Skip to content

Instantly share code, notes, and snippets.

Embed
What would you like to do?
Wilcoxon Signed Rank Test in Javascript
"use strict";
const 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;
}
};
const norm = {
/*
* Error function
*
* The MIT License, Copyright (c) 2013 jStat
*/
erf: function(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,
1.30365583558e-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
*/
cdf: function(x, mean, std) {
return 0.5 * (1 + this.erf((x - mean) / Math.sqrt(2 * std * std)));
},
sf: function(x, mean, std) {
return 1.0 - this.cdf(x, mean, std);
}
};
const getRepeatCounts = arr => {
const sorted_arr = arr.slice().sort();
let results = [];
let count = 0;
for (var i = 0; i < sorted_arr.length - 1; i++) {
const areEqual = sorted_arr[i] === sorted_arr[i + 1];
if (areEqual) {
count += 1;
}
if (!areEqual || i === sorted_arr.length - 1) {
if (count > 0) {
results.push(count);
count = 0;
}
}
}
return results;
};
const wilcoxon = (
x,
y = null,
zero_method = "wilcox",
correction = false,
alternative = "two-sided"
) => {
if (!["wilcox", "pratt", "zsplit"].includes(zero_method)) {
throw "Zero method should be either 'wilcox' or 'pratt' or 'zsplit'";
}
if (!["two-sided", "less", "greater"].includes(alternative)) {
throw "Alternative must be either 'two-sided', 'greater' or 'less'";
}
let d, n_zero;
let warning;
if (!y && x) {
d = x;
} else if (!x || x.length != (y || []).length) {
throw "Samples x and y must be the same length";
} else {
d = x.map((e, i) => e - y[i]);
}
if (["wilcox", "pratt"].includes(zero_method)) {
n_zero = d.filter(e => e === 0).length;
if (n_zero === d.length) {
throw "zero_method 'wilcox' and 'pratt' do not work if the x - y is zero for all elements.";
}
}
if (zero_method === "wilcox") {
d = d.filter(e => e !== 0);
}
const count = d.length;
if (count < 10) {
warning = "Sample size too small for normal approximation.";
}
let r, r_plus, r_minus;
const rankInput = d.map(v => ({ val: v, abs: Math.abs(v) }));
r = rank.fractional(rankInput, "abs");
r_plus = r.map(e => (e.val > 0 ? e.rank : 0)).reduce((a, b) => a + b, 0);
r_minus = r.map(e => (e.val < 0 ? e.rank : 0)).reduce((a, b) => a + b, 0);
if (zero_method === "zsplit") {
r_zero = r.map(e => (e.val === 0 ? e.rank : 0)).reduce((a, b) => a + b, 0);
r_plus += r_zero / 2.0;
r_minus += r_zero / 2.0;
}
// Min for two-sided, otherwise r_plus, from which r_minus and min can be inferred
let T, p, mn, se, z;
if (alternative === "two-sided") {
T = Math.min(r_plus, r_minus);
} else {
T = r_plus;
}
mn = count * (count + 1.0) * 0.25;
se = count * (count + 1.0) * (2.0 * count + 1.0);
if (zero_method === "pratt") {
r = r.filter(e => e.rank !== 0);
mn -= n_zero * (n_zero + 1.0) * 0.25;
se -= n_zero * (n_zero + 1.0) * (2.0 * n_zero + 1.0);
}
const repeatCounts = getRepeatCounts(r.map(e => e.rank));
if (repeatCounts && repeatCounts.length) {
// Correction for repeated elements
se -=
0.5 * repeatCounts.map(v => v * (v * v - 1.0)).reduce((a, b) => a + b, 0);
}
se = Math.sqrt(se / 24);
// Continuity correction
let corr = 0;
if (correction) {
if (alternative === "two-sided") {
corr = 0.5 * Math.sign(T - mn);
} else if (alternative == "less") {
corr = -0.5;
} else {
// if (alternative == 'greater')
corr = 0.5;
}
}
// Compute with normal approx (appropriate for n>=10)
if (alternative === "two-sided") {
const pOneSide = norm.sf(Math.abs(T - corr - mn), 0, se);
p = 2.0 * pOneSide;
} else if (alternative === "greater") {
p = norm.sf(T - corr - mn, 0, se);
} else {
p = norm.cdf(T - corr - mn, 0, se);
}
return { W: T, P: p, Warning: warning };
};
export default wilcoxon;
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
You can’t perform that action at this time.