dist_test (R part)

library(Rcpp)
sourceCpp("dist_test.cpp")

sigLvl <- 0.03
# case 1
X <- rnorm(40, 4, 10)
Y <- rnorm(20, 4, 10)

st <- proc.time()
testStat <- dist_test(X, Y, c(0.1, 0.25, 0.5, 0.75, 0.9), 10000)
proc.time() - st

if (any(abs(testStat) > qnorm(1-sigLvl))) {
  message("Two datasets are different.")
} else {
  message("Two datasets are the same.")
}

# case 2
X <- rnorm(40, 4, 7)
Y <- rnorm(20, 4, 7)

st <- proc.time()
testStat <- dist_test(X, Y, c(0.1, 0.25, 0.5, 0.75, 0.9), 10000)
proc.time() - st

if (any(abs(testStat) > qnorm(1-sigLvl))) {
  message("Two datasets are different.")
} else {
  message("Two datasets are the same.")
}

## general test

mean(sapply(1:1e4, function(i){
  X <- rnorm(40, 4, 7)
  Y <- rnorm(20, 4, 10)
  any(abs(dist_test(X, Y, c(0.1, 0.25, 0.5, 0.75, 0.9), 10000)) > qnorm(1-0.01))
}))
# 0.1706

mean(sapply(1:1e4, function(i){
  X <- rnorm(40, 4, 7)
  Y <- rnorm(20, 4, 14)
  any(abs(dist_test(X, Y, c(0.1, 0.25, 0.5, 0.75, 0.9), 10000)) > qnorm(1-0.01))
}))
# 0.4274

mean(sapply(1:1e4, function(i){
  X <- rnorm(40, 4, 7)
  Y <- rnorm(20, 8, 7)
  any(abs(dist_test(X, Y, c(0.1, 0.25, 0.5, 0.75, 0.9), 10000)) > qnorm(1-0.01))
}))
# 0.5243

mean(sapply(1:1e4, function(i){
  X <- rnorm(40, 4, 10)
  Y <- rnorm(20, 4, 10)
  any(abs(dist_test(X, Y, c(0.1, 0.25, 0.5, 0.75, 0.9), 10000)) > qnorm(1-0.01))
}))
# 0.1027

## general test 2

mean(sapply(1:1e4, function(i){
  X <- rnorm(40, 4, 7)
  Y <- rnorm(20, 4, 10)
  sum(abs(dist_test(X, Y, c(0.1, 0.25, 0.5, 0.75, 0.9), 10000)) > qnorm(1-0.01)) >= 2
}))
# 0.041

mean(sapply(1:1e4, function(i){
  X <- rnorm(40, 4, 7)
  Y <- rnorm(20, 4, 14)
  sum(abs(dist_test(X, Y, c(0.1, 0.25, 0.5, 0.75, 0.9), 10000)) > qnorm(1-0.01)) >= 2
}))
# 0.139

mean(sapply(1:1e4, function(i){
  X <- rnorm(40, 4, 7)
  Y <- rnorm(20, 8, 7)
  sum(abs(dist_test(X, Y, c(0.1, 0.25, 0.5, 0.75, 0.9), 10000)) > qnorm(1-0.01)) >= 2
}))
# 0.291

mean(sapply(1:1e4, function(i){
  X <- rnorm(40, 4, 10)
  Y <- rnorm(20, 4, 10)
  sum(abs(dist_test(X, Y, c(0.1, 0.25, 0.5, 0.75, 0.9), 10000)) > qnorm(1-0.01)) >= 2
}))
# 0.0193

## general test 3

mean(sapply(1:1e4, function(i){
  X <- rnorm(40, 4, 7)
  Y <- rnorm(20, 4, 10)
  absStat <- abs(dist_test(X, Y, c(0.1, 0.25, 0.5, 0.75, 0.9), 10000))
  sum(absStat > qnorm(1-0.01)) >= 1 && sum(absStat > qnorm(1-0.03)) >= 2
}))
# 0.092

mean(sapply(1:1e4, function(i){
  X <- rnorm(40, 4, 7)
  Y <- rnorm(20, 4, 14)
  absStat <- abs(dist_test(X, Y, c(0.1, 0.25, 0.5, 0.75, 0.9), 10000))
  sum(absStat > qnorm(1-0.01)) >= 1 && sum(absStat > qnorm(1-0.03)) >= 2
}))
# 0.2643

mean(sapply(1:1e4, function(i){
  X <- rnorm(40, 4, 7)
  Y <- rnorm(20, 8, 7)
  absStat <- abs(dist_test(X, Y, c(0.1, 0.25, 0.5, 0.75, 0.9), 10000))
  sum(absStat > qnorm(1-0.01)) >= 1 && sum(absStat > qnorm(1-0.03)) >= 2
}))
# 0.432

mean(sapply(1:1e4, function(i){
  X <- rnorm(40, 4, 10)
  Y <- rnorm(20, 4, 10)
  absStat <- abs(dist_test(X, Y, c(0.1, 0.25, 0.5, 0.75, 0.9), 10000))
  sum(absStat > qnorm(1-0.01)) >= 1 && sum(absStat > qnorm(1-0.03)) >= 2
}))
# 0.046