The P2 statistics

The P2-statistics describes the probability that the product of n independent random variables distributed uniformly in the interval [0,1] will be smaller than a number x.

The astronomical significance levels from the 87 preprints [3] are false (mainly) due to wrong independence assumptions. The pair distance c(w, w') can be regarded as a function of the shortest ELS for w, the shortest ELS for w' and the distance between them. (The same remark applies to P1.) This creates massive dependencies among the pair distances. The continued use of false significance measures in the bible code activity is one of the reasons for the self-deception which is so characteristic of that activity.

The significance level reported in the paper [2] used a method suggested by Diaconis and is $1.6 \cdot 10^{-5}$. As pointed out by Brendan McKay [1] the authors did not implement Diaconis' suggestion but a rather different variant of it which inflates the significance level. The correct significance level for the second test if you implement the Diaconis test correctly is around $1.6 \cdot 10^{-3}$.

In the analysis section of [3] (and in [2]) WRR use also another statistics - later called the P1-statistics. The P1-statistics studies, using the normal approximation to the binomial distribution, the significance of the number of pair-distances whose value is smaller than 0.2.