als-statistics/tests/analyze/correlate/kendall.test.js

Modular JS statistics toolkit for Node.js and the browser: descriptive stats, correlations (Pearson/Spearman/Kendall), t-tests & ANOVA (Student/Welch), reliability (Cronbach’s alpha), regression (linear/logistic), clustering (DBSCAN/HDBSCAN), and table/co

import { describe, it } from 'node:test';
import assert from 'node:assert';
import { Kendall } from '../../../lib/analyze/correlate/kendall.js';

function approx(a,b,eps=1e-10){
  assert.ok(Math.abs(a-b)<=eps*(1+Math.max(Math.abs(a),Math.abs(b))),`~${b}, got ${a}`);
}

describe('Kendall tau-b', () => {
  it('perfect concordance -> tau=1, p≈0.0833 for n=4', () => {
    const k = new Kendall({ X:[1,2,3,4], Y:[1,2,3,4] });
    approx(k.tau, 1, 1e-12);
    // допускаем асимптотическое отклонение: 0.05..0.10
    assert.ok(k.p > 0.05 && k.p < 0.10, `p=${k.p}`);
    // если хотите точнее:
    approx(k.p, 1/12, 0.02); // ±0.02 вокруг 0.08333
  });

  it('perfect discordance -> tau=-1, p≈0.0833 for n=4', () => {
    const k = new Kendall({ X:[1,2,3,4], Y:[4,3,2,1] });
    approx(k.tau, -1, 1e-12);
    assert.ok(k.p > 0.05 && k.p < 0.10, `p=${k.p}`);
  });

  it('ties on X and Y: tau=0.5 (двойные тай-пары исключаются)', () => {
    const k = new Kendall({ X:[1,1,2,3,3], Y:[5,5,4,7,7] });
    approx(k.tau, 0.5, 1e-12);
  });

  it('different lengths -> trimmed to min length', () => {
    const k = new Kendall({ X:[1,2,3,4], Y:[1,2,3] });
    // ОЖИДАЕМ 3, после правки конструктора (см. ниже)
    assert.strictEqual(k.n, 3);
  });
});