I have a set of data of measurements for the lateral angle of the internal acoustic meatus, taken by three different evaluators at three different points in time. Values vary from 16° to 115° (in itself this seems odd as values in the literature range from 30° to 70°, but outside this question). The final goal is to see if there are any sex differences in lateral angle.

Previous studies use linear statistics, but my co-authors are adamant that I should use circular statistics (Watson-Williams tests and similar).

Question 1 Are circular statistics always necessary when dealing with angular data? I don't have full circularity, and in itself, direction is not the main question here, but a difference in measured angle. This response from this same forum makes me think that linear statistics are sufficient, but I'd like a fuller explanation as well as a supporting reference (to justify my statistical decision). I saw a few references here, but they seem to dive straight into the statistics.

Question 2 If circular statistics are required, what is the circular equivalent of the intraclass correlation coefficient (ICC) to test for inter and intra-observer reliability? This is the one that seems the most reasonable to my data as my outcome variable is continuous.

Question 2.1 Would it be appropriate to project my data as suggested here, by converting the angles to (sin(x),cos(x)), and thus transforming it to "linear"? But if I do this, I'm not sure how to operate it or interpret it since I will have two outcome variables rather than one? Would it look like this?

I have a set of data of measurements for the lateral angle of the internal acoustic meatus (it's an angle between the canal of our inner ear and another bone structure in our skull). The measurements were taken by three different evaluators at three different points in time. Values vary from 16° to 115° (the anatomy of our skull would not let the angle vary much beyond these values - the literature actually only reports a range from 30° to 70°). The final goal is to see if there are any sex differences in lateral angle.

Previous studies use linear statistics, but my co-authors are adamant that I should use circular statistics (Watson-Williams tests and similar).

Question 1 Are circular statistics always necessary when dealing with angular data? I don't have full circularity, and in itself, direction is not the main question here, but a difference in measured angle. This response from this same forum makes me think that linear statistics are sufficient, but I'd like a fuller explanation as well as a supporting reference (to justify my statistical decision). I saw a few references here, but they seem to dive straight into the statistics.

Question 2 If circular statistics are required, what is the circular equivalent of the intraclass correlation coefficient (ICC) to test for inter and intra-observer reliability? This is the one that seems the most reasonable to my data as my outcome variable is continuous.

Question 2.1 Would it be appropriate to project my data as suggested here, by converting the angles to (sin(x),cos(x)), and thus transforming it to "linear"? But if I do this, I'm not sure how to operate it or interpret it since I will have two outcome variables rather than one? Would it look like this?

I have a set of data of measurements for the lateral angle of the internal acoustic meatus, taken by three different evaluators at three different points in time. Values vary from 16° to 115° (in itself this seems odd as values in the literature range from 30° to 70°, but outside this question). The final goal is to see if there are any sex differences in lateral angle.

Previous studies use linear statistics, but my co-authors are adamant that I should use circular statistics (Watson-Williams tests and similar).

Question 1 Are circular statistics always necessary when dealing with angular data? I don't have full circularity, and in itself, direction is not the main question here, but a difference in measured angle. This response from this same forum makes me think that linear statistics are sufficient, but I'd like a fuller explanation as well as a supporting reference (to justify my statistical decision). I saw a few references here, but they seem to dive straight into the statistics.

Question 2 If circular statistics are required, what is the circular equivalent of the intraclass correlation coefficient (ICC) to test for inter and intra-observer reliability? This is the one that seems the most reasonable to my data as my outcome variable is continuous.

Question 2.1 Would it be appropriate to project my data as suggested here, by converting the angles to (sin(x),cos(x)), and thus transforming it to "linear"? But if I do this, I'm not sure how to operate it or interpret it since I will have two outcome variables rather than one? Would it look like this?

Any help will be very appreciated!

I have a set of data of measurements for the lateral angle of the internal acoustic meatus, taken by three different evaluators at three different points in time. Values vary from 16° to 115° (in itself this seems odd as values in the literature range from 30° to 70°, but outside this question). The final goal is to see if there are any sex differences in lateral angle.

Previous studies use linear statistics, but my co-authors are adamant that I should use circular statistics (Watson-Williams tests and similar).

Question 1 Are circular statistics always necessary when dealing with angular data? I don't have full circularity, and in itself, direction is not the main question here, but a difference in measured angle. This response from this same forum makes me think that linear statistics are sufficient, but I'd like a fuller explanation as well as a supporting reference (to justify my statistical decision). I saw a few references here, but they seem to dive straight into the statistics.

Question 2 If circular statistics are required, what is the circular equivalent of the intraclass correlation coefficient (ICC) to test for inter and intra-observer reliability? This is the one that seems the most reasonable to my data as my outcome variable is continuous.

Question 2.1 Would it be appropriate to project my data as suggested here, by converting the angles to (sin(x),cos(x)), and thus transforming it to "linear"? But if I do this, I'm not sure how to operate it or interpret it since I will have two outcome variables rather than one? Would it look like this?