Find the critical value of the Mann-Whitney U Test (or the Robust Rank Order) using a Monte Carlo simulation

critical.js

// Luke Mitchell, 2016

"use strict"
var mwu = require('mann-whitney-utest');

const DEFAULT_COUNT = 1000000
const DEFAULT_P = 0.05

function min (us) {
  if (us[0] < us[1])
    return us[0]
  else
    return us[1]
}

function makeSamples (n, m, count = DEFAULT_COUNT) {
  // Samples object
  let samples = []

  // Generate 'count' pairs of samples and perform test
  for (var i = 0; i < count; i++) {
    let sample = [[], []];
    for (var ni = 0; ni < n; ni++)
      sample[0].push(Math.random())
    for (var mi = 0; mi < m; mi++)
      sample[1].push(Math.random())

    // Run the test
    const us = mwu.test(sample)
    samples.push(min(us))
  }

  // Sort the samples
  samples.sort()
  return samples
}

function estimateCriticalValue (n, m, p = DEFAULT_P, count = DEFAULT_COUNT) {
  const samples = makeSamples(n, m, count)
  return samples[p * count]
}

function findP (n, m, U, count = DEFAULT_COUNT) {
  const samples = makeSamples(n, m, count)
  return samples.indexOf(U) / count
}

// What is the critical value for p = 0.2?
console.log(estimateCriticalValue(11, 14, 0.2, 100000))

// What is the p-value for a U-value of 54?
console.log(findP(11, 14, 54, 100000))