An simulation of wilcox.test for the compositional data

wilcox_compositional.r

library(gtools)
library(ggplot2)
library(ggbrick)
set.seed(1)
wp <- numeric(10000)
ksp <- numeric(10000)
tp <- numeric(10000)
for(i in 1:10000){
  y1 <- rdirichlet(50,rep(1,10))
  y2 <- rdirichlet(50,rep(10,10))
  wp[i] <- wilcox.test(y1[,1],y2[,1])$p.value
  ksp[i] <- ks.test(y1[,1],y2[,1])$p.value
  tp[i] <- t.test(y1[,1],y2[,1])$p.value
}

hist(ksp,main="ks.test",xlab = "p-value")
hist(tp,main="t.test",xlab = "p-value")
hist(wp,main="wilcox.test",xlab = "p-value")


df <- data.frame(x=rep(LETTERS[1:2],each=50),y=c(y1,y2))

ggplot(df,aes(x=x,y=y))+
  geom_brick()+
  theme_bw()
ggplot(df,aes(x=x,y=y))+
  stat_summary(fun.y="mean",geom="col",alpha=0.8)+
  stat_summary(geom = "errorbar",width=0.5)+
  theme_bw()