The Advanced Theory of Statistics, Vol. 2: Inference and Relationship

Kendall & Stuart (1961) — the correlation ratio, Vol. 2 Chapter 26

Result

§26.21–26.22 define the population correlation ratio (26.40), (26.47) and the sample version (26.48) with $0\le r^2\le e^2\le1$ (26.49); §26.23–26.24 give the decomposition (26.50)–(26.51) and the normal-theory $F$ tests (26.52)–(26.55) for $\eta^2=0$, $\rho=0$ and linearity, attributed to Fisher, via Cochran's theorem with the arrays fixed. No large-sample variance of the correlation ratio and no moment-based non-normal form are given.

Use

lineage of O6's uncentred correlation ratio; (26.50) is the centred analogue of O6.1's RSS identity. Closes the O6 gap "Kendall & Stuart Vol. 2 Ch. 26 section".

Verification

primary text (archive.org OCR of the 1961 volume), 5 Sep 2026; Vol. 1 Chapter 10 (standard errors) not checked.