Source: https://guthlabs.ai/docs/instruments/chi-square-goodness-of-fit-genetics/

instrument / verified-clean

# Chi-Square Goodness-of-Fit (Genetics)

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/chi-square-goodness-of-fit-genetics/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/chi-square-goodness-of-fit-genetics/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/chi-square-goodness-of-fit-genetics/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/chi-square-goodness-of-fit-genetics/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Biology, Medicine & Pharmacology (educational estimates only — every panel labeled not-medical-advice)

**Tranche**: tranche-6

**Evidence ID**: t6-079

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The core method is standard, but the specification is incomplete because α, degrees-of-freedom derivation, upper-tail p-value convention, ratio normalization, and minimum expected-count handling are not explicitly defined. Add these rules before implementation.

### Formula and scope findings

- The core statistic χ²=Σ(O−E)²/E is standard for a goodness-of-fit test, but the specification does not define the significance level α required for a reject/fail-to-reject decision.

- Degrees of freedom are not generally an arbitrary input: with k categories and no estimated parameters, df=k−1; parameters estimated from the data require further subtraction from the degrees of freedom.

- The p-value must be explicitly defined as the upper-tail probability P(Χ²_df≥χ²), not a lower-tail CDF.

- Expected counts must be computed by normalizing the supplied expected ratio to the observed total. The specification does not state this normalization step.

- The test requires strictly positive expected counts. Categories with expected count zero make the statistic undefined and must be rejected or handled explicitly.

- The specification does not state assumptions such as independent observations and sufficiently large expected counts; common rules of thumb require expected counts approximately at least 5, or an explicitly documented alternative.

### Unit assumptions

- Observed values are nonnegative integer counts and are dimensionless.

- Expected ratios are nonnegative relative proportions; they are normalized so expected counts sum to the observed total.

- The observed categories are mutually exclusive and collectively exhaustive.

- The significance level α is dimensionless and must be supplied; the vectors below use α=0.05.

- The p-value is the upper-tail probability from the chi-square distribution with the stated degrees of freedom.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

An expected ratio containing a zero produces an expected count E = 0 and a 0/0 χ² term when the corresponding observed count is also zero. The instrument must reject this input or explicitly define handling; otherwise the statistic and p-value are undefined.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "observed_counts": [
      75,
      25
    ],
    "expected_ratio": [
      3,
      1
    ],
    "df": 1,
    "alpha": 0.05
  },
  "expected_outputs": {
    "expected_counts": [
      75,
      25
    ],
    "chi_square": 0,
    "p_value": 1,
    "critical_value_at_alpha": 3.841459,
    "decision": "fail to reject"
  },
  "working": "Observed total = 75+25 = 100. Ratio total = 3+1 = 4. Expected counts = 100×[3/4,1/4] = [75,25]. χ² = (75−75)²/75 + (25−25)²/25 = 0/75 + 0/25 = 0. For df=1, p=P(Χ²₁≥0)=1. Since 0 < 3.841459, fail to reject at α=0.05."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

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

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`