By Dr Arash Ardalan · · 4 min read
Key idea
Start with the population and the decision the survey will support. A sample-size calculation measures sampling precision; it cannot correct a biased sample.
Define what you need to estimate
Write down the population, the percentage you want to estimate, and the smallest difference that would matter to your decision. For example, you might want the proportion of customers who would use a new service, to within five percentage points.
The calculation below is an approximate planning method for one population proportion under simple random sampling. Estimating a mean, comparing groups, or testing an intervention needs a calculation matched to that question.
Calculate completed responses
For a large population, use a confidence level, an expected proportion p and a margin of error e expressed as a decimal. At 95% confidence, z is approximately 1.96. Use p = 0.50 when you do not have a defensible prior estimate; it gives the largest sample for this formula.
n₀ = z² × p × (1 − p) / e²
- At 95% confidence and ±5 percentage points: 1.96² × 0.50 × 0.50 / 0.05² = 384.16. Round up to 385 completed responses.
- At the same confidence level and ±3 percentage points, the calculation gives 1,067.11: round up to 1,068 responses.
- If you need separate estimates for regions or customer groups, plan the sample within each group. A large total does not guarantee useful precision for a small subgroup.
Allow for the actual survey design
A finite population correction may reduce the requirement when sampling without replacement from a known, limited population. Weighting and clustering can reduce precision, so a realistic design effect may increase the sample. These adjustments need to reflect how respondents will actually be selected.
A conventional probability-sampling margin of error does not, by itself, establish the precision or representativeness of an opt-in online poll. Coverage, recruitment and non-response all matter.
Convert responses into invitations
If you need 385 completed responses and expect 40% of those invited to respond, plan approximately 385 / 0.40 = 962.5, or 963 invitations. This is a planning estimate: response rates vary, and inviting more people does not automatically remove non-response bias.
- Check that the population is large enough to support the required invitations.
- Pilot the questionnaire and recruitment method before committing the full fieldwork budget.
- Report the achieved sample, recruitment method, fieldwork dates and any weighting with the results.
Further reading
- ECDC: sample-size guidance, including estimation of a population proportion (opens in a new tab)
- Penn State: confidence intervals for population proportions (opens in a new tab)
This guide provides general information. A study plan or business recommendation should reflect your own data, design and circumstances.
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