Given a number of K-functions from data of two populations (e.g. 10 sets with points of population 1 and 10 sets with points of population 2; non-overlapping image areas; only one population per set, so data is not marked), how can I perform testing for group difference based on the K-curves alone? Is there an appropriate test for this?

If I have a single parameter (e.g. Clark Evans or minimum nearest neighbor distance) I can simply perform a T-Test or Mann-Whitney-U-Test (depending on data normality) for the two groups.

  • $\begingroup$ (1) Ripley's K is far better suited for analysis and insight rather than tests. No single test will capture everything that can be learned from a careful look at the graph of $K$ (or better, a suitably standardized version of $L$). (2) I have never seen software for Ripley's K that did not also include a simulation-based confidence band. That can be very helpful to support visual assessments of differences. (3) OK, let's accept that you need a test. You must specify what behaviors you are comparing. What is the alternative hypothesis.? $\endgroup$ – whuber Aug 20 '15 at 14:23
  • $\begingroup$ Hi whuber, thanks for your comment. (1) You are right, the graph gives good insight and contains a lot of information. (2) I have already computed confidence bands an the basis of Monte Carlo simulations. But I am missing some comparability between data sets of different populations. (3) Well, the alternative hypothesis should be that the graph behaviour of population 1 differs from that of population 2. Maybe pop1 has small clusters that produce an elevation of the graph for small r, while the graphs of pop 2 are somewhat flatter indicating no distinct clustering? $\endgroup$ – Kardashev3 Aug 24 '15 at 10:02

I only have time for a very short answer. In the spatstat package for R there is a vignette which explains a bit of the theory for replicated point patterns, so you might want to have a look at that: https://cran.rstudio.com/web/packages/spatstat/vignettes/replicated.pdf

Furthermore, a relevant test could be the studentised permutation test developed by Ute Hahn:

Hahn, U. (2012) A studentised permutation test for the comparison of spatial point patterns. Journal of the American Statistical Association 107 (498), 754-764.

This test is implemented in the spatstat function studpermu.test, so you might also try to read the documentation for that.

Finally, a relevant thing may be to pool all the estimates of the K-function for each group to get two overall K-functions to compare. Have a look at the help file for pool (specifically the method pool.fv) in spatstat.

  • $\begingroup$ I will try the studentised permutation test for my data. Pooling of estimates seems to be another good idea! I will report back when I am done. $\endgroup$ – Kardashev3 Aug 24 '15 at 10:04
  • $\begingroup$ Now I have tried your suggestions and I am very pleased with the results :)! The vignette about replicated point patterns provides an excellent introduction to that topic. The studentised permutation test is exactly what I was looking for. Group differences can be calculated based on the actual point patterns without the need of deriving some numbers from the curves while omitting a lot of spatial information. Pooling of functions is another great thing as overall group information can be plotted and analyzed. Thank you very much for these great ressources :)! $\endgroup$ – Kardashev3 Sep 2 '15 at 15:19

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.