Specialty › Power (hypothesis tests)

ANOVA

Power analysis for one-way ANOVA uses Cohen's f, solving for any one of n per group, k, f, α or power.

What is ANOVA?

Cohen's f is the ANOVA effect-size analogue of d: f = √(η² / (1 − η²)). The Cohen anchors: f = 0.10 small, 0.25 medium, 0.40 large.

Required n grows linearly with k for a fixed f, so adding groups gets expensive. If the science allows it, prefer a 2-group t-test over a k-group ANOVA for power efficiency.

When should I use ANOVA?

Powering a one-way ANOVA with k ≥ 2 groups.

What data does it need?

k + three of {n per group, f, α, power}.

What does it report?

Fourth quantity.

Formula

non-centrality λ = f² · n_total;   compare against the central F under the noncentral F

How do I interpret the result?

Same caveats as power_t_test: pick the smallest f you'd care about, not the largest you can imagine.