Sample Size Calculator

Use this as a planning aid, then account separately for clustering, design effects, attrition, multiple outcomes, and study-specific power requirements.

Study type

Confidence level

Margin of error (%)

Population size (optional)

Expected proportion (%)

Expected response rate (%)

For proportions, 50% is conservative when no prior estimate is available.

Fieldwork & design-effect planner

Stress-test the required sample for clustering, subgroup analysis and alternate margins.

Planning evidence

Design effect

Key subgroups

Scenario	Completed n	Field target	Evidence

Use the tool above, then refresh this audit.

Formula context

n₀ = z²p(1-p)/e²

Classical planning formula only. It does not automatically include clustering, weighting, design effects, attrition beyond the response-rate adjustment, or study-specific power requirements.

Core describe → test → interpret workflows

Use descriptive context first, choose the method that matches the design, then keep inputs, settings and result evidence reproducible instead of copying a p-value without its analysis recipe.

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Interpret statistical results in context

Use plots and descriptive summaries before formal tests. Check the sampling/design assumptions that matter for the chosen method, report effect size and uncertainty where available, and avoid treating a threshold such as p < .05 as proof of importance, causation, or truth. Browser calculations are educational/planning utilities, not domain-specific professional advice.

How to use this Sample Size Calculator

Use this as a planning aid, then account separately for clustering, design effects, attrition, multiple outcomes, and study-specific power requirements.

Practical guide and verification

Use the interactive product above first. These notes add interpretation, verification and limits below the results and product controls.

Margin-of-error planning is not statistical power analysis

This calculator sizes estimation precision for a mean or proportion. Detecting a specified treatment effect in ANOVA, regression, correlation or another hypothesis test requires a power model with effect-size and design assumptions.

Use 50% proportion when uncertainty is genuine

For a proportion, p = 0.5 maximizes p(1-p) and therefore gives the largest conservative sample size when no prior estimate is defensible. A more optimistic proportion should come from prior data or a pilot rather than convenience.

Finite-population correction matters only when the sampling fraction is meaningful

When the population is very large relative to the sample, the correction barely changes the answer. For a bounded population, compare the uncorrected and corrected results to see whether the population size actually affects planning.

Design effect and response rate solve different fieldwork problems

Design effect inflates the number of completed observations needed when sampling is less efficient than simple random sampling. Response rate converts that completion target into invitations or contacts. Do not combine them as if they describe the same loss.

Round required completes upward

A fractional calculated sample is a minimum requirement, so the completed-sample target should be rounded up. Then separately allow for nonresponse, exclusions and subgroup needs before deciding how many people to recruit.