# $\eta^2$ and Cohen's $d$

by user39531   Last Updated January 14, 2018 08:19 AM

After conducting a one way repeated measures ANOVA, I obtained the following value for eta squared=0.2861 (28.61%) and for Cohen's d =1.25

Cohen's guideline for effect's size: Small: 0.01; Medium: 0.059; Large: 0.138;

I understand that 28.61% of the independent var influenced the dependent var. How do I interpret my results?

1) Can we deduce that it is a large effect size by referring to eta-squared and cohen's d?

2) I have manually calculated the output by referring to my descriptive IBM SPSS statistics output.Kindly advise if there is a way to obtain cohen's d and eta-squared directly in the IBM SPSS output.

Thanks

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I think what complicates the analysis of the effect size(s) here is the repeated measures (or within-subjects) design. Because of this, the calculation of the effect sizes might be different from simple one-way ANOVA. This article compares different effect sizes for within- and between-subject designs. At the end of the article you will see that, it suggests, for within-subjects designs, "effect sizes that control for intra-subjects variability ($\eta^2_p$ and $\omega^2_p$), or that take the correlation between measurements into account (Cohen's dz)" (Lakens, 2013).

So, it might be better to take into consideration repeated measures design in your estimation of the effect size. But if we assume that your calculations are correct, Cohen's d (1.25) indicates a large effect size (Gamst et.al., 2008, p.44). However, the interpretation of the eta-squared depends on the context of your research.

I am not an SPSS user but as far as I understand SPSS already reports partial eta-squared ($\eta^2_p$). Here is an example of how to do ANOVA with repeated measures using SPSS (it also shows how to get effect size).

Gamst, G., Meyers, L. S., & Guarino, A. J. (2008). Analysis of Variance Designs: A Conceptual and Computational Approach with SPSS and SAS. Cambridge: Cambridge University Press.

Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4. http://doi.org/10.3389/fpsyg.2013.00863

T.E.G.
September 12, 2016 00:12 AM