Assumptions and method

When to be cautious

Normal approximation only; it does not correct selection bias, clustering or nonresponse. Zero population selects the large-population formula.

n₀ = z²p(1−p)/e²; n = n₀/[1+(n₀−1)/N]

Test a scenario

Use your own inputs

Inputs stay in your browser. Shared scenario links include your inputs.

Use the result in a decision

Understand the sampling design, units and distribution assumptions.

Normal approximation only; it does not correct selection bias, clustering or nonresponse. Zero population selects the large-population formula.

Set a baseline and change one assumption to compare outcomes.

A worked example

Follow the fixed teaching example
  1. Use p = 0.5 and margin = 0.05.
  2. n₀ = 1.96² × 0.5 × 0.5 / 0.05² = 384.16; round up to 385 completed responses. Population 0 means no finite-population correction.

These illustrative inputs describe a project scenario, not a published benchmark. All monetary inputs use the same currency and price basis.

Expected proportion (%)
50
Margin in percentage points
5
Normal critical value (1.96 for approximate 95%)
1.96
Finite population (0 for large population)
0
Completed responses required
385 responses

Interpret the output only within the assumptions above. Changing the inputs changes the result; it does not validate the inputs.

Source & credit

Standard mathematical statistics; the handbook is an authoritative technical reference, not a claim of sole origin.

NIST/SEMATECH: statistical methods

This is independently written code and explanation of the underlying method. The linked publication, its diagrams and its trademarks remain its owner’s material; no permission to reuse them is implied.

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