I am simulating RM-ANOVA data with three treatment conditions (one-way within subjects designs). I would like to be able to add an effect to the data so that eta-squared has a specific value.
Imagine a more simple case for two independent groups and Cohen's d. Here, if I know both standard deviations in the two groups, I can have a look at the formula of Cohen' d to see that it's possible to multiply the mean of both standard deviations (the denominator) with the desired effect size, say 0.4, and I get the difference both means should have (numerator) and add this to one of the groups.
I am wondering if that's also possible for eta squared (or some of its variants, partial etc.). It is somewhat more difficult because one has to work with sums of squares instead of mean differences.
Do you have any suggestions on how to achieve this?