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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[t]=sum(abs(sort(perm[1:10])-sort(perm[11:20])))

when $n=20$. It is obviously much closer to zero than previously.

An interesting change is that the regression of the log-mean on $log(n)$ produces

> lm(log(memean)~log(enn))
Call:
lm(formula = log(memean) ~ log(enn))
Coefficients:
(Intercept)     log(enn)
-1.162        1.499

meaning that the mean is in $n^{3/2}$ rather than in $n$ or $n^2$:

> summary(lm(memean~eth-1))
Coefficients:
Estimate Std. Error t value Pr(>|t|)
eth 0.3117990  0.0002719    1147   <2e-16 ***

with a very good fit.

Filed under: R, Statistics Tagged: Le Monde, puzzle, R, Spearman rank test