Calculator
Formula Used
This calculator supports four common planning cases. It applies the selected confidence level, optional design effect, finite population correction when relevant, and a dropout adjustment at the end.
1) Estimate a mean
n0 = ((Z × σ) / E)^2 × DEFF
Z is the critical value, σ is the standard deviation, E is the desired margin of error, and DEFF is the design effect.
2) Estimate a proportion
n0 = (Z^2 × p × (1 − p) / E^2) × DEFF
p is the expected proportion. When p is unknown, 0.50 gives the most conservative estimate.
3) Compare two independent means
n per group = 2 × (Zα + Zβ)^2 × σ^2 / Δ^2 × DEFF
Zα comes from the confidence level, Zβ comes from the selected power, σ is the common standard deviation, and Δ is the detectable difference.
4) Compare two independent proportions
n per group = [(Zα√(2p̄(1−p̄)) + Zβ√(p1(1−p1)+p2(1−p2)))^2 / (p1−p2)^2] × DEFF
p̄ is the average of p1 and p2. The result assumes equal group sizes.
Finite population correction
n = n0 / (1 + ((n0 − 1) / N))
Use this when the total population N is known and not very large.
Dropout adjustment
n adjusted = ceil(n / (1 − dropout rate))
This protects your final usable sample after attrition or nonresponse.
How to Use This Calculator
- Pick the study design that matches your data science problem.
- Enter the confidence level and choose one-sided or two-sided planning.
- For estimation, enter a margin of error and either σ or p.
- For comparisons, enter power and the smallest effect worth detecting.
- Add design effect when clustering or complex sampling inflates variance.
- Enter a finite population only when that correction is appropriate.
- Add expected dropout or nonresponse to protect the final completed sample.
- Press calculate to view the recommended size, summary table, graph, and download options.
Example Data Table
| Scenario | Key Inputs | Recommended Result |
|---|---|---|
| Estimate a mean | 95% confidence, σ = 15, E = 3, DEFF = 1.00, dropout = 10% | 107 total observations |
| Estimate a proportion | 95% confidence, p = 0.50, E = 0.05, DEFF = 1.00, dropout = 10% | 427 total observations |
| Compare two means | 95% confidence, 80% power, σ = 12, Δ = 5, dropout = 10% | 102 per group, 204 total |
| Compare two proportions | 95% confidence, 80% power, p1 = 0.50, p2 = 0.65, dropout = 10% | 189 per group, 378 total |
FAQs
1) What does this calculator estimate?
It estimates the number of observations needed for common study goals: estimating a mean, estimating a proportion, comparing two means, and comparing two proportions.
2) When should I use p = 0.50?
Use 0.50 when you do not know the expected proportion. It produces the largest variance and usually the safest conservative sample size.
3) Why does a smaller margin of error increase n?
Tighter precision demands more information. Because margin of error appears in the denominator squared, small changes in precision can greatly increase required sample size.
4) What is design effect?
Design effect inflates the sample size when data come from clustered, weighted, or otherwise complex designs that increase variance compared with simple random sampling.
5) When should I use finite population correction?
Use it when the population is known, limited, and your sample will be a meaningful fraction of that population. It usually reduces n.
6) What does power mean here?
Power is the chance of detecting the chosen effect if it is truly present. Higher power lowers missed detections but raises required sample size.
7) Are the comparison results per group or total?
For two-group comparisons, the calculator shows the adjusted sample size per group and the combined total, assuming equal allocation between groups.
8) Can I export the result?
Yes. After calculating, use the CSV button for spreadsheet-friendly output or the PDF button for a clean report that includes the summary table and graph.