Source: https://guthlabs.ai/docs/instruments/sample-size-power-calculator-clinical-study-education/mechanism/

instrument mechanism / verified-clean

# Sample Size / Power Calculator (clinical study education) mechanism

The inspectable method record for Sample Size / Power Calculator (clinical study education), kept separate from implementation and qualification.

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

## Model scope

The means formula is mathematically correct under its stated simplified assumptions, but the instrument specification is incomplete because the proportions variant, rounding behavior, input meaning of variance versus standard deviation, and exact hypothesis-test convention are not defined. The existing educational/not-medical-advice label is appropriate, but the panel should also state that this is not a substitute for a prespecified statistical analysis or professional sample-size review.

- The means formula is standard only for a two-sided, two-arm comparison of means with equal allocation, equal known variances, and normal-approximation assumptions; these constraints should be explicit.

- The specification says there is a proportions variant but provides no formula. A proportion sample-size calculation requires baseline proportion(s), effect definition, one- versus two-sided testing, allocation, and whether continuity correction is used.

- The specification does not state that the raw result must be rounded up to the next whole participant; the test vectors assume n=ceil(raw n).

- The symbol σ must mean standard deviation, not variance. If the input is variance, the formula must use that variance directly as σ².

- The notation z_α/2 is ambiguous; it should explicitly mean the upper standard-normal quantile z_(1−α/2), and z_β should mean z_(power)=z_(1−β).

## Units and conventions

- σ and Δ must use the same units; their ratio is unitless, so converting both from kilograms to grams leaves n unchanged.

- σ is a positive standard deviation and Δ is a nonzero absolute difference in means.

- α is a two-sided type-I error probability, 0<α<1; power is 1−β with 0<power<1.

- The z-values use the standard normal distribution: z_(1−α/2) for a two-sided test and z_(power) for β=1−power.

- The output is participants per group for equal allocation, before any dropout or attrition inflation.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "design": "two-arm means, equal allocation",
    "sigma": 10,
    "sigma_units": "units",
    "delta": 5,
    "delta_units": "units",
    "alpha": 0.05,
    "power": 0.8,
    "z_(1-alpha/2)": 1.96,
    "z_power": 0.841621
  },
  "expected_outputs": {
    "raw_n_per_group": 62.792642,
    "required_n_per_group": 63
  },
  "working": "β=1−0.80=0.20. z-sum=1.96+0.841621=2.801621. Square: 2.801621²=7.849080. Variance factor: 2σ²/Δ²=2×10²/5²=200/25=8. Raw n=8×7.849080=62.792642. Round up: ceil(62.792642)=63 per group."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The edge vectors expose undefined or invalid outputs unless the calculator validates zero effect size and zero variance. The branch and convention probes also produce materially different sample sizes when outcome type or alpha sidedness is interpreted differently.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/sample-size-power-calculator-clinical-study-education/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/sample-size-power-calculator-clinical-study-education/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/sample-size-power-calculator-clinical-study-education/qualification/>)

## 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`

- `BOUNDARY_HAZARD_CATALOG.json`