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.
📊 t-Test (Two-Sample)
Small (d=0.2): 394 per group
Medium (d=0.5): 64 per group
Large (d=0.8): 26 per group
pwr.t.test
Medium (d=0.5): 64 per group
Large (d=0.8): 26 per group
n per group × 2 = total N
📊 t-Test (One-Sample / Paired)
Small (d=0.2): 197
Medium (d=0.5): 34
Large (d=0.8): 15
pwr.t.test
Medium (d=0.5): 34
Large (d=0.8): 15
type = "one.sample" or "paired"
🎯 One Proportion
Small (h=0.2): 197
Medium (h=0.5): 33
Large (h=0.8): 14
pwr.p.test
Medium (h=0.5): 33
Large (h=0.8): 14
Uses arcsine transformation
🔀 Two Proportions (Equal n)
Small (h=0.2): 394 per group
Medium (h=0.5): 65 per group
Large (h=0.8): 26 per group
pwr.2p.test
Medium (h=0.5): 65 per group
Large (h=0.8): 26 per group
h = ES.h(p1, p2)
🔗 Pearson Correlation
Small (r=0.1): 782
Medium (r=0.3): 84
Large (r=0.5): 28
pwr.r.test
Medium (r=0.3): 84
Large (r=0.5): 28
Fisher Z' transformation applied
📈 One-Way ANOVA (k=4 groups)
Small (f=0.1): 274 per group
Medium (f=0.25): 45 per group
Large (f=0.4): 18 per group
pwr.anova.test
Medium (f=0.25): 45 per group
Large (f=0.4): 18 per group
Balanced design (equal group sizes)
χ² Chi-Squared (df=2)
Small (w=0.1): 964 total
Medium (w=0.3): 108 total
Large (w=0.5): 40 total
pwr.chisq.test
Medium (w=0.3): 108 total
Large (w=0.5): 40 total
df = (rows−1)(cols−1)
📐 Regression / GLM (u=5)
Small (f²=0.02): N≈485
Medium (f²=0.15): N≈92
Large (f²=0.35): N≈50
pwr.f2.test
Medium (f²=0.15): N≈92
Large (f²=0.35): N≈50
N = v + u + 1; u = predictors
Select a test, fill in parameters,
and click Calculate to see results.
Result
Sample Size
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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.