Power Analysis Calculator: t-Test
How many participants do you need? Answer the ethics committee's favourite question without downloading G*Power: choose the test type (independent two-sample, paired, or one-sample), enter the expected effect size Cohen's d, your alpha level and target power, and get the required sample size per group — computed from the exact noncentral t distribution, matching G*Power and R's power.t.test() to at least six significant digits. The same screen also works backwards (post-hoc): enter a sample size to see the power you actually achieved. Conventions: d = 0.2 small, 0.5 medium, 0.8 large; 80% power at α = .05 is the standard planning default.
AI Report
Let AI interpret your results: a downloadable Word document in APA 7 / business report format.
Frequently asked questions
How many participants do I need for a t-test?
For a medium effect (d = 0.5), α = .05 two-tailed and 80% power, you need 64 participants per group (128 total) for an independent t-test, or 34 pairs for a paired design. Smaller expected effects increase the requirement steeply — d = 0.2 needs 394 per group.
Is this calculator equivalent to G*Power?
Yes for t-tests: it uses the same parameters (effect size d, α, power, tails) and the same exact noncentral t distribution, so the sample sizes and power values match G*Power's 'means' modules. It runs in the browser with nothing to install.
How do I report a power analysis in APA format?
State the software/method, test, parameters and result, e.g.: "An a priori power analysis for an independent samples t-test (two-tailed, d = 0.5, α = .05, power = .80) indicated a required sample of 64 participants per group." The AI Report formats this justification paragraph for your methods section.
What effect size should I assume if I have no pilot data?
Use effect sizes from published studies on similar questions, or a meta-analytic estimate; failing that, power for the smallest effect that would still matter practically (SESOI). Avoid defaulting to 'medium' without justification — reviewers increasingly ask for it.