Forgive me if this is trivial, I want to make sure I understand the output of bedtools fisher. I've used it to compare several sets of intervals in the human genome and want to say whether two sets of intervals have a statistically significant overlap or not. Here are the abbreviated outputs from 6 tests (I can give the full outputs if needed):

Code:

Test left right two-tail ratio
1: 0 1 0 3.655
2: 1 1.3018e-39 2.5115e-39 1.180
3: 1 4.9869e-47 9.3199e-47 1.198
4: 1 3.7421e-45 6.909e-45 1.194
5: 0.71641 0.40143 0.61502 1.123
6: 0.63306 0.49828 0.86348 1.040

Is it correct that: a small left p-value indicates the intervals overlap significantly more than expected (test #1 above), a small right p-value indicates the intervals overlap significantly less than expected (tests 2,3,4), and if neither the left or right p-values are small (tests 5,6) the intervals overlap "randomly" (not sure what the correct term is, basically they don't overlap more or less than would be expected)? Also I don't understand how to interpret the two-tail p-value and ratio for these tests. Thank you to anyone who can help clarify this for me.