Power Analysis for t-tests Calculator Guide
Power Analysis for t-tests
Statistical power is the probability of detecting a true effect. For a two-sample t-test with equal group sizes, power depends on effect size d, significance level α, tails, and sample size per group.
Parameters
- Effect size d (Cohen’s d)
- α (significance level)
- One-tailed or two-tailed test
- Sample size per group n
Formulas
- Critical Z depends on α and tails
- Noncentrality δ = d × √(n ÷ 2)
- Approximate power uses the standard normal CDF with δ and Zα
- Required n per group ≈ 2 × ((Zα + Zβ) ÷ d)²
Practical Guidance
- d ≈ 0.2 small, 0.5 medium, 0.8 large
- Common α values: 0.01, 0.05, 0.10
- Typical power target is 80% or higher
- Two-tailed tests require larger n than one-tailed for the same d and α
Related tools: Cohen’s d, t-test, statistical power.
Example
With d = 0.5, α = 0.05, two-tailed, and n = 50 per group, δ ≈ 2.5. The approximate power exceeds 80%. Increasing d or n increases power.