These are bootstraping p-values. The second formula on this page here gives a reference where this comes from.

From the source code of the regioneR package (`permTest`

function) they implement it as:

```
pval <- (sum(orig.ev >= rand.ev, na.rm = TRUE) + 1) / (num.valid.values + 1)
```

So the p-value, here testing that the overlap (or whatever you test) is greater for the observed events compared to the randomly-permutated events, is the number of times that the observed event is larger or equal divided by the number of permutations.

The Z-score is the deviation of the observed events by the mean of the permutated events (corrected for standard deviation) so basically a significant event should have a large Z-score since the observed event should be quite different from the mean of the random events.

```
zscore <- round((orig.ev - mean(rand.ev, na.rm = TRUE))/stats::sd(rand.ev, na.rm = TRUE), 4)
```

Did you check their publication?

regioneR: an R/Bioconductor package for the association analysis of genomic regions based on permutation tests

6.7kYes, and there are no explanation why for different z-score there are the same p-value.

0They are not the same z-score.

67k