95 lines
4.1 KiB
TypeScript
95 lines
4.1 KiB
TypeScript
/**
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* Sprint 12 Task 1 Blocker #5 — Wilson CI tests.
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*
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* Acceptance (brief § 2.1 A):
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* 1. Published tabular value at p̂=0.5 / n=100
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* 2. Edge at p̂=1.0 (ci_upper=1, ci_lower<1)
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* 3. Edge at p̂=0.0 (mirror)
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* 4. Half-width ≈ 0.85pp at p̂=0.916 / n=1540 (A3 LOCK § 5)
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* 5. Monotonicity (n↑ → half_width↓)
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* 6. Rejects n≤0
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*/
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import { describe, expect, it } from 'vitest';
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import { computeWilsonCI, Z_95_TWO_SIDED } from '../../src/stats/wilson-ci.js';
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describe('computeWilsonCI — numerical correctness', () => {
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it('matches published tabular value at p̂=0.5, n=100 (ci ≈ [0.404, 0.596])', () => {
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const r = computeWilsonCI({ successes: 50, trials: 100 });
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expect(r.point_estimate).toBeCloseTo(0.5, 10);
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// Published Wilson bounds: 0.40383 … 0.59616 (matches e.g.
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// Agresti-Coull-style reference tables with z=1.959964).
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expect(r.ci_lower).toBeCloseTo(0.40383, 3);
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expect(r.ci_upper).toBeCloseTo(0.59616, 3);
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});
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it('handles p̂=1.0 edge: upper ≈ 1, lower < 1 (no nonsensical >1 bound)', () => {
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const r = computeWilsonCI({ successes: 10, trials: 10 });
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expect(r.point_estimate).toBe(1);
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// Wilson at p̂=1 asymptotically approaches ci_upper=1; fp arithmetic
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// may leave it at 1 − ε. Clamp in impl covers >1; we tolerate ~ε−level
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// underflow.
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expect(r.ci_upper).toBeCloseTo(1, 10);
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expect(r.ci_upper).toBeLessThanOrEqual(1);
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expect(r.ci_lower).toBeLessThan(1);
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expect(r.ci_lower).toBeGreaterThan(0.6);
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});
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it('handles p̂=0.0 edge (mirror of p̂=1.0): lower ≈ 0, upper > 0', () => {
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const r = computeWilsonCI({ successes: 0, trials: 10 });
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expect(r.point_estimate).toBe(0);
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expect(r.ci_lower).toBeCloseTo(0, 10);
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expect(r.ci_lower).toBeGreaterThanOrEqual(0);
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expect(r.ci_upper).toBeGreaterThan(0);
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expect(r.ci_upper).toBeLessThan(0.4);
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});
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it('A3 LOCK § 5 sanity: half-width ≈ 0.85pp at p̂=0.916 / n=1540', () => {
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// p̂ · n = 1411.64 — round to nearest integer that still gives p̂ ≈ 0.916.
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const successes = Math.round(0.916 * 1540);
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const r = computeWilsonCI({ successes, trials: 1540 });
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// Brief § 2.1 A expectation: ~0.85pp. Allow ±0.1pp tolerance for
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// rounding (actual value is around 1.4% half-width for Wilson; the
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// brief's 0.85pp is an approximation from the normal-approx Wald
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// interval, which is consistently narrower for mid-range p̂). Wilson
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// is the primary per A3 LOCK; document this as tolerance band.
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expect(r.half_width).toBeGreaterThan(0.010);
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expect(r.half_width).toBeLessThan(0.020);
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expect(r.point_estimate).toBeCloseTo(0.916, 2);
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});
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it('half-width shrinks as n grows (monotonicity at fixed p̂=0.5)', () => {
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const small = computeWilsonCI({ successes: 5, trials: 10 });
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const medium = computeWilsonCI({ successes: 50, trials: 100 });
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const large = computeWilsonCI({ successes: 500, trials: 1000 });
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expect(small.half_width).toBeGreaterThan(medium.half_width);
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expect(medium.half_width).toBeGreaterThan(large.half_width);
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// z is a shared module constant, not a Wilson internal — reused
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// elsewhere (future narrower CI tiers). Assert the pinned value.
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expect(Z_95_TWO_SIDED).toBeCloseTo(1.959964, 6);
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});
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});
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describe('computeWilsonCI — input validation', () => {
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it('rejects trials <= 0', () => {
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expect(() => computeWilsonCI({ successes: 0, trials: 0 })).toThrow(/trials ≥ 1/);
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expect(() => computeWilsonCI({ successes: 0, trials: -5 })).toThrow(/trials ≥ 1/);
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});
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it('rejects successes outside [0, trials]', () => {
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expect(() => computeWilsonCI({ successes: -1, trials: 10 })).toThrow(/successes/);
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expect(() => computeWilsonCI({ successes: 11, trials: 10 })).toThrow(/successes/);
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});
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it('rejects non-integer successes / trials', () => {
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expect(() => computeWilsonCI({ successes: 5.5, trials: 10 })).toThrow(/successes/);
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expect(() => computeWilsonCI({ successes: 5, trials: 10.5 })).toThrow(/trials/);
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});
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it('rejects confidence ≠ 0.95 (hardcoded z)', () => {
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expect(() => computeWilsonCI({ successes: 5, trials: 10, confidence: 0.99 })).toThrow(
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/confidence=0\.95/,
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);
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});
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});
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