The classic case
- Input
- 95%, margem 5%, p = 50%
- Expected output
- n = 385
n₀ = 384.15, rounded up.
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sample size 95% confidence 5% margin of error
In the Size: proportion tab, the values 95%, 5% and 50% come filled in and the result is 385. The sensitivity table right below shows the number for other margins and confidence levels.
n₀ = 384.15, rounded up.
z = 2.5758.
Almost triple 385.
p(1 − p) falls from 0.25 to 0.16.
385 / 0.30 = 1,283.3, rounded up.
For a proportion, use n₀ = z² · p · (1 − p) / E². At 95% confidence (z = 1.96), a 5% margin and p = 50%, n₀ = 384.15, so 385 people. If the population is finite, apply n = n₀ / (1 + (n₀ − 1) / N). Then multiply by the design effect, if any, and divide by the expected response rate to learn how many to invite.
You can, it is more conservative: with 400 respondents the margin falls to ±4.90 percentage points. Many people round up to 400 for convenience. The exact minimum for 5% is 385.
Hardly at all, if the population is large. For N = 100,000 the number is 383, and for N = 1,000,000 it stays at 384. It only becomes a relevant factor when the sample is a notable fraction of the population.
Use 50%. It is the worst case and guarantees the margin asked for whatever the real proportion is. Lower it only if there is a previous study or a reliable estimate.
When unsure, use 50%: it is the case that needs the largest sample.
1 means simple random sampling. Cluster surveys use values above 1.
How many of those invited should answer. 100% means everyone answers.
With 385 respondents, the estimate of a proportion around 50% will have a margin of error of ±5 percentage points, at 95% confidence.
z = 1.96 (95%)n₀ = z² · p · (1 − p) / E² = 1.96² · 0.5 · 0.5 / 0.05² = 384.15⌈384.15⌉ = 385| Margin | 90% | 95% | 99% |
|---|---|---|---|
| ±1% | 6,764 | 9,604 | 16,588 |
| ±2% | 1,691 | 2,401 | 4,147 |
| ±3% | 752 | 1,068 | 1,844 |
| ±4% | 423 | 601 | 1,037 |
| ±5% | 271 | 385 | 664 |
| ±7% | 139 | 196 | 339 |
| ±10% | 68 | 97 | 166 |