I have very large sets of biological data, ca. 5,000,000 points, which are the proportion of methylation throughout the genome. Data is therefore on 0-1 scale. I am looking at testing distribution between samples, and also in replicates within samples. I have done some stats before but am no expert. I use R for analysis.
I have tested using Kolmogorov Smirnov but data has many 'ties' where positions are equal. I have used Wilcoxon but am unsure if it handles large datasets well(?)
I have also looked at the ECDF and plotted this, see image. The unusual thing with this is that distributions look very similar, but are obviously 'reduced' in one sample vs. another. I believe this phenomenon represents fewer events occurring, in this case in the red vs. blue sample. I arrive at this from the ECDF x axis representing methylation level, and y representing the proportion of data points which are at or below this level. Does this make sense? Is the ECDF useful in testing divergence of distribution or just exploratory analysis/visualisation?
Any help on what other test might be appropriate would be great, even looking at binning data and testing, which I tried using Chi Squared.