[R] Combinatorics for nonparametric tests

Trenkler, Dietrich
Wed, 03 May 2000 06:13:12 -0000

For some small sample sizes I would like to exemplify the combinatorics
underlying certain nonparametric tests like Mann-Whitney-Wilcoxon,
Kruskal-Wallis and Spearman's rank correlation.  I have written a
function all.perm which delivers all permutations of 1,2,...,n and
which works reasonably well.  This can be used to generate P(R=r) of
Spearman's rank correlation:

n_6;plot(table(apply(all.perm(n),1,cor,y=1:n)),type="h")

all.perm_function(n){
p_matrix(1,ncol=1)
for(i in 2:n){p_pp_cbind(p,i)
v_c(1:i,1:(i-1))
for(j in 2:i){v_v[-1]
p_rbind(p,pp[,v[1:i]])}}
p}


Until now I hesitated to dwell on writing  functions to generate all
n!/(k!(n-k)!) k-combinations of an n-element set or more generally all
n!/(k_1!k_2!...n_k!) choices of placing n objects into k boxes where
box j has n_j objects.

Not intending to re-invent the wheel I turn to the R community to ask
if someone has already written these functions.

Any help is thankfully appreciated.

   --- D.Trenkler ---

************************************************************************
*********
   Dietrich Trenkler
(trenkler at oec.uni-osnabrueck.de)
   Statistik / Empirische Wirtschaftsforschung
   Universitaet Osnabrueck
   Rolandstrasse 8                             Phone: +49(0)
541-969-2753
   D-49069 Osnabrueck                        Fax  : +49(0) 541-969-2744
   GERMANY
************************************************************************
*********



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