Smallest two-sided p a rank-sum test can produce at these group sizes
Source:R/stats-abundance.R
rank_sum_p_floor.RdWHY THIS MATTERS ON A SMALL COHORT. A Wilcoxon rank-sum test has
choose(n1 + n2, n1) equally likely rank arrangements under the null, so the
most extreme possible separation gives a two-sided p of
2 / choose(n1 + n2, n1) and nothing smaller is reachable. At 4 against 5 that
floor is 0.016; after correcting across a dozen populations, no population can
reach 0.05 no matter how cleanly the groups separate. A reader looking at a
volcano plot with an empty top has no way to tell "nothing differs" from "this
design cannot produce a significant p", and those are opposite conclusions.
Drawing the floor answers it on the figure.