Figure 1

Assessment of tightness. (A) Four lines are shown for N = 10: the mmHG score, which also serves as a lower bound for the p-value; the exact p-value calculated by enumerating all 10! permutations; our refined upper bound B2; and the Bonferroni corrected p-value. (B) Here again the four lines are shown - for N = 20. However, instead of an exact p-value, which cannot be calculated exhaustively, an empirical p-value is produced by randomly sampling 10⁷ permutations. (C) In addition to the four lines shown in B, the upper bound B1 is shown (N = 20). (D) Four lines are shown for N = 100: the mmHG score, our upper bound B2, the bound B3 and the Bonferroni corrected p-value. The exact p-value line is positioned between the green and the blue lines. An empirical p-value was not calculated here as even if we sample 10⁷ permutations, a p-value smaller than 10^-7 cannot be obtained.