t-Test for Means
One-sample, two-sample (equal or unequal sizes), or paired t-test.
Solve For
Cohen's Effect Size Presets
Effect Size Reference
Cohen's conventional benchmarks
| Test | ES Measure | Small | Medium | Large |
|---|---|---|---|---|
| t-test | d | 0.20 | 0.50 | 0.80 |
| Proportion | h | 0.20 | 0.50 | 0.80 |
| Correlation | r | 0.10 | 0.30 | 0.50 |
| ANOVA | f | 0.10 | 0.25 | 0.40 |
| Chi-squared | w | 0.10 | 0.30 | 0.50 |
| Regression | f² | 0.02 | 0.15 | 0.35 |
| Power (1−β) | Interpretation | Common Use |
|---|---|---|
| 0.50 | Underpowered | Exploratory |
| 0.80 | Standard | Most research |
| 0.90 | High power | Clinical trials |
| 0.95 | Very high | High-stakes decisions |
| Alpha (α) | Type I Error Risk | Common Use |
|---|---|---|
| 0.10 | 10% | Exploratory studies |
| 0.05 | 5% | Standard convention |
| 0.01 | 1% | Strict criteria |
| 0.001 | 0.1% | Genome-wide studies |
Minimum N required per test (power = 0.80, α = 0.05, two-sided) at Cohen's conventional effect sizes. Values are computed live by the calculator's own engine.
Select a test, fill in parameters,
and click Calculate to see results.
Result
Sample Size
—
Quick Reference
🎯 What is Power?
Statistical power (1−β) is the probability of correctly rejecting a false null hypothesis. The conventional minimum is 0.80 (80%).
⚠️ Type I vs Type II
α = False positive rate (Type I error). β = False negative rate (Type II). Power = 1−β.
📐 Effect Size
Standardized measure of the magnitude of an effect. Larger effects require smaller samples to detect at the same power level.
📚 Reference
All calculations follow Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences, 2nd ed.