do cores tend to group together

[roblanf]

One obvious question we might have of our PF2 runs is whether the central windows of the UCEs tend to group together. We can address this with permutations as follows (and I note here that asking whether left or right flanks group together probably isn't sensible because there's no biological meaning (AFAIK) to being either 'left' or 'right', so the only question we really need to ask is whether the cores group together).

First, we define a test statistic as some summary statistic (e.g. mean, median) of the proportion of cores in each subset of sites. E.g. if cores always and exclusively grouped together, the mean would be 1.0 - any subset with a core in it would ONLY have cores in it.

Then, we calculate the observed test statistic, e.g. for the mean we'd calculate:

1. the proportion of cores in each subset of sites
2. the mean of 1.

Now our null distribution comes from permutations of the data, where we keep the number and size of each subset constant (by size I mean the number of data blocks in that subset), but we shuffle the identity of the data blocks in each subset. For our null distribution, we just do 999 shufflings, and re-calculate the test statistic each time.

Now, PF2 tends to group the cores more often than chance, we expect the observed proportion to be higher than null distribution would suggest. For this we can use a 1-tailed test, since I see no sensible reason how cores could 'repel' each other and so the proportion could be lower than the null distribution. But we should think very carefully about that before doing the stats... We can only do a one-tailed test if the answer that the observed proportion was lower was in no way at all interesting or meaningful.