#Mann-Whitney / Wilcoxon Rank Sum Test

#Data for reaction time under simulated driving conditions
 plac = c(0.9, 0.37, 1.63, 0.83, 0.95, 0.78, 0.86, 0.61, 0.38, 1.97)
 alco = c(1.46, 1.45, 1.76, 1.44, 1.11, 3.07, 0.98, 1.27, 2.56, 1.32)

#W-M-W non-parametric test
 wilcox.test(plac,alco,paired=FALSE,correct=F,exact=F)  #NB: W=S-n2*(n2+1)/2

#T-test on the RANKs of the data
 dat = NULL 
 dat$response = c(plac, alco)
 dat$group = c(rep("plac",10), rep("alco", 10))
 dat
 dat$rank = rank(dat$response)
 t.test(dat$rank ~ dat$group)

 sum(rank(dat$response)[dat$group=="plac"])

#Normal approximation for sampling distribution of S
 S=70; n1=10; n2=10
 mu.s = n1*(n1+n2+1)/2
 sd.s = sqrt(n1*n2*(n1+n2+1)/12)
 z.s = (S-mu.s)/sd.s
 pnorm(z.s) 

 wilcox.test(response~group, paired=FALSE, correct=F, exact=F, data=dat)  
 wilcox.test(plac,alco,paired=FALSE,correct=F,exact=F)  #NB: W=S-n2*(n2+1)/2

 S-n2*(n2+1)/2 #W statistic used by R