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I need to calculate the likely/possible effect size of my study for a research proposal, based on the effect sizes of previous studies.

The end goal is to determine the sample size needed for medium-to-large power in my study.

The study I'm looking at used a fully factorial, within-subjects design with two factors, each having 2 levels. So I'm looking at two-way ANOVA, F(1,12)=11.79, p=0.005 and a sample size (n) of 13.

Is it possible to calculate the effect size from this information alone?

I can only find a formula of calculating the effect size without the MSE when the F-test compares one condition to one other condition (Thalheimer, 2002), which isn't the case here as there are 4 conditions.

Reference: Thalheimer, W., & Cook, S. (2002). How to calculate effect sizes from published research: A simplified methodology. Work-Learning Research, 1-9.

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