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I carried out an repeated measures ANOVA in SPSS with two within subjects predictors, and requested for measures of effect size.

SPSS provides partial Eta Squared as a measure of effect size, but I was requested by a reviewer to change that to partial R squared. As I understand it R squared = Eta squared, so partial Eta Squared should be essentially the same as partial R square (a measure of the proportion of variance explained by that variable in relation to the total variance, while accounting for the variance explained by the other variables in the model).

Is this correct? Or is there some sort of formula that I should be using to transform partial Eta Squared to partial R Square?

Thank you in advance.

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Partial $\eta^2$ can be derived directly from the sums of squares table from a single fitted model:

Partial $\eta^2 = \frac{SS_{\textrm{effect}}}{SS_{\textrm{effect}} + SS_{\textrm{error}}}$

For partial $R^2$, two models need to be fitted: One with the predictor(s) for which partial $R^2$ is computed (full), and one without (reduced):

Partial $R^2 = \frac{SS_{\textrm{error}}^{\textrm{red. mod.}} - SS_{\textrm{error}}^{\textrm{full mod.}}}{SS_{\textrm{error}}^{\textrm{red. mod.}}}$

Roughly, one could interpret the numerator for $R^2$ as the $SS_{\textrm{effect}}$, and the denominator as the $SS_{\textrm{effect}} + SS_{\textrm{error}}^{\textrm{full model}}$. Thus they are indeed very similar, and I would expect them to have the same value, given independence of all predictors in the full model.

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  • $\begingroup$ Thank you very much for the clarification! My question is whether they can be interpreted in similar manners. As I understand, both represent the proportion of variance in the model explained by that variable (although in different ways, if you sum all the R squared it should = 100% whereas with partial eta it can be above 1, for example). Is this correct? Also, am I correct to assume that in ANOVAs, eta squared and partial eta squared are used rather than R-squared? (I am also considering using Omega squared, as suggested by Andy Fields). Thanks in advance! $\endgroup$ Commented Sep 2, 2022 at 14:33
  • $\begingroup$ @AndreDorini You're welcome! I've added a paragraph to the answer about the (similar) interpretation. Also: Indeed, partial $\eta^2$ is more commonly used in ANOVAs, while partial $R^2$ is more commonly used in regression designs. Note, partial $R^2$s need not sum to 1. $\endgroup$ Commented Sep 3, 2022 at 9:58

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