Calculate the minimum sample size needed to detect your expected effect — or determine the power of your completed study.
Power Analysis determines the minimum sample size required to detect a given effect size with a specified probability (power) at a given significance level. Statistical power (1 − β) is the probability of correctly rejecting the null hypothesis when it is false. The standard benchmark is 80% power (β = .20), with α = .05. Underpowered studies waste resources, produce unreliable results, and are less likely to replicate.
Power analysis is required by most ethics boards, grant reviewers, and journals before data collection begins. It can also be used post-hoc to determine whether a completed study had adequate power, though pre-registration with a priori power analysis is strongly preferred.
StatRyx computes sample size for the most common tests: independent t-test, paired t-test, one-sample t-test, one-way ANOVA, correlation, and linear regression — using Cohen's effect size conventions or a user-specified effect size.
Power is the probability that a study detects an effect that really exists. Four quantities are linked — sample size, effect size, significance level (α) and power — and fixing any three determines the fourth. The convention is 80% power at α = .05, so an a priori power analysis asks: how many participants do I need to detect the smallest effect I care about with 80% probability?
| Test | Effect Size | α | Power | Required n |
|---|---|---|---|---|
| Independent t-test | d = 0.50 | .05 | .80 | 52 per group |
| One-Way ANOVA (3 groups) | f = 0.25 | .05 | .80 | 52 per group |
| Pearson correlation | r = .30 | .05 | .80 | 84 total |
A priori power analysis (G*Power 3.1; Faul et al., 2009) for an independent samples t-test with a medium effect size (d = 0.50), α = .05 (two-tailed), and power = .80 indicated a required sample of n = 52 per group (N = 104 total).
Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.
Use a published meta-analytic estimate from your research area, the smallest effect that would be meaningful in practice, or Cohen's conventional benchmarks (small/medium/large) as a last resort.
Observed power is the power computed from the actual sample size and obtained effect size. It is not useful for interpreting a non-significant result (it is mathematically tied to the p-value), but can be reported descriptively.
For an independent t-test at α = .05 and 80% power: about 64 per group for a medium effect (d = 0.5), about 26 per group for a large effect (d = 0.8), and about 394 per group for a small effect (d = 0.2).
Name the test, the effect size and its source, α, the power and the resulting sample size: "An a priori power analysis for an independent t-test (d = 0.50, α = .05, two-tailed, power = .80) indicated a required sample of 128 participants (64 per group)."
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