio. Ratios above 1 increase treatment enrollment, while ratios below 1 reduce it.

6. What is the difference between means and proportions here?

Means are for continuous outcomes such as scores or blood pressure. Proportions are for binary outcomes such as success, response, or event rates.

7. Why does higher power require more participants?

Higher power lowers the chance of missing a true superiority effect. That stronger assurance requires more information, so the needed sample rises.

8. Is this output exact?

No. It is an approximation based on standard normal theory. It is useful for planning, but formal trial design should still be verified statistically.