############################################
#MATH 5301 Nonparametric Statistics
#
#Quade permutation test


#Lotion Example
y = matrix(c( 5,  4,  7, 10, 12,
              1,  3,  1,  0,  2,
              16, 12, 22, 22, 35,
              5,  4,  3,  5,  4,
              10,  9,  7, 13, 10,
              19, 18, 28, 37, 58,
              10,  7,  6,  8,  7),
           nrow = 7, byrow = TRUE,
           dimnames =
             list(Store = as.character(1:7),
                  Brand = LETTERS[1:5]))


quade.test(y)



#Permutation Test

quade.permutation=function(x,num.replicates){
  n=nrow(x)
  p=ncol(x)
  
  F.obs=quade.test(x)$statistic
  F.vect=rep(0,num.replicates)
  
  temp = x
  
  for(i in 1:num.replicates){
    for(j in 1:nrow(x)){
      index=sample(p,p)
      temp[j,]=x[j,index]
    }
    F.vect[i]=quade.test(temp)$statistic
  }
  
  p.value=mean(F.obs<=F.vect)
  
  plot(density(F.vect))
  
  return(p.value)
}

quade.permutation(y,100000)
quade.test(y)


x.index=seq(from=0,to=8,length=1000)
y.index=df(x.index,df1=4,df2=24)
lines(x.index,y.index,col="red")