Glossary

Margin of Error

The margin of error is the maximum expected difference between the true population parameter and a sample estimate, typically expressed as ± a percentage. A smaller margin of error demands a larger sample.

Definition

Why It Matters

The margin of error quantifies the precision of a survey or study estimate, giving stakeholders a clear sense of how much the sample result might differ from the true population value. A poll reporting 48% support with a margin of error of ±3 percentage points means the true support likely falls between 45% and 51%. Understanding the margin of error is crucial for responsible reporting and informed decision-making; without it, small differences between candidates or groups appear meaningful when they may simply reflect sampling variability. Sample size calculations in survey design are driven almost entirely by the desired margin of error.

Example

A national survey estimates that 62% of adults favour a new policy, with a margin of error of ±2.5 percentage points at the 95% confidence level. This means the analyst is 95% confident that the true proportion of adults who favour the policy lies between 59.5% and 64.5%. If a rival poll reports 60% with a margin of error of ±4 percentage points, the wider interval (56% to 64%) indicates less precision due to a smaller sample.

Related Terms

Software Notes

SPSS: Not computed by default; calculate manually or use Analyze > Descriptive Statistics > Frequencies with confidence intervals for proportions
R: For a proportion: margin <- qnorm(0.975) sqrt(p (1 - p) / n); for a mean: qt(0.975, df) * sd(x) / sqrt(n)
Stata: proportion varname displays margin of error; for custom calculations: display invnormal(0.975) sqrt(p(1-p)/n)