engineering.uncertainty.pooled_sd

Three distinct suites: educational examples on the calculator page, this legacy regression count (8/8 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.0.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-23.o2-o3. Calculation version 1.0.1. CVP 1.0.0-proposed. 4/4 golden · 4/4 CVP boundary · 8/8 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 4/4 cross-interface · 6/6 CVP contract. digest 20cd5760d858. O2: s_p = √(Σ ν_i s_i² / Σ ν_i) vs a separate-module identity (≤2 ULP). Not Type A from one sample, not Welch–Satterthwaite ν_eff, and not ISO 21748 u of a mean. ≤2 ULP vs O3 applies only to the published tabulated pooled-standard-deviation vectors (two groups, equal s, sample sizes, an alias, a zero component, and one awkward triple). It is not a whole-domain guarantee and does not cover Type A from one sample, Welch–Satterthwaite ν_eff, or ISO 21748 u of a mean.

• Golden (oracle-backed) 4 / 4
• CVP boundary 4 / 4
• Invalid input 8 / 8
• Property 1 / 1
• Metamorphic 1 / 1
• O3 high-precision 8 / 8
• Cross-interface 4 / 4
• CVP contract 6 / 6
• Interfaces PASS · UI (SSR) / REST / MCP
• Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
• Verified scope s_p = √(Σ ν_i s_i² / Σ ν_i) for k≥2 stated groups, + O3 mpmath tabulated s_p.
• Assurance Engineering
• Deferred Not Type A from one sample, not Welch–Satterthwaite ν_eff, and not ISO 21748 u of a mean.

• release artifacts aligned PASS
• schema output required declared PASS
• schema valid input executes PASS
• engine success output validates schema PASS
• schema rejects incomplete input PASS
• rest success payload validates schema PASS

Fingerprint sha256:81abc6702740f295efb09c81a2e5a644ab62fc54968c770436df060cd19b3660

Input schema sha256:4cbf584cea32d116db72e4e8b97853e345acda42e629d71862a261cce916aeb4 · Output schema sha256:2d51663f8669526f3d5d2ce13d8f750c0828e44a381a35ce56af34cf244e247a · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Tool

pooled-sd

Engine

pooled-sd

Engine build

2026-09-23

Evidence core

2026-09-23T13:16:44.307Z

Rendered

2026-10-23T01:27:11.179Z

Last reviewed

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Assumptions

• Pooled standard deviation: s_p = √(Σ ν_i s_i² / Σ ν_i) from k≥2 stated groups. ν_i > 0 and finite.
• s_i ≥ 0. Both zero is valid (s_p = 0).
• Not Type A from one sample, not Welch–Satterthwaite ν_eff, and not ISO 21748 u of a mean.

Limitations

• Takes stated s_i and ν_i — not a single sample of observations
• k=1 is rejected so this cannot wrap Type A / identity s
• Does not compute Welch–Satterthwaite ν_eff
• Does not compute ISO 21748 u of a mean