Since my first representation of the rank statistic as paired was incorrect, here is the histogram produced by the simulation perm=sample(1:20) saple=sum(abs(sort(perm)-sort(perm))) when . It is obviously much closer to zero than previously. An interesting change is that the regression of the log-mean on produces > lm(log(memean)~log(enn)) Call: lm(formula = log(memean) ~ log(enn)) Coefficients: (Intercept)