What the margin of error means
The margin of error is the “±” in “52% ± 3%”: half the width of a confidence interval. It measures uncertainty due to random sampling. See margin of error explained.
Worked examples
- Percentage: 52% of 1,000 respondents, at 95%: 1.96 × √(0.52 × 0.48 / 1000) = ±3.10 points.
- Mean: mean 100, SD 15, n = 40 at 95%: 2.023 × 15 / √40 = ±4.80.
- Small population: 1,000 responses from a population of 5,000 shrinks ±3.10 to ±2.77.
How to reduce it
Halving the margin needs four times the sample, because it shrinks with √n. To plan a study, use the survey sample size calculator.
Limits
This is the normal-approximation formula, reasonable when there are at least about 10 in each category. It assumes a random sample and says nothing about non-response or leading questions. The margin on a difference between two candidates or two groups is larger than the margin on each figure.
Frequently asked questions
What is a good margin of error?
Polls commonly aim for about plus or minus 3%. Below 5% is often acceptable for surveys, depending on the decision the result supports.
How do I calculate margin of error?
For a proportion, multiply the critical value by the square root of p(1-p)/n. For a mean, multiply the t critical value by s divided by the square root of n.
Does the population size matter?
Only if the sample is a sizeable share of the population, roughly over 5%. Otherwise the correction is negligible.