A colleague wants to examine the directionality of amphibian dispersal to and from a pond. He set up a drift fence around the pond and had buckets at different positions to capture the amphibians. He measured the angle from the center of the pond to each bucket. There are 23 buckets arrayed around the pond; due to physical constraints, the angle between each bucket (and resulting arc length of the sector) is not perfectly regular.
He wants to use methods from circular statistics to examine directionality (or conversely, uniformity). The data can be treated as bearings to each bucket (with counts) or as sectors around each bucket (with counts). Unfortunately, I can't find a good discussion in the literature (or on CrossValidated) as to what sort of methods are preferred for this sort of design...as most methods are based on continuous measures of bearing (or time) around the unit circle. There seems to have been some work on circular methods for discrete variables, but they don't seem to apply to irregular data with relatively large intervals.
An ad hoc method seems to be the use of a chi-square goodness-of-fit test based on comparison of observed counts to expected counts (here based on the total sample size times the arc length)...but this seems sketchy due to the high number of zeros for some species (buckets where amphibians were not captured) and potential circular autocorrelation among neighboring buckets (and hence lack of independence).
I have seen some papers that have used Rayleigh's z test and Rao's spacing test for sector data, but I am not sure whether this is "kosher" or not (as I can't find a discussion about the pitfalls). I thought I might try examining the fit to a parametric distribution (such as von Mises) to see if I am in the ballpark, but I feel insecure about it.
I would be very grateful for any guidance as to which methods might be most applicable to this sort of design...or if somebody could point me in the direction of a paper or book chapter where this issue discussed. I have skimmed through Jammalamadaka and SenGupta...and the table of contents of more recent monographs, but I can't seem to find any obvious discussion about sector data...and I can't justify throwing down the money for a book without being sure if this content is covered.