## Use of Binomial in Sign test 

 n <- 15 
 K <- 14

 pvalue <- 2*(1- pbinom(K-1, size = n, p = 0.5) )
 pvalue

  # finding a 95% C.I. 


range <- 10:15
pval <- matrix(0,1,length(range))

ind <- 1   
for (k in range){
  pval[ind] <- 2*(1- pbinom(k-1, size = n, p = 0.5) )
  ind <- ind + 1   # next entry in the array
  }

round(rbind(range, pval), 4)    # print the results 
   


 afakesample <- c(1:14,-1.5)   # also, do -1 to show ties  

 S <- sum(rank(abs(afakesample))*sign(afakesample))
 wilcox.test(afakesample)     # Wilcoxon rank-sum test for later 


 # later, let's input the real data; will also get the C.I.

 X <- read.csv("U:/public_html/588/Class6/schizo.csv")
 Y <- X[,1] - X[,2]

 wilcox.test(Y)
 




##  the Book's illustration of the rank-sum test

X <- read.csv("U:/public_html/588/Class6/cognitive.csv", header = TRUE)     # replace by your own path here
boxplot(X[,1] ~ X[,2])

R <- rank(X[,1])
  N <- length(R)
  n1 <- sum(X[,2] == 'MODIFIED')
  n2 <- N - n1

order(X[,1])     # shows the permutation that orders X
 X[,1]
 sort(X[,1])

T <- sum(R[1:n1])    # T = rank-sum statistic

# normal approximation 

meanT <- mean(R)*n1
SDT <- sd(R)*sqrt(n1*n2/N)

 Z <- (T - meanT)/SDT
 pvalue <- 2*(1 - pnorm(abs(Z), mean = 0, sd = 1))    # two-tailed p-value 
 
 print(paste("Approximate p-value=", round(pvalue,4)," on Z-stat=", round(Z,2)) )
 
## now the built-in R routine 

 wilcox.test( c(3,4,39), c(1,5,7)    )                        # our first example 

 wilcox.test(X[,1] ~ X[,2], conf.int = TRUE)    # 

wilcox.test(X[1:14,1], X[15:28,1])    # swap the two samples  
wilcox.test(X[15:28,1], X[1:14,1])


 # google   "wilcox.exact" for a package that can do ties