## Nonparametric tests for matched pairs and randomized block designs

#############################
# sign test and Friedman test
#############################

y1<-c(8.4,12.8,9.6,9.8,8.4,8.6,8.9,7.9)
y2<-c(9.4,15.2,9.1,8.8,8.2,9.9,9.0,8.1)
y<-cbind(y1,y2)

help(friedman.test)
> friedman.test(y)

        Friedman rank sum test

data:  y 
Friedman chi-squared = 0.5, df = 1, p-value = 0.4795


###########################
# Wilcoxon signed-rank test
###########################
> help(wilcox.test)
> wilcox.test(y1,y2,paired=T,correct=F)

        Wilcoxon signed rank test

data:  y1 and y2 
V = 12.5, p-value = 0.4406
alternative hypothesis: true mu is not equal to 0 

Warning message: 
Cannot compute exact p-value with ties in: wilcox.test.default(y1, y2, paired = T, correct = F) 

> y1-y2
[1] -1.0 -2.4  0.5  1.0  0.2 -1.3 -0.1 -0.2
> rank(abs(y1-y2))
[1] 5.5 8.0 4.0 5.5 3.0 7.0 1.0 2.0   
# not sure why the two values of "0.2" get ranks of 2 and 3, instead of 2.5 
# for both

> wilcox.test(y1,y2,paired=T)

        Wilcoxon signed rank test with continuity correction

data:  y1 and y2 
V = 12.5, p-value = 0.4833
alternative hypothesis: true mu is not equal to 0 

Warning message: 
Cannot compute exact p-value with ties in: wilcox.test.default(y1, y2, paired = T) 

## exact test
y<-c(-4,2,7,6)
> wilcox.test(y)

        Wilcoxon signed rank test

data:  y 
V = 8, p-value = 0.375
alternative hypothesis: true mu is not equal to 0 
## exact=T is the default

> 3/16
[1] 0.1875
> (3/16)*2
[1] 0.375