Draft the power analysis paragraph
Turns the numbers above into a sample-size justification you can adapt for an ethics application, preregistration or methods section.
Uses an AI model via Vercel AI Gateway. It only sees what you send here; check anything you publish.
The four quantities of a power analysis
Power analysis is bookkeeping between four numbers. α is the false-positive rate you accept. Power (1 − β) is the chance your study detects an effect that really exists. Effect size is how big that effect is in standardised units. Sample size is what you control. Fix three and the fourth follows.
See power change as you move the inputs
The curves use the current effect size and α from the calculator (for t-tests). Drag n to see the H₁ curve pull away from H₀.
Which design should I choose?
- Two independent groups: treatment vs control, two schools, two conditions with different people. Effect size d = (M₁ − M₂)/SDpooled.
- Paired / one-sample: pre–post on the same people, matched pairs, or comparing one group to a known value. Use dz = mean difference / SD of differences, which is usually larger than d because the within-person correlation removes noise.
- Correlation: testing whether r differs from zero. Computed with Fisher's z; within about one participant of exact methods.
- Two proportions: pass rates, conversion, prevalence in two groups. Uses the normal approximation with pooled variance under H₀.
- One-way ANOVA: three or more independent groups. f = σmeans/σ; f = 0.25 is a medium effect and equals η² ≈ 0.06.
- Chi-square: association in a contingency table or goodness of fit. w = √(χ²/N); df = (rows − 1)(columns − 1).
Reference values (α = .05, two-tailed, power = .80)
| Design | Small | Medium | Large |
|---|---|---|---|
| Two-sample t (n per group; d = .2/.5/.8) | 394 | 64 | 26 |
| Paired t (pairs; dz = .2/.5/.8) | 199 | 34 | 15 |
| Correlation (N; r = .1/.3/.5) | 783 | 85 | 30 |
| ANOVA, 3 groups (n per group; f = .1/.25/.4) | 323 | 53 | 22 |
| Chi-square, df = 1 (N; w = .1/.3/.5) | 785 | 88 | 32 |
Values computed with this calculator; they agree with G*Power 3.1 and Cohen (1988), give or take one participant from rounding.
Frequently asked questions
What is a power analysis?
A power analysis links four quantities: sample size, effect size, significance level (α) and power (1 − β). Fix any three and you can solve for the fourth. Before a study (a priori) you usually fix effect size, α = .05 and power = .80 and solve for the sample size.
Is this a free alternative to G*Power?
Yes, for the most common designs. It uses the same exact noncentral t, F and χ² distributions as G*Power, so a priori sample sizes match: for example d = 0.5, α = .05 two-tailed, power = .80 gives 64 per group.
What effect size should I use?
Best: the smallest effect that would matter in practice, or an estimate from a meta-analysis or pilot. Cohen’s benchmarks (d = 0.2/0.5/0.8, f = 0.1/0.25/0.4, r = 0.1/0.3/0.5, w = 0.1/0.3/0.5) are a last resort because published effects are often inflated.
Should I report post-hoc (observed) power?
Generally no. Observed power is a direct function of the p-value and adds no information (Hoenig & Heisey, 2001). Report a sensitivity analysis instead: the smallest effect your sample could detect with 80% power.
Why 80% power?
It is a convention from Cohen (1988): a 20% chance of missing a real effect is treated as acceptable relative to a 5% chance of a false positive. Many funders now prefer 90%.
How do I account for dropout?
Divide the required n by the expected retention rate. If you need 64 per group and expect 15% attrition, recruit 64 / 0.85 = 76 per group.