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Mann Whitney U test Javascript implementation
'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);
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