Wilcoxon signed-rank test using R

[Mengkelyu]

背景：Wilcoxon signed-rank test是用来检验两个数组是否来自同一分布的

n = 1000
x <- rnorm(n,0,1)
y <- rnorm(n,0,5)
# x和y是要检验的变量

df <- data.frame(x, y)
# alpha是置信水平参数
Wil_test <- function(dataframe_or_x, y = 1, alpha = 0.05){
  if(is.data.frame(dataframe_or_x)){
    x = dataframe_or_x['x']
    y = dataframe_or_x['y']
  }
  else {
    x = dataframe_or_x
  }
  d <-  x - y
  d <- d[d != 0]
  n = length(d)
  d_absolute = abs(d)
  r = rank(d_absolute, na.last = TRUE,
           ties.method ="average")
  SR_plus = sum(r[d > 0])
  SR_minus = sum(r[d < 0])
  t = min(SR_plus, SR_minus)
  E_t = n * (n + 1)/4
  Var_t = n * (n + 1) *(2*n + 1) / 24
  z = (t - E_t) / sqrt(Var_t)
  if(abs(z) > qnorm(1 - alpha/2)){
    print("NUll hypothesis rejected.")
  }
  else {
    print("NUll hypothesis not rejected.")
  }
  p <- 2 * (1 - pnorm(abs(z)))
  return(p) 
}
# when x and y are both provided
Wil_test(x, y)
## [1] "NUll hypothesis not rejected."
## [1] 0.8835577
# when a dataframe is provided
Wil_test(df)
## [1] "NUll hypothesis not rejected."
## [1] 0.8835577

[Mengkelyu]

当然，也可以用stats包来完成这一任务

library(stats)

wilcox.test(x, y)