How to convert data around a circle for circular statistics?

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Ajay Goyal 2018-8-9

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https://ww2.mathworks.cn/matlabcentral/answers/414189-how-to-convert-data-around-a-circle-for-circular-statistics

评论： Ajay Goyal 2018-8-15

I have generated 36 values at equidistant distances at an interval of 10. I want to convert it to circular data. Is there a way?

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Adam Danz 2018-8-12

Hi Ajay, You're right that the inputs must be in radians. Columns 2 and 3 of your data are cell counts so you can't, and don't want to, convert them to radians.

You'll probably want to use first and second inputs of the circ_wwtest() as follows. The first one is a vector of your radian values in column 1 and the second is a grouping variable that groups the first input into the different groups (your two columns). So, if row 1 is [pi, 4, 2], you'll replicate Pi 6 times and your grouping vector will have four ones and two twos which represents Group 1 and 2, your columns 2 and 3. you'll repeat that for all of the rows of your data which will end up with two large vectors. See the first link below, starting at the bottom of page 12 for a description of this function.

The second link is an example of this function but in a different software. I couldn't find a Matlab example.

I'm posting this on my smartphone and I do not have Matlab available right now so if you get stuck let me know and I can help more another time.

http://www.jstatsoft.org/v31/i10/paper

https://www.wavemetrics.com/products/igorpro/dataanalysis/statistics/tests/statistics_pxp32

Ajay Goyal 2018-8-15

cal_vs_exp_data.xls

Thank you, Adam. You are a nice person. Please find the attached file for the actual data. Column 1 represents the angular positions measured in counterclockwise direction with respect to 0 degrees. 2nd and 3rd column shows the actual and analytically calculated bone thickness (measured in millimeters) respectively. I have to test whether 2nd and 3rd column are significantly same or not. For this, I have previously used Cramer's von mises test, KS test as well as Anderson darling test on this data. They have predicted that both data is significantly same. However, as my data is measured around a circle (a bone section), to my understanding, these tests are not applicable to my data. Therefore, I have studied some literature regarding circular statistics. From there, I understand that there are different fits such as wrapped, uniform, von mises that can be used. I also understand the concept of maximum likelihood to determine parameters involved in these fits. One thing I was unable to understand is that the inputs to these parameters are given in radians though my data is in millimeters. Based on your guidance, I understood that the problem can be solved by repeating angular position depending on data in column 2 and 3. However, my actual data in column 2 and 3 is in decimals. Therefore, I still concern about applicability of circular statistics to my data. Currently, type of circular test is not my concern. I am just keen to learn that how my data can be modified for ready input to a circular statistic test.

Adam Danz 2018-8-15

Previously you mentioned that your data were cell counts (integers) which could be used to produce populations with units of degrees or radians which is why I suggested the Watson test but this is different.

I understand that you want to determine whether or not the two distributions are significantly different and that those measurements are taken around a circular object (bone, I suppose). Your measurements are in millimeters (thickness) and are sampled at intervals in degrees (surface). While it is easy to convert between degrees and mm when measuring distance[1], that's not what you're doing. Correct me if I'm wrong but you're measuring thickness of bone at various location around a circular object and in that context, thickness isn't related to anything circular. Example: my book is 50mm thick - there's no way to convert that to degrees or radians. So, even though your data were collected around a circular object, your data itself isn't circular.

In neuroscience (my field) we often measure the spike rates of neurons as we move the subject in different directions around a circle in order to understand the neuron's heading tuning. While the independent variable is circular, the dependent variable (spike rate) is not. And we don't use circular statistics in that case.

I plotted out your data (below) and the two distributions look different. I don't know whether or not your data from column 2 and 3 are independent or not but a simple paired t-test concludes that the distributions are significantly different (p < 0.5, tstat = -2.33). However your data aren't normally distributed so perhaps a Wilcoxon’s matched-pairs test would be more appropriate.

Take my suggestions with a grain of salt since I only partially understand the context of your data.