Plan sample precision without promising representativeness or power

Specify the estimate and precision target

A planned descriptive question might concern the proportion of eligible worksheet users who complete one defined task under a specified process. Name the unit, outcome, period and population/frame. Five tasks from one person are not automatically five independent people, and native feed posts do not become independent reader outcomes merely because they are separate rows.

Distinguish an absolute half-width, such as five percentage points, from a five-percent relative change or the probability of detecting a difference between conditions. This article concerns an approximate single-proportion planning model. A two-condition power calculation, clustered design or sequential analysis needs its own appropriate method.

Use a declared approximation and scrutinize its assumptions

NIST’s sample-size guidance connects a declared estimate and precision to a probability model and practical constraints. For this teaching model, use n approximately equal to z squared times p times (1 minus p), divided by delta squared. We explicitly choose z=1.96 for nominal two-sided 95% normal coverage and round the computed n upward; this is not an exact binomial guarantee.

When a plausible planning proportion is unavailable, p=0.5 gives the largest p(1−p) within this formula. A guessed p near zero cannot be used to announce that almost no data are needed. Approximation quality, random/design conditions, finite-population corrections, clustering and nonresponse are not validated by typing values into an equation.

Reproduce the original planning exercise

With the constructed p=0.5 and delta=0.05, 1.96 squared ×0.25/0.05 squared is 384.16, giving 385 completed units after rounding up. For delta=0.10, the same inputs give 96.04 and therefore 97 units. Halving the half-width multiplies the unrounded requirement by four under this model.

These figures are invented planning exercises, not sample requirements for every creator question or a replacement for a study’s own registered design. NIST’s own page uses a rounded z of about two in its examples; our values use the explicitly stated 1.96. Keep that distinction instead of claiming both calculations should produce identical counts.

Resolve three feasibility decisions

P1 — Constructed limited pool: only 15 eligible completed independent units would be available. Under the same normal planning assumptions, 1.96×sqrt(0.25/15) is about 0.253, or 25.3 percentage points. Decision: report that conditional scale and reconsider the question or precision honestly. Outcome: no invented 385 participants or guaranteed narrow estimate.

P2 — Constructed outcome loss: the planning target is 385 completed units and the assumed usable-outcome yield is 80%. The arithmetic budget is ceil(385/0.8)=482 candidate units. Decision: preserve that yield as an unverified forecast and inspect missingness/design. Outcome: not 482 invitations sent, promised completions or permission to count missing results as failures.

P3 — Constructed self-selection: 385 voluntary replies arrive from an open post. Decision: retain the actual nonprobability mechanism and limit precision claims to an appropriately justified model. Outcome: matching the teaching count does not establish population coverage, balanced representation or the validity of a conventional survey margin of error.

Keep planning, observed analysis and power separate

Before any authorized collection, keep the design, stopping plan, outcome definitions, exclusions and treatment of missingness with the calculation. Afterward, analyze the actual eligible outcomes under an appropriate method; do not report the planned n or half-width as the interval that was achieved.

Do not claim “95% power,” “95% probability the true value is here” or a causal advantage from the displayed planning count. AAPOR requires nonprobability precision claims to disclose the model and assumptions. A useful outcome can be a decision to improve a descriptive explanation rather than launch an infeasible statistical claim.

Keep a model-and-feasibility record

The private record retains estimate/unit/population, sampling/dependence assumptions, p/z/delta, unrounded and rounded requirement, expected missingness, available capacity and allowed conclusion. The offline checker reproduces the declared arithmetic; it does not validate the real design, consent or recruitment.

NIST’s relevant formula and AAPOR’s precision/disclosure guidance were read on 1 November 2026. No reader data, sample, survey, message or actual effect was collected. These teaching examples supply neither observed task completion nor explicit preference, and do not replace an actual study’s registered outcomes.