I have been trying to determine the proper statistical test for comparing binned proportional data between groups. My data set is individual subjects (4-5 per group) with 76-165 cells per individual. Each cell has a variable X that can range from 0-1. I binned the data for each individual in 0.2 sized bins, converted each bin to a proportion of the total (for each individual), and averaged by group (WT/KO). (link to example data plotted in MATLAB, https://imgur.com/WyMGMyS).
It seems like a common method is to run a Wilcoxon test on each bin independently. My question would be, is this an appropriate method given that, as proportion data, the values in bins are not independent of each other? Alternatively, I have tried an ANOVA method in JMP (Analyze->Fit Model->Standard Least Squares->Y=variable, constructor model group*bin interaction), but this method seems very insensitive to effects in single bins if "bin" is a continuous variable, but listing bin as ordinal seems inappropriate (example JMP data entry for 1 individual, https://imgur.com/MANc58S). Has anyone encountered a similar issue? Also, if the Wilcoxon test is appropriate is there a way to run it in JMP on each bin independently without having to exclude all the other bins in the chart and run it 5 times per variable, X? Or would that be simpler to code in MATLAB using the ranksum function?
Thank you, and please let me know if this question is not appropriate/appropriate format.
*edit: link to data, https://github.com/kylemxm/ShepherdGit/blob/master/ODI%20example%20Data.mat