| 'use strict'; |
| |
| (function(exports) { |
| |
| var rank = { |
| /* |
| * Standart ranking |
| * |
| * The MIT License, Copyright (c) 2014 Ben Magyar |
| */ |
| standard: function(array, key) { |
| // sort the array |
| array = array.sort(function(a, b) { |
| var x = a[key]; |
| var y = b[key]; |
| return ((x < y) ? -1 : ((x > y) ? 1 : 0)); |
| }); |
| // assign a naive ranking |
| for (var i = 1; i < array.length + 1; i++) { |
| array[i - 1]['rank'] = i; |
| } |
| return array; |
| }, |
| /* |
| * Fractional ranking |
| * |
| * The MIT License, Copyright (c) 2014 Ben Magyar |
| */ |
| fractional: function(array, key) { |
| array = this.standard(array, key); |
| // now apply fractional |
| var pos = 0; |
| while (pos < array.length) { |
| var sum = 0; |
| var i = 0; |
| for (i = 0; array[pos + i + 1] && (array[pos + i][key] === array[pos + i + 1][key]); i++) { |
| sum += array[pos + i]['rank']; |
| } |
| sum += array[pos + i]['rank']; |
| var endPos = pos + i + 1; |
| for (pos; pos < endPos; pos++) { |
| array[pos]['rank'] = sum / (i + 1); |
| } |
| pos = endPos; |
| } |
| return array; |
| }, |
| rank: function(x, y) { |
| var nx = x.length, |
| ny = y.length, |
| combined = [], |
| ranked; |
| while (nx--) { |
| combined.push({ |
| set: 'x', |
| val: x[nx] |
| }); |
| } |
| while (ny--) { |
| combined.push({ |
| set: 'y', |
| val: y[ny] |
| }); |
| } |
| ranked = this.fractional(combined, 'val'); |
| return ranked |
| } |
| }; |
| |
| /* |
| * Error function |
| * |
| * The MIT License, Copyright (c) 2013 jStat |
| */ |
| var erf = function erf(x) { |
| var cof = [-1.3026537197817094, 6.4196979235649026e-1, 1.9476473204185836e-2, -9.561514786808631e-3, -9.46595344482036e-4, 3.66839497852761e-4, |
| 4.2523324806907e-5, -2.0278578112534e-5, -1.624290004647e-6, |
| 1.303655835580e-6, 1.5626441722e-8, -8.5238095915e-8, |
| 6.529054439e-9, 5.059343495e-9, -9.91364156e-10, -2.27365122e-10, 9.6467911e-11, 2.394038e-12, -6.886027e-12, 8.94487e-13, 3.13092e-13, -1.12708e-13, 3.81e-16, 7.106e-15, -1.523e-15, -9.4e-17, 1.21e-16, -2.8e-17 |
| ]; |
| var j = cof.length - 1; |
| var isneg = false; |
| var d = 0; |
| var dd = 0; |
| var t, ty, tmp, res; |
| |
| if (x < 0) { |
| x = -x; |
| isneg = true; |
| } |
| |
| t = 2 / (2 + x); |
| ty = 4 * t - 2; |
| |
| for (; j > 0; j--) { |
| tmp = d; |
| d = ty * d - dd + cof[j]; |
| dd = tmp; |
| } |
| |
| res = t * Math.exp(-x * x + 0.5 * (cof[0] + ty * d) - dd); |
| return isneg ? res - 1 : 1 - res; |
| }; |
| |
| /* |
| * Normal distribution CDF |
| * |
| * The MIT License, Copyright (c) 2013 jStat |
| */ |
| var dnorm = function(x, mean, std) { |
| return 0.5 * (1 + erf((x - mean) / Math.sqrt(2 * std * std))); |
| } |
| |
| var statistic = function(x, y) { |
| var ranked = rank.rank(x, y), |
| nr = ranked.length, |
| nx = x.length, |
| ny = y.length, |
| ranksums = { |
| x: 0, |
| y: 0 |
| }, |
| i = 0, t = 0, nt = 1, tcf, ux, uy; |
| |
| while (i < nr) { |
| if (i > 0) { |
| if (ranked[i].val == ranked[i-1].val) { |
| nt++; |
| } else { |
| if (nt > 1) { |
| t += Math.pow(nt, 3) - nt |
| nt = 1; |
| } |
| } |
| } |
| ranksums[ranked[i].set] += ranked[i].rank |
| i++; |
| } |
| tcf = 1 - (t / (Math.pow(nr, 3) - nr)) |
| ux = nx*ny + (nx*(nx+1)/2) - ranksums.x; |
| uy = nx*ny - ux; |
| |
| return { |
| tcf: tcf, |
| ux: ux, |
| uy: uy, |
| big: Math.max(ux, uy), |
| small: Math.min(ux, uy) |
| } |
| } |
| |
| exports.test = function(x, y, alt, corr) { |
| // set default value for alternative |
| alt = typeof alt !== 'undefined' ? alt : 'two-sided'; |
| // set default value for continuity |
| corr = typeof corr !== 'undefined' ? corr : true; |
| var nx = x.length, // x's size |
| ny = y.length, // y's size |
| f = 1, |
| u, mu, std, z, p; |
| |
| // test statistic |
| u = statistic(x, y); |
| |
| // mean compute and correct if given |
| if (corr) { |
| mu = (nx * ny / 2) + 0.5; |
| } else { |
| mu = nx * ny / 2; |
| } |
| |
| // compute standard deviation using tie correction factor |
| std = Math.sqrt(u.tcf * nx * ny * (nx + ny + 1) / 12); |
| |
| // compute z according to given alternative |
| if (alt == 'less') { |
| z = (u.ux - mu) / std; |
| } else if (alt == 'greater') { |
| z = (u.uy - mu) / std; |
| } else if (alt == 'two-sided') { |
| z = Math.abs((u.big - mu) / std); |
| } else { |
| console.log('Unknown alternative argument'); |
| } |
| |
| // factor to correct two sided p-value |
| if (alt == 'two-sided') { |
| f = 2; |
| } |
| |
| // compute p-value using CDF of standard normal |
| p = dnorm(-z, 0, 1) * f; |
| |
| return {U: u.small, p: p}; |
| } |
| |
| })(typeof exports === 'undefined' ? this['mannwhitneyu'] = {} : exports); |