Table of Contents
What Is Margin of Error?
The margin of error represents the maximum expected difference between the sample statistic and the true population parameter. In polling, it tells you how close the poll result is likely to be to the actual value if you could survey everyone.
A margin of error of ±3% at 95% confidence means that if the poll were repeated many times, 95% of the results would fall within 3 percentage points of the true value. Smaller margins require larger sample sizes.
Formula
Sample Size Table (95% confidence, p=0.5)
| Margin of Error | Required Sample Size |
|---|---|
| ±1% | 9,604 |
| ±2% | 2,401 |
| ±3% | 1,068 |
| ±5% | 385 |
| ±10% | 97 |
Frequently Asked Questions
Why does the sample size have diminishing returns?
The margin of error decreases with the square root of the sample size. To halve the margin of error, you need to quadruple the sample size. Going from ±5% to ±2.5% requires 4x the sample.
What proportion should I use if unknown?
Use p = 0.5 (50%), which gives the maximum margin of error and the most conservative (largest) sample size estimate. This ensures your actual margin will be at most this large regardless of the true proportion.
Does population size matter?
For large populations (over 20x the sample size), population size has minimal effect. For small populations, applying the Finite Population Correction (FPC) reduces the required sample size.