src/science/stats.ts

Functions

Imports

It imports no other module of this repo. Imported by src/science/index.ts, src/science/titer.ts.

Source

1/** Small statistics used by the scientific charts. Pure, and tested against published values. */
2
3/** Two-sided 95% Student's t critical values for 1 to 30 degrees of freedom. */
4const T_975 = [
5  12.706, 4.303, 3.182, 2.776, 2.571, 2.447, 2.365, 2.306, 2.262, 2.228, 2.201, 2.179, 2.16, 2.145,
6  2.131, 2.12, 2.11, 2.101, 2.093, 2.086, 2.08, 2.074, 2.069, 2.064, 2.06, 2.056, 2.052, 2.048,
7  2.045, 2.042,
8];
9
10/**
11 * The 97.5th percentile of Student's t distribution, for a two-sided 95% interval. Exact to three
12 * decimals up to 30 degrees of freedom, then the normal value 1.96 with a first-order correction.
13 */
14export function tCritical95(df: number): number {
15  if (!Number.isInteger(df) || df < 1)
16    throw new Error(`degrees of freedom must be a positive integer, is ${df}`);
17  const exact = T_975[df - 1];
18  if (exact !== undefined) return exact;
19  return 1.96 + 2.4 / df;
20}
21
22/** A geometric mean with its 95% confidence interval, computed on the log scale. */
23export interface GeometricSummary {
24  readonly n: number;
25  readonly mean: number;
26  /** Undefined when n is 1: one value has no interval. */
27  readonly lower?: number;
28  readonly upper?: number;
29}
30
31/**
32 * The geometric mean of positive values, and its 95% confidence interval from Student's t on the
33 * log-transformed values: the standard summary for antibody titers.
34 */
35export function geometricSummary(values: readonly number[]): GeometricSummary {
36  if (values.length === 0) throw new Error("geometric summary of no values");
37  for (const v of values) {
38    if (!(v > 0) || !Number.isFinite(v))
39      throw new Error(`geometric summary needs positive values, got ${v}`);
40  }
41  const logs = values.map(Math.log);
42  const n = logs.length;
43  const mean = logs.reduce((a, b) => a + b, 0) / n;
44  if (n === 1) return { n, mean: Math.exp(mean) };
45  const variance = logs.reduce((a, b) => a + (b - mean) ** 2, 0) / (n - 1);
46  const half = (tCritical95(n - 1) * Math.sqrt(variance)) / Math.sqrt(n);
47  return { n, mean: Math.exp(mean), lower: Math.exp(mean - half), upper: Math.exp(mean + half) };
48}