Sample Size Calculator
Sample size calculator
Estimate required completes for proportion studies with scenario presets, design-effect inflation, and invite planning.
Result
Target completes n = 385
Base n = 385; invites needed = 385; z = 1.959964.
planning summary
Response
Completes / invites
Advanced options
Planning details
Planning summary
Custom study
Base n
385 (large population)
Target completes
385
Invite estimate
385 at 100% response
Confidence / Margin / Proportion
95% / ±5% / 50%
Sensitivity by margin of error
| Margin (%) | Base n | FPC n | Target completes | Invite estimate |
|---|---|---|---|---|
| ±4 | 601 | — | 601 | 601 |
| ±5 | 385 | — | 385 | 385 |
| ±6 | 267 | — | 267 | 267 |
Planning assumptions
- Custom scenario selected. Validate design assumptions with your own research protocol.
- The model assumes simple random sampling for a proportion outcome.
- Design effect inflates required completes for clustered or weighted samples.
- Invite count assumes observed response rate is stable across sampling waves.
Flow
- Choose a planning scenario preset or keep Custom study.
- Choose confidence level and margin of error.
- Enter estimated proportion; use 50% for conservative planning when unknown.
- Set design effect and expected response rate to convert base n into completion and invite targets.
- Optionally add finite population size for corrected sample requirement and review the sensitivity table.
Example
Worked example: 95% confidence, 5% margin, p = 50%, population 5,000
- 1 z = 1.96, p = 0.5, e = 0.05
- 2 Base n = (1.96^2 × 0.5 × 0.5) / 0.05^2 ≈ 384.16 -> 385
- 3 Finite-population correction gives n = 357
- 4 With design effect 1.2 and response rate 60%, target completes = 429 and invites ≈ 715
Use 429 target completes and send about 715 invites for this planning scenario.
How
- Choose a planning scenario preset or keep Custom study.
- Choose confidence level and margin of error.
- Enter estimated proportion; use 50% for conservative planning when unknown.
- Set design effect and expected response rate to convert base n into completion and invite targets.
- Optionally add finite population size for corrected sample requirement and review the sensitivity table.
Avoid
- Using overly optimistic margin of error without budget feasibility checks.
- Ignoring design effect when sampling includes clustering or weighting.
- Treating response rate as guaranteed instead of monitoring and reforecasting invites.
- Forgetting finite-population correction on small populations.
- Treating confidence level as guarantee of zero bias.
FAQ
Why is 50% often used for estimated proportion?
It yields the most conservative (largest) sample requirement when prevalence is uncertain.
Do I always need finite population correction?
Only when population is relatively small compared with computed sample size.
Can this replace full study design?
No. It supports planning, while design effects, stratification, and bias controls still require formal study design.
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