Calculator Inputs
Example Data Table
| Mode | Scenario Inputs | Final Sample Size | Use Case |
|---|---|---|---|
| Estimate | p = 50%, error = 5%, confidence = 95%, nonresponse = 10% | 427 | Fast conservative planning case |
| Estimate | p = 42%, error = 3%, confidence = 95%, N = 5,000, deff = 1.2, nonresponse = 15% | 1,277 | Higher precision with field adjustments |
| Estimate | p = 20%, error = 4%, confidence = 90%, N = 800 | 214 | Smaller finite population study |
| Test | p0 = 50%, p1 = 60%, alpha = 5%, power = 80%, two-sided | 216 | Detect a ten-point improvement |
| Test | p0 = 35%, p1 = 45%, alpha = 2.5%, power = 90%, one-sided | 325 | Stricter testing with extra inflation |
These rows show how different assumptions change the final requirement before data collection starts.
Formula Used
Estimation mode: n₀ = Z² × p × (1 − p) ÷ E²
Finite population correction: nFPC = n₀ ÷ [1 + (n₀ − 1) ÷ N]
Design and field adjustment: nfinal = ceil(n × design effect ÷ (1 − nonresponse) × (1 + safety inflation))
Test mode: n = [(Zα√(p₀(1−p₀)) + Zβ√(p₁(1−p₁)))²] ÷ (p₁ − p₀)²
These formulas use standard normal approximations for binomial-proportion planning. For exact or regulatory designs, confirm the final specification with a statistician.
How to Use This Calculator
- Choose whether you want a precision-based estimate or a hypothesis test.
- Enter your expected proportion, or enable the conservative 50% option.
- Add confidence and margin of error for estimation, or alpha and power for testing.
- Apply population size when sampling from a limited frame.
- Inflate the result with design effect, expected nonresponse, and any safety margin.
- Submit the form, review the summary table, inspect the graph, then export the result as CSV or PDF.
FAQs
1) What does this calculator estimate?
It estimates the number of Bernoulli observations needed for a target proportion study or a one-sample proportion test. It supports precision planning, power planning, finite populations, design effects, nonresponse, and extra safety inflation.
2) Why would I use the conservative 50% option?
A proportion of 50% creates the largest variance, so it often gives the largest required sample for a fixed margin of error. Use it when you lack prior evidence and want a cautious planning estimate.
3) When should finite population correction be applied?
Apply it when you sample from a known and limited population, such as 800 members or 5,000 records. It reduces required sample size because sampling without replacement lowers uncertainty as coverage increases.
4) What does power mean in test mode?
Power is the probability of detecting the specified difference when the alternative is true. Higher power requires more observations, but it lowers the chance of missing a real effect.
5) Why adjust for nonresponse?
Fieldwork rarely converts every invited unit into usable data. A nonresponse adjustment increases the contact target so the completed sample remains large enough after refusals, ineligibility, or missing records.
6) What is the design effect for?
Design effect adjusts for clustering, unequal weights, or complex sampling plans that increase variance relative to simple random sampling. A value above 1 inflates the required sample to protect precision or power.
7) Are the results exact for every binomial study?
No. The page uses standard normal-approximation formulas, which are widely used for planning. Very small samples, rare events, or regulated studies may require exact, Bayesian, or sequential methods.
8) Can I use this for A/B checks or quality control?
Yes, for quick one-sample proportion planning or pass-rate monitoring. For two-group experiments, matched designs, or acceptance sampling with strict operating-characteristic rules, use a method tailored to that design.