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In general linear modeling (GLM), eta squared ( η  2 ) is the dominant statistic for the explaining power of an independent variable. This article discusses a less-studied deficiency in  η  2 : its values are seriously deflated, because the estimates by coefficient eta ( η ) are seriously deflated. Numerical examples show that the deflation in  η  may be as high as 0.50–0.60 units of correlation and in  η  2  as high as 0.70–0.80 units of explaining power. A simple mechanism to evaluate and correct the artificial attenuation is proposed. Because the formulae of  η  and point-biserial correlation are equal,  η  can also get negative values. While the traditional formulae give us only the magnitude of nonlinear association, a re-considered formula for  η  gives estimates with both magnitude and direction in binary cases, and a short-cut option is offered for the polytomous ones. Although the negative values of  η  are not relevant when  η  2  is of interest, this may be valuable additional information when  η  is used with non-nominal variables.

behaviormetrika

Artificial systematic attenuation in eta squared and some related consequences: attenuation-corrected eta and eta squared, negative values of eta, and their relation to Pearson correlation