als-statistics/lib/analyze/correlate/spearman.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 CDF from '../cdf/index.js';
import { TestBase } from '../test-base/index.js';

function rankAverage(arr) { /** Compute average ranks with tie handling. Returns { ranks, tieGroups } */
   const n = arr.length;
   const idx = Array.from({ length: n }, (_, i) => i).filter(i => Number.isFinite(arr[i]));
   const pairs = idx.map(i => [arr[i], i]).sort((a, b) => (a[0] - b[0]));
   const ranks = new Array(n).fill(NaN);
   const tieGroups = []; // sizes of tied groups
   let i = 0; let r = 1;
   while (i < pairs.length) {
      let j = i + 1;
      while (j < pairs.length && pairs[j][0] === pairs[i][0]) j++;
      const size = j - i;
      const avgRank = (r + (r + size - 1)) / 2;
      for (let k = i; k < j; k++) { ranks[pairs[k][1]] = avgRank; }
      if (size > 1) tieGroups.push(size);
      r += size; i = j;
   }
   return { ranks, tieGroups };
}

export class Spearman extends TestBase {  /** Spearman rank correlation (двухвыборочный) */
   constructor(samples) {
      super(samples, 'Spearman', ['r', 't', 'df', 'p'], { sameSize: false, minK: 2 });
      this.#calc()
   }

   #calc() {
      const s1 = this.samples[0], s2 = this.samples[1];
      const n = Math.min(s1.n, s2.n);
      if (s1.n !== n) s1.values = s1.values.slice(0, n);
      if (s2.n !== n) s2.values = s2.values.slice(0, n);
      this.n = n;

      const x = s1.values, y = s2.values;
      const rx = rankAverage(x).ranks, ry = rankAverage(y).ranks;
      const mx = rx.reduce((a, b) => a + b, 0) / n, my = ry.reduce((a, b) => a + b, 0) / n; // 4) Пирсон по рангам

      let num = 0, sx = 0, sy = 0;
      for (let i = 0; i < n; i++) {
         const dx = rx[i] - mx, dy = ry[i] - my;
         num += dx * dy;
         sx += dx * dx;
         sy += dy * dy;
      }
      if (sx === 0 || sy === 0) this.#zeroXY(); // Если дисперсия в одном из рангов нулевая (все значения одинаковые)
      else this.#calcpr(sx,sy,num)
   }

   #zeroXY() { this.r = 0; this.df = this.n - 2; this.t = 0; this.p = 1; }

   #calcpr(sx,sy,num) {
      this.r = num / Math.sqrt(sx * sy);
      this.df = this.n - 2;

      if (Math.abs(this.r) >= 1) {
         this.t = this.r > 0 ? Infinity : -Infinity;
         this.p = 0;
      } else {
         this.t = this.r * Math.sqrt(this.df / (1 - this.r * this.r));
         this.p = 2 * (1 - CDF.t(Math.abs(this.t), this.df));
      }
   }
}