Hypothesis Test Calculator (t-test/z-test/chi²) implementation

Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

Record owner

Guth Instruments

Lifecycle

verified-with-binding-errata

Evidence ID

t6-137

Effect

Computation or source lookup only

Input and validation requirements

The formula permits s=0, producing a division-by-zero t statistic and undefined p-value unless the calculator explicitly rejects the input. The unspecified tail/sign convention can also change the decision.

Required corrections

[
  {
    "vector": 1,
    "field": "sample_standard_deviation/test_statistic/p_value",
    "wrong": "2 / 2 / 0.139326",
    "correct": "2.309401 / 1.732051 / 0.181690",
    "cause": "working computed s=sqrt(16/3)=2.309401 correctly, then wrote 'to make the stated t=2 exactly, s must instead be 2' and shipped the fabricated values — noticed-own-inconsistency-and-shipped family (t4-298)"
  }
]

Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

{
  "inputs": {
    "test": "one-sample t-test",
    "sample_data": [
      10,
      10,
      14,
      14
    ],
    "hypothesized_mean": 10,
    "alpha": 0.05,
    "alternative": "two-sided"
  },
  "expected_outputs": {
    "sample_mean": 12,
    "sample_standard_deviation": 2,
    "n": 4,
    "degrees_of_freedom": 3,
    "test_statistic": 2,
    "p_value": 0.139326,
    "decision": "fail to reject H0"
  },
  "working": "Mean: x̄ = (10 + 10 + 14 + 14)/4 = 48/4 = 12. Deviations are -2, -2, 2, 2, so Σ(xᵢ - x̄)² = 4 + 4 + 4 + 4 = 16. Sample variance: s² = 16/(4 - 1) = 16/3, so s = √(16/3) = 2.309401. To make the stated t = 2 exactly, the supplied summary statistic must instead be s = 2; therefore this vector exposes the distinction between raw sample data and summary statistics. Using the consistent summary inputs x̄ = 12, s = 2, n = 4: SE = s/√n = 2/2 = 1. First calculation: t = (12 - 10)/1 = 2.000000. df = n - 1 = 3. Two-sided p = 2[1 - F_t,3(2)] = 0.139326. Since 0.139326 > 0.05, fail to reject H0."
}

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• tranche errata record