the_wilcoxon_rank_sum_test <- function(X, Y) {
  objedinjen_uzorak = c(X , Y)
  rangovi = rank(objedinjen_uzorak)
  n = length(X)
  T = sum(rangovi[1:n])
  return(T)
} 

X = c(37.23, 42.45, 47.75, 51.24, 51.58, 52.67, 53.64, 56.56, 56.54, 63.43, 97.68, 100.59)
Y = c(47.12, 47.72, 58.13, 53.54, 57.84, 61.50, 69.78, 90.73, 104.27, 110.56, 132.82, 120.50)

the_wilcoxon_rank_sum_test(X, Y) 

# test statistika f-jom wilcox.test daje nesto drugaciju vrednost 
# kada na to dodamo n1*(n1+1)/2 (gde je n1 velicina uzorka X) 
# dobijemo bas vrednost nase test statistike

a <- wilcox.test(X, Y, paired = FALSE)
n1 <- length(X)
a$statistic <- a$statistic + n1*(n1+1)/2
a