Non-transitive dice

README.md

An example of the non-transitivity of the Wilcoxon test, using Efron's non-transitive dice.

refron() generates numbers from a set of four non-transitive dice, so that a beats b beats c beats d beats a two-thirds of the time, with optional Gaussian smoothing.

example.R does Wilcoxon rank-sum tests to show that a > b > c > d > a

example.R

dd<-efron(1000,s=0.2)
wilcox.test(dd[,1],dd[,2],alternative="greater")
wilcox.test(dd[,2],dd[,3],alternative="greater")
wilcox.test(dd[,3],dd[,4],alternative="greater")
wilcox.test(dd[,4],dd[,1],alternative="greater")

refron.R

refron<-function(n,which=c("a","b", "c", "d"), smooth=0){
    M<-matrix(nrow=n,ncol=4)
    colnames(M)<-c("a","b", "c", "d")
	M[,1]<-sample(c(0,0,4,4,4,4),n,replace=TRUE)
	M[,2]<-sample(c(3,3,3,3,3,3),n,replace=TRUE)
	M[,3]<-sample(c(2,2,2,2,6,6),n,replace=TRUE)
	M[,4]<-sample(c(1,1,1,5,5,5),n,replace=TRUE)
	if (smooth>0) M<-M+rnorm(length(M),s=smooth)

	M[,which]
}