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

نویسندگان

چکیده

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

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ژورنال

عنوان ژورنال: Behaviormetrika

سال: 2022

ISSN: ['0385-7417', '1349-6964']

DOI: https://doi.org/10.1007/s41237-022-00162-2