Generalized Eta and Omega Squared Statistics: Measures of Effect Size for Some Common Research Designs

Department of Educational Psychology, College of Education, University of Georgia, Athens, GA 30602-7143, USA.
Psychological Methods (Impact Factor: 4.45). 01/2004; 8(4):434-47. DOI: 10.1037/1082-989X.8.4.434
Source: PubMed


The editorial policies of several prominent educational and psychological journals require that researchers report some measure of effect size along with tests for statistical significance. In analysis of variance contexts, this requirement might be met by using eta squared or omega squared statistics. Current procedures for computing these measures of effect often do not consider the effect that design features of the study have on the size of these statistics. Because research-design features can have a large effect on the estimated proportion of explained variance, the use of partial eta or omega squared can be misleading. The present article provides formulas for computing generalized eta and omega squared statistics, which provide estimates of effect size that are comparable across a variety of research designs.

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    • "Note that—in contrast to partial eta squared (g P 2 )—g G 2 is calculated with a denominator that includes the variance across participants , even in repeated-measures designs, to facilitate comparisons across different types of experimental design. For within-subject designs, therefore, g G 2 is systematically smaller than g P 2 (Bakeman, 2005; Olejnik & Algina, 2003), and our effect sizes should be interpreted with this in mind. For paired t tests, we report effect sizes as Cohen's d (J. "
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    • "For all statistical tests, the alpha level was set to 0.05. We report partial eta squared ( P 2 ) for comparison with studies using a similar design and generalized eta squared ( G 2 ) for comparison with studies employing different designs (Bakeman, 2005; Lakens, 2013; Olejnik & Algina, 2003). To investigate contextual cuing, we performed three-way mixed-design ANOVAs with the between-subjects factor experimental group (control, central scotoma, peripheral scotoma) and the within-subjects factors epoch (1,4) and configuration (repeated , novel) for the learning phase and two-way mixed-design ANOVAs with the between-subjects factor experimental group (control, central scotoma, peripheral scotoma) and configuration (repeated, novel) for the test phase. "
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    • "). Omega-squared was used instead of eta-squared because the latter overestimates effect sizes, especially for small samples (Olejnik & Algina, 2003 "
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