Power Analysis Calculator
Free power analysis calculator. Sample size, power, effect size for t-tests, proportions, ANOVA, cor
Why This Statistical Analysis Matters
Why: Statistical calculator for analysis.
How: Enter inputs and compute results.
Power Analysis — Sample Size & Power
Solve for sample size, power, effect size, or α. Two-sample t, one-sample t, proportion, ANOVA, correlation. Interactive power curves.
Real-World Scenarios — Click to Load
Test Configuration
Calculation Breakdown
Power Curve vs n
Power vs Effect Size (Cohen d)
Sample Size Comparison (α=0.05, power=0.8)
| Effect | Cohen d | n per group | Total n |
|---|---|---|---|
| Small | 0.2 | 393 | 786 |
| Medium | 0.5 | 63 | 126 |
| Large | 0.8 | 25 | 50 |
For educational and informational purposes only. Verify with a qualified professional.
Key Takeaways
- Power = 1 − β = P(reject H₀ | H₁ true). Target typically 0.8 (Cohen 1988).
- Two-sample t: n per group = 2((z_α/2 + z_β) / d)². d = Cohen's d.
- One-sample t: n = ((z_α + z_β) / δ)². δ = (μ₁ − μ₀)/σ.
- Proportion: n = (z_α√(p₀(1−p₀)) + z_β√(p₁(1−p₁)))² / (p₁−p₀)².
- Correlation: n ≈ ((z_α + z_β) / z_r)² + 3. z_r = Fisher z-transform of r.
- ANOVA: n per group depends on Cohen f and number of groups.
Power Analysis Workflow
1. Define parameters
α (significance level, usually 0.05), desired power (usually 0.8), effect size (d, r, f, or proportion difference).
2. Choose effect size
Use Cohen's conventions (d: 0.2=small, 0.5=medium, 0.8=large) or prior literature. Never guess optimistically.
3. Solve for unknown
Given two of {n, power, effect size, α}, solve for the third using the appropriate formula.
4. Account for attrition
Increase n by 10–20% if dropout is expected.
5. Pre-register
Document your power analysis plan before data collection.
Cohen Effect Size Guidelines
| Effect | Cohen d | r | Cohen f |
|---|---|---|---|
| Small | 0.2 | 0.1 | 0.1 |
| Medium | 0.5 | 0.3 | 0.25 |
| Large | 0.8 | 0.5 | 0.4 |
Did You Know?
Expert Tips
Target 80% power
Most studies aim for 80% power. Higher power needs larger samples.
Use realistic effect sizes
Base d, r, or proportion difference on prior literature or pilot data.
Two-sided tests
Default α/2 for two-tailed. Use one-sided only when justified.
Account for attrition
Increase n by 10–20% if dropout is expected.
Frequently Asked Questions
What is statistical power?
Power = probability of correctly rejecting H₀ when H₁ is true. Low power means high risk of false negatives.
Why target 80% power?
Convention balances cost (sample size) vs risk of missing real effects. Some fields use 90%.
What is Cohen d?
Standardized mean difference: (μ₁ − μ₂)/σ. Measures effect size in standard deviation units.
How do I choose effect size?
Use prior studies, meta-analyses, or define smallest clinically/practically meaningful difference.
What if my study is underpowered?
Increase n, use a larger effect size if justified, or consider a one-sided test when appropriate.
Power Analysis by the Numbers
Official Sources
Disclaimer: These formulas use normal approximations. For small samples, use t-distribution. Chi-square uses noncentral distribution. Consult G*Power or statistical software for exact values.
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