GIFSQ Tools · Module 16 — Statistics, Experimental Design & Research · Tool 319 of 500
Size a two-sided comparison of means: the sample size for a target power, or the power a planned sample size gives — the calculation that belongs in every study protocol.
Try sample values — fills the form with the worked example below.
–
Sample size (n)
–
Power
–
z (1 − α/2)
Equation: One-sample: n = ((z₁₋α/₂ + z_power) × σ ÷ δ)², rounded up. Two-sample (per group): n = 2 × ((z₁₋α/₂ + z_power) × σ ÷ δ)², rounded up. Power (one-sample) = Φ(|δ| ÷ (σ ÷ √n) − z₁₋α/₂) + Φ(−|δ| ÷ (σ ÷ √n) − z₁₋α/₂); two-sample uses σ√(2 ÷ n).
Method: Normal-approximation sample-size formulae (standard textbook method; Chow, Shao and Wang, Sample Size Calculations in Clinical Research). The z values are computed from the normal distribution itself, not read from a table.
Assumptions: the data are approximately normal with a known (or well-estimated) standard deviation; the test is two-sided; the two-sample case assumes equal variances and equal group sizes.
Limitations: the normal approximation slightly understates n for small samples — for n below about 30, confirm with a t-based calculation or add a few extra subjects. The tool does not allow for drop-outs: inflate the result yourself for the expected loss rate.
Rounding: sample size is a whole number, rounded up; power to 4 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Normal-approximation sample-size formulae (standard textbook method; Chow, Shao and Wang, Sample Size Calculations in Clinical Research). The z values are computed from the normal distribution itself, not read from a table.
Assumptions: the data are approximately normal with a known (or well-estimated) standard deviation; the test is two-sided; the two-sample case assumes equal variances and equal group sizes.
Limitations: the normal approximation slightly understates n for small samples — for n below about 30, confirm with a t-based calculation or add a few extra subjects. The tool does not allow for drop-outs: inflate the result yourself for the expected loss rate.
Rounding: sample size is a whole number, rounded up; power to 4 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: Detect δ = 5 with σ = 10 at α = 0.05 and 80% power (one-sample): n = 32 (31.40 before rounding up).
Enter values above to see results.
Halving the difference you want to detect quadruples the sample size. Tool 319 of 500 — GIFSQ
