Le Monde rank test (corr’d)

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.

One Response to “Le Monde rank test (corr’d)”

  1. […] Monde [reverse] rank test This is the fourth and hopefuly last post about this puzzle. If I translate the problem, it reads as […]

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