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I'm running a simulation to assess what my minimum detectable effect size for a synthetic control study where the sample size is fixed and I'm noticing a strange relationship between power and effect size. Normally you would expect that power and effect size have a logistic relationship where power grows as effect size increases and then levels off (s-shaped curve). What I'm observing however is a u-shape, where power is high for low effect sizes, and again for high effect sizes, following this pattern. The MDE in the figure below is a relative effect size, so 1.001 is a 0.1% lift in the metric.

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Is this a valid form for the relationship between effect size and power or is it possible this is happening due to random variation?

Thank you for the help!

dimitriy
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Brett
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    This is odd. Typically the curve should be longhorn-like, like in figure 2 [here](https://mackinstitute.wharton.upenn.edu/wp-content/uploads/2020/03/Wernerfelt-Nils-Doudchenko-Nick-Gilinson-David-and-Taylor-Sean_Designing-Experiments-with-Synthetic-Controls.pdf). – dimitriy Jan 27 '22 at 18:11

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