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I have two sets of randomly generated data with the wrapped normal circular distribution. I would like to test for homogeneity of means between these two samples. I was considering using Watson-Williams test but which requires that the samples are drawn from populations with a Von Mises distribution. Therefore, I am wondering if there is any two-sample test that can be applied to data with wrapped normal distribution.

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Such a test in certainly not inconceivable, but I can't remember coming across any.

However, from a practical perspective, the two distributions (von Mises and Wrapped Normal) have extremely similar shape, so it is generally hard to tell whether the data was generated from one or the other.

Thus, any analysis on a real-life dataset is very likely to be robust against using the Watson-Williams (for von Mises), while the data was in reality generated from the Wrapped Normal. That is, in almost all imaginable cases, both tests would come to the same conclusion.

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