It has been a while since the last answer, but the question remained opened, and it may help people looking for that in the future.

I don't have the answer about the dependence/independence of tooth, but I would tend to think that you can actually consider a each teeth as an independent sample.

You were doing the right thing by describing your distribution. Just keep in mind that when you use the Rayleigh test, the parameters obtained (mean, r and k ) are only relevant if your data distribution is unimodal, since they are usually meaningless if bimodal (Batschelet, 1981). 

If you want to compare if your distributions are different in/or both mean and variance, you can indeed use one of the Watson's U2, the Kuiper's or the Mardia-Watson-Wheeler tests. They test the same thing (if the distributions are somehow different) but using different methods. The Watson's U2 test uses the sum of squares of deviations, the Kuiper's test uses the maximum deviations, and the MWW test pools all samples together, spaces the points by equal distances keeping the original order, and computes and compares the resultant vector of the samples based on this new distributions. However, I don’t know if any of the three is more powerful than the others. I have only used the MWW test because it is implemented in R package {circular}. 

To compare if your distributions are different in mean angles only, you can use the Watson-Williams test. 

To compare if your distributions are different in angular variances only, then you can use the Wallraff test.

Ref: Batschelet, E. 1981. Circular Statistics in Biology. 

by what I see, it can not be used for dependent samples. I recommend you see McNemar test or sign test,

Thank you for your suggestion. I recon that both McNemar and sign test are for linear data, but my dataset is circular. Any suggestions for that?

Might explain the case?. but look Watson-Williams Test Dependent case, Wheeler Watson Test for independent samples

Thanks Carlos for your contribution. I think the Watson-WIlliams Test compares if the circular means of two distributions differ. I am looking for a test which compares the overall distribution of angles, not only the mean or median.

Try the von Mises circular distribution then.

Thank you James, but I am afraid my case is still more difficult. I hope I am correct in saying the von Mises circular distribution tests whether circular data is distributed unimodal. My data is mostly scattered, sometimes bimodal, but I am afraid just testing for unimodality will not give sufficient resolution. Maybe the whole idea of using ONE test for comparing agular distribution is wrong.....maybe I need to describe the data with several parameters. So far I have been using concentration (k) and length of mean vector (r) to characterize whetehr the distribution is concentration or dispersed. This in combination with a Wheeler-Watson test could be sufficient???

We do not have enough information on your data and so we will not be able to help you with the exact thing you need. If you could write a little about the kind of data and some statistics therein to help verify for you which approach or approaches will be okay for you. I will be waiting.

Thanks Jamens, I'll try to give you an idea what the whole thing is about. As always, I cannot give all details, because it is still work in progress and I am in the instant to publishing.

I work on teeth, and measure how certain ridges are oriented towards a fixed direction. The data is usually rather dispersed, but some samples are concentrated (more unimodal distribution) around the median. I am unsure whether I need to treat teeth within one jaw as dependent or independet; a from a developmental perspective they are dependant, but they are all independent units.

Further I need to characterize if the overall angle distributions differ. If they fit to von Mises would not be sufficient. So I tried to characterize them with concentration (k), mean vector (r) and median/mean. And applied Watson's U2 and Mardia-Watson-wheeler. Hope you understand my case.

It has been a while since the last answer, but the question remained opened, and it may help people looking for that in the future.

I don't have the answer about the dependence/independence of tooth, but I would tend to think that you can actually consider a each teeth as an independent sample.

You were doing the right thing by describing your distribution. Just keep in mind that when you use the Rayleigh test, the parameters obtained (mean, r and k ) are only relevant if your data distribution is unimodal, since they are usually meaningless if bimodal (Batschelet, 1981). 

If you want to compare if your distributions are different in/or both mean and variance, you can indeed use one of the Watson's U2, the Kuiper's or the Mardia-Watson-Wheeler tests. They test the same thing (if the distributions are somehow different) but using different methods. The Watson's U2 test uses the sum of squares of deviations, the Kuiper's test uses the maximum deviations, and the MWW test pools all samples together, spaces the points by equal distances keeping the original order, and computes and compares the resultant vector of the samples based on this new distributions. However, I don’t know if any of the three is more powerful than the others. I have only used the MWW test because it is implemented in R package {circular}. 

To compare if your distributions are different in mean angles only, you can use the Watson-Williams test. 

To compare if your distributions are different in angular variances only, then you can use the Wallraff test.

Ref: Batschelet, E. 1981. Circular Statistics in Biology. 

Thank you, Robin, for that extensive answer! That sums it all up very comprehensively and I think I am now prepared to analyse the data. Thanks again!