On the Generality of Univariate Eta

Abstract

Eikeland, H. M. (1971). On the Generality of Univariate Eta. Scand. J. educ. Res. 15, 149‐167. The correlation ratio, or eta, is conceived of as a generic concept, covering varying complexities of data analysis designs, from a simple point‐biserial design to general multiclassification designs, orthogonal as well as nonorthogonal ones. When independent variables are categorical and the dependent variable metric, one can define a multiple eta as the correlation among observed and predicted scores, the prediction being based on two or more classification variables conjointly. Multiple eta is compared to multiple correlation. Worked examples of multiple eta are shown for both the orthogonal and the nonorthogonal case, illustrating the use of analysis of variance as a correlational technique. Only univariate eta is considered, but its two cases, bivariate and multiple eta, are related to the multivariate case.