# What is the difference between Partial Eta Squared and Partial R Squared in factorial repeated ANOVA?

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?

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.
• @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. Commented Sep 3, 2022 at 9:58