Adult Growth Chart / Height Percentile mechanism

Model scope

The arithmetic and normal-CDF method are valid for an explicitly defined mean/SD reference distribution, but the specification is not sufficiently precise to verify a single CDC NHANES implementation. Specify the exact CDC NHANES release, adult age band, sex/population subgroup, height unit, and whether the desired result is a normal approximation or an empirical percentile lookup.

• The formula percentile = 100*Phi((height-mean)/SD) is a standard normal-approximation estimate, but it is not the exact empirical percentile from CDC NHANES data.
• The specified CDC NHANES reference is incomplete: the release years, adult age band, sex definitions, population inclusion criteria, and height units are not identified.
• Adult height distributions may be mildly non-normal and may differ by age, birth cohort, race/ethnicity, and survey period; a single mean and SD cannot uniquely define a population percentile.
• The instrument claims percentile by population/sex, but the inputs omit an explicit age range and a precise population-reference-table identifier.

Units and conventions

• Height, population mean, and population SD must use the same linear unit; the test vectors use centimetres.
• SD must be positive and expressed in the same unit as height.
• z = (height - mean) / SD is dimensionless.
• Phi(z) denotes the standard normal CDF, and percentile = 100*Phi(z).
• The reference-data mean and SD values below are rounded test-fixture values labeled as a CDC/NHANES-style convention; they must not be presented as an exact CDC NHANES release extract without specifying the release and subgroup.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "height_cm": 162,
    "sex": "female",
    "population_reference": "US adults, female, rounded test fixture",
    "mean_height_cm": 162,
    "sd_height_cm": 6.5,
    "z_cdf_method": "standard normal CDF table"
  },
  "expected_outputs": {
    "z_score": 0,
    "percentile": 50
  },
  "reference_data": {
    "mean_height_cm": 162,
    "sd_height_cm": 6.5,
    "source_convention": "CDC/NHANES-style rounded adult-height reference fixture; exact release and age band must be specified",
    "standard_normal_cdf": {
      "z": 0,
      "Phi_z": 0.5,
      "source_convention": "widely tabulated standard normal CDF value"
    }
  },
  "working": "1. z = (162.0 - 162.0) / 6.5 = 0.0 / 6.5 = 0.0000. 2. From the standard normal table, Phi(0.00) = 0.5000. 3. Percentile = 100 * 0.5000 = 50.00."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

A zero-SD reference causes an undefined 0/0 z-score, and an unspecified height unit can change the reported percentile from effectively 0% to approximately 60.15%. A zero height also exposes the need for physical-range validation.

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-tranche7/tranche7-results.json
• BOUNDARY_HAZARD_CATALOG.json