What it fits
Estimating one prevalence or proportion in a cross-sectional study using a defined probability-sampling frame.
PROTOCOL PLANNING TOOL · RMA-SSP 1.1 · NO SIGN-UP
Survey sample size
planner.
Build a transparent sampling record for one prevalence or population proportion. Separate complete responses from recruitment, document the design, and export the assumptions for review.
PLANNING ESTIMATE READYSingle-proportion prevalence frameworkInputs update the result immediately; no personal or study data is stored.
participants to approach using simple random sampling, after finite-population and non-response adjustments.
MINIMUM COMPLETE RESPONSES385Recruitment target and analyzable responses are reported separately.
- Cochran base
- 385
- After design adjustment
- 385
- Complete responses required
- 385
- Final recruitment target
- 427
The 50% expected proportion is conservative. Replace it with a credible prior estimate when one exists.
METHODS-READY WORDINGTransparent and editable—not a substitute for protocol review.
For a cross-sectional survey estimating one population proportion, a 95% confidence level, ±5 percentage-point precision and an expected proportion of 50% produced a Cochran base sample of 385. A design effect of 1 was used. No finite-population correction was applied because the population was treated as large or unknown. A minimum of 385 complete responses is required. Allowing 10% non-response, 427 people should be approached.
METHOD
One question. Four sampling paths.
n₀ = z² × p(1 − p) ÷ e²Every path starts with Cochran's large-population formula. Simple and systematic designs use a design effect of 1. Stratified sampling applies proportional or Neyman allocation to the adjusted total. Cluster/multistage planning estimates design effect as 1 + (average cluster size − 1) × ICC and rounds recruitment to cluster-sized groups. An optional finite-population correction and non-response adjustment are then applied.
What needs review
Complex PPS or unequal-cluster designs, repeated measures, case-control, cohort, regression and hypothesis-testing studies need a tailored calculation.
What the number does not prove
A sufficient target cannot repair biased sampling, weak measurement, high missingness or an analysis plan that does not match the design.
METHODOLOGICAL BASIS
Built to show its work.
The planner is independently produced by Research Metrics Africa. These public sources inform the terminology, design checks and reporting structure; their inclusion does not imply review or endorsement of this tool.
WHO STEPSSurvey planning and sampling tools
Context for documenting population surveys, sample-size assumptions and field planning.
CDC EPI INFOPopulation survey / descriptive studyBinary outcomes, representative samples, design effects, clusters and confidence-based planning.
PENN STATE STAT 506Stratification and allocationProportional allocation, optimal allocation and the role of population size, variability and cost.
AUSTRALIAN BUREAU OF STATISTICSProbability-sampling principlesClear distinctions among simple random, systematic, stratified and non-probability samples.
Scope boundary
This is not a power calculator for comparing groups, testing hypotheses, fitting regression models, case-control studies, cohort studies or clinical trials. Those questions require effect sizes and design-specific methods.
NEED A DEFENSIBLE METHODS SECTION?
Have the assumptions reviewed before recruitment begins.
Bring the research question, outcome, sampling approach and any prior estimate. We will check whether this formula fits and document the recommended calculation.