A technical remark: The program computing the distances using the algorithm of WRR had repeated minor modifications (or debugging) and we do not have now the program used for the numbers appearing in the Statistical Science article and not in the earlier preprints.
At present there are two variants of the program. One
variant (REAL_GEOMETRIC = OFF) is just a
debugged (or slightly modified) version of the original one
and the other variant (REAL_GEOMETRIC = ON) represents a slight
methodological change which occurred after the paper appeared in
Statistical science. The distributions
of P2 ratios in both these variants are fairly close together
(at least in the range of interest to us) and the 0.0092 figure is
the probability of P2 ratio below 1.1217 in both of them.
The individual P2 scores for the original partition did modify.
The P2 scores in the modified version of the original
concept is for the first
list
for the second and the ratio is 1.1487. The probability to be below
this ratio is 0.0113. (For the new variant, which is irrelevant,
the P2 score of the first list is
for the
second list it is
the ratio is 1.40394 and the
chance to be below it is 0.0278.)
We think 0.0092 is the right number to take and in any case the WRR preprint contains the original pair-scores so it is possible to insert them to the computer and use the original data.