Two-Sample T-Test Sample Size Calculator
FreeCalculate the sample size needed to detect a difference in means between two independent groups.
Study Parameters
Results
Required Sample Size
126
Group 1: 63 | Group 2: 63
Achieved Power
80.1%
Effect Size
0.500
Method: Two-sided two-sample t-test
Allocation ratio1:1
Cohen's d0.500
- •Independent samples from two populations
- •Normally distributed outcome (or large sample via CLT)
- •Equal variances in both groups (pooled SD)
- •Two-sided hypothesis test
- •Equal allocation (1:1 randomization)
Formula
n₁ = (z_{α/2} + z_β)² × σ²(1 + 1/k) / δ², n₂ = k × n₁
References
- Lachin JM. Introduction to sample size determination and power analysis for clinical trials. Controlled Clinical Trials. 1981;2(2):93-113.
- Chow SC, Shao J, Wang H, Lokhnygina Y. Sample Size Calculations in Clinical Research. 3rd ed. Chapman & Hall/CRC; 2017.
Power Curve
Sensitivity Analysis
Sample size (N) varying Effect multiplier and Power
| Effect multiplier \ Power | 70% | 80% | 85% | 90% | 95% |
|---|---|---|---|---|---|
| 0.5× (δ=2.5) | 396 | 504 | 576 | 674 | 834 |
| 0.75× (δ=3.8) | 176 | 224 | 256 | 300 | 370 |
| 1× (δ=5.0) | 100 | 126 | 144 | 170 | 210 |
| 1.25× (δ=6.3) | 64 | 82 | 92 | 108 | 134 |
| 1.5× (δ=7.5) | 44 | 56 | 64 | 76 | 94 |
| 2× (δ=10.0) | 26 | 32 | 36 | 44 | 54 |