What this answers

This calculator answers "given the per-group sample size I have, how likely is my one-way ANOVA to detect an effect of the size I assume?" using the exact statistical relationship this design follows, not a shortcut approximation.

How it is calculated

Achieved power for an ANOVA design depends on the noncentral F distribution, which shifts the ordinary (central) F distribution based on a noncentrality parameter driven by Cohen's f and the total sample size. This calculator computes the exact critical F value for your alpha and then reads the exact probability of exceeding that critical value under the noncentral distribution implied by your assumed effect size, the same underlying infrastructure this site's Sample Size for One-Way ANOVA planner uses to solve the reverse problem.

Worked example

Feeding this calculator the exact per-group sample size this site's own Sample Size for One-Way ANOVA calculator recommends for a medium effect size (Cohen's f of .25) with 3 groups returns an achieved power at or just above 80%, the target that sample size was originally solved for.

Assumption audit

Calculated from your data: the exact achieved power given your assumed effect size, group count, per-group sample size, and alpha.

Evidence to review: how confident you are in the assumed Cohen's f; power is highly sensitive to this input, and an overly optimistic assumption inflates the reported power beyond what a real study would likely achieve.

You must verify: that your design is genuinely balanced (equal n in every group); this calculator's exact noncentral F computation assumes that balance.

What this result does not mean

A high achieved power describes the omnibus test's sensitivity to detecting that some difference exists somewhere among the groups; it says nothing about which specific groups would be found to differ, a separate question a post-hoc test answers only after the omnibus test itself.

Common mistakes

Treating a low achieved power as proof an already-completed study found nothing meaningful is a common misreading; a low computed power is a caution about how much weight to place on a nonsignificant result, not evidence the true effect is zero. A second mistake is comparing power across designs with different group counts without also matching the total sample size, since power depends on how the same total N is distributed as much as on the number of groups itself.

Limitations

This calculator assumes equal variances across groups (the standard ANOVA assumption) and a balanced design; an unbalanced design or unequal variances would require different power calculations not offered here.