Margin of Error
3 min read
Definition
Margin of error (also called confidence interval) is a statistic that expresses the amount of random sampling error in survey results. It tells you how much the results from your sample might differ from the true value of the entire population. A margin of error of +/-3% means the true value is likely within 3 percentage points of your observed result.
How It Works
MoE = z x sqrt(p(1-p) / n)
z = z-score (1.96 for 95% confidence)
p = expected proportion (0.5 for maximum uncertainty)
n = sample size
Example
You survey 400 people and 60% say they prefer Product A. With a +/-5% margin of error at 95% confidence, the true preference is likely between 55% and 65%.
Factors That Affect Margin of Error
| Factor | Effect |
|---|---|
| Sample size | Larger samples reduce margin of error. |
| Confidence level | Higher confidence (99% vs 95%) increases margin of error. |
| Population variability | More diverse populations increase margin of error. |
| Population size | Only matters for small populations (<20,000). |
Why It Matters for Surveys
- Credibility: reporting margin of error makes your survey results trustworthy.
- Decision confidence: know whether differences in results are statistically meaningful.
- Sample planning: calculate the minimum sample size needed before launching a survey.
- A/B testing: determine if the difference between variants is real or just noise.
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