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Imagine I have a sample distribution for a circular data set with a mean group direction and known variation. I would like to do a power analysis for a known effect size (e.g. to determine what sample size I need to be able to determine a certain angular difference) but on the circle. Do I have to convert circular data to linear and then apply the known power analysis or is there any other approach? Many thanks. Dmitry

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Converting the data to linear is a step that would need to be factored into the power analysis. Therefore, that approach will not give you the correct answer for the required sample size.

There are no standard tools available for power analysis of circular tests (that I'm aware of). Therefore, the only solution that I see is to repeatedly simulate data similar to yours, and calculate the power based on this small simulation study.

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