various significance levels. To do so, we binned the adjusted P-values obtained from beta approximations and estimated for each bin, by exhaustive search, the number of permutations required by the direct method to match the same sampling variation (Supplementary material 3). We find that this number drastically increases as small-adjusted P-values are targeted (Fig. 2c). For instance, beta approximations made from 1000 permutations give adjusted P-values of 10−4 as accurately as the direct approach with ∼50K permutations.
