Specialty › Power (hypothesis tests)

Correlation

Power analysis for a correlation tests against ρ = 0, solving for any one of n, r, α or power.

What is Correlation?

Uses Fisher's z transform: z = ½ log((1+ρ)/(1−ρ)) with SE = 1/√(n − 3). Detectable r typically needs much larger n than people expect — r = 0.3 at 80% power, α = 0.05 needs n ≈ 84.

When should I use Correlation?

Powering a correlation study.

What data does it need?

Three of {n, r, α, power} + alternative.

What does it report?

Fourth quantity.

Formula

n ≈ 3 + [(z_{1 − α/2} + z_{power}) / z(r)]²,  with z(r) = atanh(r)

How do I interpret the result?

Required n grows steeply as the target r shrinks; r = 0.1 at 80% power needs n ≈ 783, vs r = 0.5 needing n ≈ 29.