Example Data Table
| Stratum |
Population |
SD |
Use Case |
| Urban |
5,000 |
1.20 |
Large group with moderate variability |
| Suburban |
3,200 |
1.05 |
Middle group with stable responses |
| Rural |
1,800 |
1.45 |
Smaller group with higher variation |
| Remote |
700 |
1.80 |
Small group needing careful coverage |
Formula Used
Initial sample size: n0 = Z² × p × (1 − p) ÷ e²
Finite population correction: n = n0 ÷ [1 + ((n0 − 1) ÷ N)]
Design effect adjustment: adjusted n = n × design effect
Proportional allocation: nh = n × Nh ÷ N
Neyman allocation: nh = n × (Nh × Sh) ÷ Σ(Nh × Sh)
Sampling weight: Wh = Nh ÷ nh
Z is the confidence score. p is the expected proportion. e is margin of error. N is total population. Nh is stratum population. Sh is stratum standard deviation.
How To Use This Calculator
Enter your confidence level, margin of error, and expected proportion. Add the design effect if your survey has clustering or complex fieldwork.
Enter each stratum name and population count. Add standard deviation values when you want Neyman allocation. Add custom sample counts only when the custom method is selected.
Press calculate. Review the completed sample, invited count, weights, sampling fractions, and random position preview. Export the plan as CSV or PDF when needed.
Stratified Sampling Guide
Stratified random sampling helps you protect important groups. A population is split into strata before selection begins. Each stratum should contain similar units. Different strata should represent meaningful differences. Common strata include age groups, regions, classes, income bands, branches, or product segments. This design is useful when a simple random sample may miss small but important groups. It also improves subgroup precision when groups differ in size, behavior, or variability, and when decisions require dependable comparisons across groups.
Why This Calculator Helps
The calculator estimates an overall sample size first. It uses confidence level, expected proportion, margin of error, design effect, and finite population correction. Then it allocates the sample across listed strata. You can choose proportional, equal, Neyman, or custom allocation. Proportional allocation follows each stratum population share. Equal allocation gives each stratum the same completed sample. Neyman allocation gives more sample to larger or more variable strata. Custom allocation lets you enter your own final counts.
Planning Better Surveys
Good stratification starts with a clean sampling frame. Each unit should appear once. Each unit should belong to one stratum only. Population counts should be checked before fieldwork. Very small strata may need a minimum sample rule. Large strata may need more cases to support detailed reporting. Response rate matters because completed interviews are usually fewer than invitations. The calculator therefore shows invited counts using your expected response rate.
Interpreting The Output
The table shows completed samples, invited counts, sampling fractions, and design weights. A design weight is the population count divided by completed sample count. Higher weights mean each respondent represents more units. Very high weights can increase variance. Review them before using final estimates. The random number preview gives example unit positions. Use it with a numbered list for each stratum, or replace it with your approved randomization process.
Best Practice Notes
Use current population totals. Select strata before viewing outcomes. Keep the same definitions through analysis. Avoid changing allocations after collection begins unless the survey plan allows it. Record the seed, assumptions, and method. This makes the sample easier to audit. Export the results before sharing the plan with field teams. A clear plan reduces sampling bias and improves trust in final statistics.
FAQs
1. What is stratified random sampling?
It is a sampling method that divides a population into groups first. A random sample is then selected from each group. This helps important groups remain represented.
2. When should I use proportional allocation?
Use proportional allocation when each stratum should follow its population share. It is simple, balanced, and common for general surveys.
3. What does Neyman allocation do?
Neyman allocation gives more sample to strata with larger populations and higher variability. It can improve precision when standard deviation values are reliable.
4. Why is response rate included?
Response rate estimates how many people must be invited. If only some people respond, the invited count must be higher than the completed sample.
5. What is a design effect?
Design effect adjusts sample size for complex survey designs. Larger values increase the required sample because clustering or weighting can reduce precision.
6. What is a sampling weight?
A sampling weight shows how many population units one respondent represents. It equals stratum population divided by completed sample count.
7. Can I use custom allocation?
Yes. Select custom allocation and enter completed sample counts for each stratum. This is useful when your project has fixed quotas.
8. What does the random preview mean?
It shows example numbered positions to select from each stratum list. Use a complete numbered sampling frame for real selection.