Statistical inference when using vector coding (issues with circular variables)

[Bernard]

Dear community,

I am planning to do vector coding. Although circular mean and variability (descriptive) have been emphasized, when I delve into the vector coding literature, there has been very little mention of using circular statistical inferential methods (packages and software), for variables such as coupling angle.

Most times inestigators perform traditional stats on variables like phase bins, variability, but it would be cool to do something on coupling angle.

So far I am using R package and am aware of packages (eg. circular, Directional), but they do not allow repeated measures ANOVA or a more general mixed model, for my study design. One roundabout way in an article (http://www.eva.mpg.de/documents/Else...09_1552981.pdf), performed traditional stats on the xy coordinates (e.g. x = Rcos(theta), y = Rsin(theta)).

I was wondering if anyone has used (or know) of packages/software that would allow circular statistical inference, with particular emphasis on outputs from vector coding?

Any advice/help is greatly appreciated.

Kind regards,
Bernard

[Ross Miller]

Re: Statistical inference when using vector coding (issues with circular variables)

Hi Bernard,

Batschelet (1981) is a good reference on circular statistics:

https://www.amazon.com/Circular-Statistics-Biology-Mathematics-biology/dp/0120810506

The quantity he defines as the "Angular Deviation" is in my opinion the closest analog for the "Standard Deviation" in traditional statistics:

AD = (2*(1-r))^0.5

where r is the mean vector length of n vector angles q:

r = (x^2 + y^2)^0.5
x = sum(cos(q))/n
y = sum(sin(q))/n

The theory is that r decreases from 1 to 0 as the data are more dispersed around the circle.

The Batschelet text is out of print but most institutional libraries will probably have a copy.

Hope this helps,
Ross

[Bernard]

Re: Statistical inference when using vector coding (issues with circular variables)

Thanks Ross,

Many thanks for the reference. I have also read your works on vector coding which is a great reference for me. In addition to generating summary statistics using circular statistics, I am also interested in performing statistical test (e.g. repeated measures ANOVA) on coupling angle. This means I must use some form of circular analogue to the ANOVA (as I know circular data have circular normal distribution etc). I may be wrong, but I think most researchers when performing vector coding circumvent the issue of circular stats on coupling angle by 1) performing traditional stats on bin counts, and 2) variability.

Would you be able to advice on how to approach the statistical testing of coupling angle?

Many thanks for taking the time to respond (including anyone who have some inputs)

Kind regards,
Bernard

[Ross Miller]

Re: Statistical inference when using vector coding (issues with circular variables)

Hi Barnard,

I've alway just used "traditional" statistical tests on vector coding and CRP data (e.g. t-tests). The Batschelet text also has chapters on confidence intervals and hypothesis testing for circular data.

Ross

[Ryan Chang]

Re: Statistical inference when using vector coding (issues with circular variables)

Hi Barnard,

I have used a difference test of group means for circular data (such as mean coupling angles). As Ross said, it is available in the Batschelet book. I have also used a Watson-Wiliams test prior to the means test to ensure that my data were normally (circularly) distributed - sometimes they were not. I performed the tests by hand (with Matlab), and did not use any software suites.

Good luck,
Ryan