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I have two data sets to compare, each containing 20 azimuths (no vector length). I'm struggling to find an appropriate test to use in R to compare and look for significant similarity. I have been using the "CircStats" and "Circular" packages in "R", but cannot figure out how to properly use the Watson's Two Sample test for homogeneity, and don't even know if it's the right test to use. Any suggestions?

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  • $\begingroup$ Asking for R functions is off topic here. Questions about how to use Watson's test or if it is the right test, are on topic. You may want to edit your post to emphasize those & deemphasize the request for code. $\endgroup$ – gung - Reinstate Monica Mar 16 '16 at 0:14
  • $\begingroup$ Significant -similarity- is a much harder topic than significant -dissimilarity-. In particular, Watson's test tests for group differences, not similarities. The problem is that if we want a test that becomes significant if the groups are similar, in the 'null' hypothesis [groups are different] the size of this difference is not easily specified. $\endgroup$ – Kees Mulder Mar 16 '16 at 16:09
  • $\begingroup$ Hi folks. I apologize if I am not adhering to a formal rubric here - I am not a statistician, and I am out of my depth. However, I am literally desperate for assistance as I finish my Master's thesis, and no one at my university is familiar with circular statistics. I thought this forum could put my questions into the world of experts. Can anyone point me to a helpful resource? I could certainly use a test that tests for significant dissimilarity. Do the x and y components of the Watson's Two-Sample function (CircStats) mean that I would simply plug in my two data sets as vectors? $\endgroup$ – cados Mar 16 '16 at 18:41
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A Watson Two test is a kind of rank sum test that accounts for true circularity, in that it doesn't assume any normal, or otherwise parametrized distribution. Since you have azimuths they won't span a full circular range, but probably only a 90 or 180 degree range. However, since you didn't tell us this, full circularity might still be present and warrant a Watson Two test.

In case you don't have full circularity, a "simpler" or at least more "standard" test might be equally appropriate as a Watson Two test or more so. If there is no full circularity, I would first see if the data is normally distributed (e.g. with a Kolmogorov-Smirnov test) and go from there. If it is normally distributed, there is little to argue against a t-test and otherwise, a non-parametric test, such as a Wilcoxon signed rank test would probably also be fine.

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