How t-test power analysis works
Power is the probability of correctly rejecting the null hypothesis when a real effect of the specified size exists. It depends on four quantities — effect size, sample size, alpha, and the design — and any one can be solved for once the other three are fixed. This calculator uses Cohen's d (the standardized mean difference) as the effect size and computes power from the exact noncentral t distribution, not a normal approximation, so results match what dedicated power-analysis software reports.
Cohen's (1988) benchmarks are d = .20 (small), .50 (medium), and .80 (large), though a defensible effect size should come from prior research or the smallest difference that would matter substantively — not a default. For the independent-samples design, this calculator assumes equal group sizes; unequal allocation reduces power relative to a balanced design with the same total N. Conventionally, power of .80 is treated as the minimum acceptable for a planned study, meaning a 20% chance of missing a real effect of the assumed size.
Worked example
Planning an independent-samples comparison with a medium effect (d = 0.50), two-tailed α = .05, and target power of .80 calls for 64 participants per group (128 total) — the textbook benchmark from Cohen (1988).
N per group = 64, achieved power = 80.1%, critical t(126) = 1.979.