Overview

The margin of error is a statistical measure that expresses the amount of sampling uncertainty in an estimate drawn from a sample rather than an entire population. It is commonly reported alongside survey results and election polls to indicate a range within which the true population value is likely to lie. When writers say a result is "plus or minus" a number of percentage points, they are reporting the margin of error, which is conceptually the radius (half the width) of a confidence interval. The issue arises whenever a population is not measured in full, as is typical in most statistical surveys.

How it is estimated

At a basic level the margin of error depends on three ingredients: the desired confidence level, the variability of the measured quantity, and the sample size. For proportions (such as the share supporting a candidate) a common approximation is z × sqrt(p(1−p)/n), where z is the critical value for the chosen confidence level (for example, about 1.96 for 95% confidence), p is the sample proportion, and n is the sample size. For means, a similar form z × (σ/√n) is used when the population standard deviation σ is known or estimated. These formulas assume a simple random sample; survey designs that use weighting, clustering, or stratification require adjusted calculations and often increase the reported margin of error.

Factors that change the margin of error

  • Sample size: larger samples reduce the margin of error roughly in proportion to 1/√n.
  • Variability: more variable attributes produce larger margins of error for a given sample size.
  • Confidence level: higher confidence (more certainty) requires a larger multiplier z and therefore a larger margin.
  • Design effects and weighting: complex sampling or heavy weighting can increase uncertainty beyond simple formulas.
  • Finite population correction: when a large fraction of the population is sampled, the margin shrinks compared with infinite-population formulas.

Uses, interpretation and common pitfalls

The margin of error helps readers interpret whether observed differences are likely real or could arise from sampling variability. For example, if two candidates’ support levels differ by less than the combined margins of error, the difference is not statistially conclusive. However, the margin of error does not capture systematic errors such as poorly worded questions, nonresponse bias, or sampling frame problems. Journalists and researchers sometimes misuse the term by applying simple-sample margins to results from complex surveys; responsible reports indicate the confidence level and note design adjustments.

Context and notable points

Margins of error have a long history in public-opinion research and are a standard part of reporting for polls, market studies, and social-science surveys. They are a useful summary of sampling uncertainty but should be read alongside information about methodology, sample representativeness, and possible non-sampling errors. For technical readers, further details on calculation and adjustment for complex designs are available in survey-methods literature and from methodological guidance provided with most reputable polls (see sources linked above).