Wilcoxon Signed Rank Distribution (Part 2)

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### Program Code

## ##
## Understanding the Wilcoxon Signed Rank Distribution ##
## ##


#### example 1
(tmp1<-expand.grid(0:1, 0:1, 0:1))
(tmp2<-rep(1:3, rep(2^3, 3))*tmp1)
(tmp3<-rowSums(tmp2))
(tmp4<-table(tmp3))
prop.table(tmp4)


### General function to calculate Wilcoxon Signed Rank Distribution
### This is not an efficient method!!
### Only for illustrative purposes

sign.rank<-function(n) prop.table(table(rowSums(rep(1:n, rep(2^n, n)) *


#### example 2
n<-4
sign.rank(n)
barplot(2^n * sign.rank(n))

n<-15;barplot(2^n * sign.rank(n))

### built-in R function!
n<-4
dsignrank(0, n)
dsignrank(4, n)
dsignrank(0:(n*(n+1)/2), n)

n<-40
dsignrank(0:(n*(n+1)/2), n)
barplot(2^n * dsignrank(0:(n*(n+1)/2), n))

statisticsmatt