Assumptions and method
Normal approximation only; it does not correct selection bias, clustering or nonresponse. Zero population selects the large-population formula.
Test a scenario
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
- Use p = 0.5 and margin = 0.05.
- 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.