Power Analysis Calculator
Power analysis helps you plan your study by determining the sample size needed to detect an effect, or the statistical power of your existing study design. This is essential for ensuring your research has a good chance of finding a real effect if one exists.
What is Power Analysis?
Statistical power is the probability that a test will correctly reject a false null hypothesis (i.e., detect a real effect). A study with low power may fail to detect effects that truly exist (Type II error), while a study with adequate power gives you confidence that negative results are meaningful.
The Four Components
Power analysis links effect size, sample size, significance level and power. This calculator solves for sample size or power; it does not solve for effect size or alpha.
- Effect Size: The magnitude of the difference or relationship you expect to find
- Sample Size (n): The number of participants or observations
- Significance Level (α): The probability of Type I error (typically 0.05)
- Power (1-β): The probability of detecting a true effect (typically 0.80)
Common Use Cases
A Priori (Before Study)
Calculate required sample size before collecting data to ensure adequate power for detecting the expected effect.
Sensitivity to Assumed Effects
Explore power for your sample size under specified hypothetical effects. Use confidence intervals to assess an observed effect; observed power does not provide independent evidence about a nonsignificant result.
Effect Size Guidelines (Cohen)
| Test Type | Measure | Small | Medium | Large |
|---|---|---|---|---|
| T-Tests | Cohen's d | 0.2 | 0.5 | 0.8 |
| ANOVA | Cohen's f | 0.1 | 0.25 | 0.4 |
| Correlation | r | 0.1 | 0.3 | 0.5 |
| Chi-Square | Cohen's w | 0.1 | 0.3 | 0.5 |
| Proportions | Cohen's h | 0.2 | 0.5 | 0.8 |
Supported Tests
- One-sample t-test
- Paired (dependent) t-test
- Independent samples t-test
- One-way ANOVA
- Correlation (Pearson)
- Chi-square test
- Two proportions test
Methods and limits
Independent t-test power assumes equal population variances. T, ANOVA and chi-square calculations use noncentral distributions. Correlation uses a Fisher-z normal approximation; proportions use a normal approximation without continuity correction. Small samples and rare events can make these approximations inaccurate. One-tailed power assumes the effect is in the prespecified direction.
Sample-size solutions show the actual power achieved after rounding up to a whole observation. A zero effect or an unattained target produces an error, rather than a recommendation at the search limit.
Recommendations
- Power of 0.80: This is the conventional minimum, meaning an 80% chance of detecting a true effect. For critical research, consider 0.90 or higher.
- Alpha of 0.05: The standard significance level. Use 0.01 for more stringent testing or 0.10 for exploratory research.
- Effect size: Base this on previous research, pilot studies, or the minimum effect that would be practically significant. Avoid using conventions blindly.
