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I have circular data and want to check whether it is a normal (Von Mises) distribution or not.

I do the following steps:

  1. Create a Von Mises distribution with the same mean and kappa as my main data.
  2. Use two sample Kuiper test to compare the two sets of data (My main data and the Von Mises data that I created based on the main data)

If the null hypothesis is rejected, I then conclude that my input data does not have a normal distribution.

I want to know whether it is a correct approach to find whether an input data of angles is Von Mises or not. Any help is greatly appreciated.

Nick Cox
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Aep
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  • [This is not quite the same situation as yours, but noncircular normality testing is less helpful than one might hope.](https://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless) +1 for a question on circular statistics, though! – Dave Aug 15 '21 at 04:57
  • Thanks for your response @Dave. However, I think I did not get what you mean completely. Can you please explain more? Do you mean that the normality test is useless for circular data? If yes, why? If no, Do you think the approach I mentioned here is correct? – Aep Aug 15 '21 at 06:55
  • When sample sizes get large, these tests have the power to reject trivial (but correct!) deviations from the assumed population. Sure, the population might not be normal, but that might be such a minor deviation that subsequent analysis is valid, and the distribution test has little ability to tell you if the deviation is important. – Dave Aug 15 '21 at 12:26
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    As in the non-circular case, testing is fairly useless here. Better questions are 1. Are systematic differences discernible on a quantile plot? 2. Is the Von Mises definitely a better idea than alternative distributions, most simply the circular uniform? – Nick Cox Aug 15 '21 at 14:36
  • Thanks for your response @Dave. However, how large do you mean? my dataset has about 2000 arrays. Do you think the test is useless for the sizes in this orders? – Aep Aug 15 '21 at 17:33
  • That’s probably a large enough sample size to have enough power to catch differences that will not be of interest to you. (Note that this just means that hypothesis testing is working *exactly* the way it is supposed to work.) – Dave Aug 15 '21 at 17:54
  • Thanks @Dave. Do you have any other suggestions to compare the datasets in this case? – Aep Aug 15 '21 at 17:58
  • I don’t know visual examination techniques for circular data, but you might get somewhere looking for analogues of what is described in the link. – Dave Aug 15 '21 at 18:39
  • OK, Thanks @Dave. So putting other tests aside (assuming the data size has a value that it is reasonable to do normality testing on it), if we want to go on with the Kuiper test for instance, do you think the procedure I mentioned in the question above (creating another Von Mises data with the same mean and Kapaa of main data and then comparing it with the main data) make sense? – Aep Aug 15 '21 at 18:51
  • Any comments are greatly appreciated. – Aep Aug 16 '21 at 05:02

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