Power and sample size for two groups
Find the number of participants per group needed to compare two means or two proportions, or the power you get with a given number.
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- Participants needed per group
- Total participants
- Power
How it is calculated
Enter the difference you want to detect and the power you want; the calculator returns the number per group, rounded up. If you enter a number per group instead, it returns the power you would have.
Plan for drop-outs: divide the result by the share of participants you expect to keep.
n per group = 2 × (z₁₋α/₂ + z₁₋β)² / d²n per group = (z₁₋α/₂ + z₁₋β)² × [p₁(1 − p₁) + p₂(1 − p₂)] / (p₁ − p₂)²power = Φ(d × √(n / 2) − z₁₋α/₂)
Worked example: Standardised difference 0.5, power 80 %, 95 % confidence: 63 participants per group.
Sources
These calculators support research; they do not replace the advice of a statistician or a clinician.
Questions
Why do my numbers differ slightly from other software?
This tool uses the normal approximation. Programs that use the t distribution give a result one or two participants higher for small samples.