A note on the distribution of the correlation ratio

Wishart (1932) — distribution of the correlation ratio

Result

normal-theory exact distribution of the sample correlation ratio $\eta^2$ (between-group over total centred sum of squares).

Use

lineage only — O6's $\hat\eta$ is the uncentred correlation ratio of $S$ on $Z$ with a fixed partition; nothing normal-theory transfers.

Verification

existence and pages from the Biometrika contents index; text not read.