Sample size & power
How many subjects a trial needs — or, given a fixed sample size, how much power it has. All sample sizes are rounded up (ceiling), per regulatory convention.
1.1 · Two-sample t-test (continuous, superiority)
Sample size per group to detect a mean difference Δ between two independent arms.
| n per group (n₁) | 63 |
|---|
| n in group 2 (n₂) | 63 |
|---|
| Total N | 126 |
|---|
| Total N, dropout-inflated | 126 |
|---|
- Formula
- n₁ = σ²(1 + 1/r)·(z₁₋α/₂ + z₁₋β)² / Δ²; n₂ = r·n₁
- Reference
- Chow, Shao & Wang, Sample Size Calculations in Clinical Research, 3rd ed. (2018), §3.2; Machin et al., Sample Size Tables for Clinical Studies, 3rd ed. (2008).
- Assumptions & notes
- Normal approximation; exact non-central-t calculation is a documented v1 limitation.
- Warns when the standardized effect Δ/σ < 0.2.
- Note
- Normal approximation; exact noncentral-t calculation is a documented v1 limitation.
Exploratory / educational use only — not validated for regulatory submissions. See footer.
1.2 · Two proportions (superiority)
Sample size per group to detect a difference between two independent response rates.
| n per group | 93 |
|---|
| Total N | 186 |
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| Total N, dropout-inflated | 186 |
|---|
- Formula
- n/group = [z₁₋α/₂·√(2p̄(1−p̄)) + z₁₋β·√(p₁(1−p₁) + p₂(1−p₂))]² / (p₁−p₂)²
- Reference
- Chow, Shao & Wang (2018), §4.2.1; Fleiss, Levin & Paik, Statistical Methods for Rates and Proportions, 3rd ed. (2003).
- Assumptions & notes
- Unpooled variance — standard for superiority.
- Continuity correction is a planned v1 enhancement (currently off).
- Note
- Continuity correction is a planned v1 enhancement (currently off).
Exploratory / educational use only — not validated for regulatory submissions. See footer.
1.3a · One-sample mean vs. reference
Sample size to compare a single mean against a reference value.
- Formula
- n = σ²·(z₁₋α/₂ + z₁₋β)² / Δ²
- Reference
- Chow, Shao & Wang (2018), §3.1.
Exploratory / educational use only — not validated for regulatory submissions. See footer.
1.3b · One-sample proportion vs. reference
Sample size to compare a single proportion against a reference rate.
- Formula
- n = [z₁₋α/₂·√(p₀(1−p₀)) + z₁₋β·√(p₁(1−p₁))]² / (p₁−p₀)²
- Reference
- Chow, Shao & Wang (2018), §4.1.
Exploratory / educational use only — not validated for regulatory submissions. See footer.
1.4a · Non-inferiority — means
Sample size per group for a non-inferiority trial on a continuous endpoint, given a pre-specified margin.
| n per group | 393 |
|---|
| Total N | 786 |
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| Total N, dropout-inflated | 786 |
|---|
- Formula
- n/group = 2σ²·(z₁₋α + z₁₋β)² / (δ+M)² (one-sided α)
- Reference
- Chow, Shao & Wang (2018), §3.3; FDA guidance Non-Inferiority Clinical Trials to Establish Effectiveness (2016).
- Assumptions & notes
- The margin must be pre-specified and clinically/statistically justified in the protocol — this tool does not validate the margin itself.
- Note
- The margin must be pre-specified and clinically/statistically justified in the protocol — this tool does not validate the margin itself.
Exploratory / educational use only — not validated for regulatory submissions. See footer.
1.4b · Non-inferiority — proportions
Sample size per group for a non-inferiority trial on a binary endpoint, given a pre-specified absolute risk-difference margin.
| n per group | 377 |
|---|
| Total N | 754 |
|---|
| Total N, dropout-inflated | 754 |
|---|
- Formula
- n/group = [z₁₋α·√(2p̄(1−p̄)) + z₁₋β·√(pT(1−pT)+pC(1−pC))]² / (δ+M)² (one-sided α)
- Reference
- Chow, Shao & Wang (2018), §3.3; FDA guidance Non-Inferiority Clinical Trials to Establish Effectiveness (2016).
- Assumptions & notes
- The margin must be pre-specified and clinically/statistically justified in the protocol — this tool does not validate the margin itself.
- Note
- The margin must be pre-specified and clinically/statistically justified in the protocol — this tool does not validate the margin itself.
Exploratory / educational use only — not validated for regulatory submissions. See footer.