Sample size & power
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Rev 4.7 · reviewed Sep 2026Sample size & power
Explore supported sample-size and power calculations. Match the assumptions to your design; complex studies may need a separate calculation or simulation.
Source formula: Lehr R. Stat Med 1992;11:1099–102 (sample size).
Design (matches the test you'll run)
α (two-sided)
Power (1 − β)
Mean difference to detect
SD (either group)
Result. Estimated requirement
| Standardized effect d | 0.42 |
| n per group | 91 |
| Total sample | 182 |
* Lehr R. Stat Med 1992;11:1099–102 (sample size).
Rule of thumb
Two-sided normal approximation with equal allocation and a common SD; an exact t-test calculation can require more. Lehr's rule: n/group ≈ 16/d² for 80% power (21/d² for 90%). Here 16/d² ≈ 92.
To detect a difference of 5.00 (SD 12.00, d = 0.42) at α 0.05 and 80% power, plan about 91 per group. Add for dropout.
These are planning approximations (normal-approximation formulas; noncentral F for ANOVA). Inflate for expected dropout, and confirm with a statistician for clustered, repeated-measures, interim-analysis, or unequal-allocation designs.
Understand what this is measuring