Margin of Error

The margin of error is the half-width of a Confidence Interval, showing how far a sample estimate could plausibly differ from the true population value at a given confidence level.

A poll reporting “52% support, ±3% at 95% confidence” means that if re-run many times, 95% of the resulting intervals [49%, 55%] would contain the true population proportion.

What drives it:

• Sample size: larger $n$ shrinks the margin (proportional to $1/\sqrt{n}$)
• Population variability: more spread gives a larger margin
• Confidence level: 99% intervals are wider than 95%

For a population proportion $p$ with sample size $n$ at 95% confidence: $\text{MOE}\approx 1.96\sqrt{\frac{p(1-p)}{n}}$ where:

• $p$ is the true population proportion
• $n$ is the sample size
• $1.96$ is the 95% normal critical value

Common mistakes when reading polls

• Treating “52% vs 48%” as a clear lead when MOE is ±3%
• Assuming MOE covers non-response bias, question wording, or Selection Bias (it does not)
• Comparing two polls’ point estimates without accounting for both margins

Related

• Confidence Interval
• Sample vs Population
• Statistical Significance