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Partial eta-squared is a measure of variance, like r-squared. It tells us what proportion of the variance in the dependent variable is attributable to the factor in question. You can get these measures by choosing the 'Estimates of effect size' option when setting up an ANOVA.
This is because partial eta-squared in factorial ANOVA arguably more closely approximates what eta-squared would have been for the factor had it been a one-way ANOVA and it is presumably a one-way ANOVA which gave rise to Cohen's rules of thumb.