How one-way ANOVA power analysis works
This calculator covers the omnibus F test comparing means across k independent groups, using Cohen's f as the effect size — a standardized measure of how spread out the group means are relative to within-group variability. Cohen's (1988) benchmarks are f = .10 (small), .25 (medium), and .40 (large). Power is computed from the exact noncentral F distribution with numerator df = k − 1 and denominator df = N − k, matching what dedicated power-analysis software reports.
This tool assumes equal group sizes, which maximizes power for a given total N; unbalanced designs need a larger total sample to reach the same power. A significant omnibus F only indicates that at least one group differs from another — it does not identify which. Planned or post hoc comparisons between specific pairs of groups have their own power, generally lower than the omnibus test's, and are not what this calculator computes.
Worked example
Comparing three groups with a medium effect (f = 0.25) at α = .05 with target power of .80 calls for roughly 52 participants per group (156 total).
N per group = 53, total N = 159, achieved power = 80.5%, critical F(2, 156) = 3.054.