Eta Squared

Synonyms

Correlation ratio or R ² ; Effect size; Proportion of variance accounted for

Definition

Eta squared (η²) is a squared measure of association defined as the ratio of variance in an outcome variable explained by a predictor variable, after controlling for other predictors. More intuitively, it is the amount of variation explained by the predictor variable (X) in the total variation for the outcome variable (Y). The equation below describes eta squared:

$$ {\eta^2} = {\sigma^2}_{\rm{effect}}/\ {\sigma^2}_{\rm{total}} $$

where the effect variance is the sum of squares of the predictor and the total variance is sum of squares of the predictor variable (or set of variables) and error.

Description

Eta squaredis a measure of effect size for analysis of variance (ANOVA) models. It is a standardized estimate of an effect size, meaning that it is comparable across outcome variables measured using different units. Eta squared is a commonly reported measure of association for group...