Explanation
The margin of error is usually defined as the "radius" (or half the width) of a confidence interval for a particular statistic from a survey. One example is the percent of people who prefer product A versus product B. When a single, global margin of error is reported for a survey, it refers to the maximum margin of error for all reported percentages using the full sample from the survey. If the statistic is a percentage, this maximum margin of error can be calculated as the radius of the confidence interval for a reported percentage of 50%.
The margin of error has been described as an "absolute" quantity, equal to a confidence interval radius for the statistic. For example, if the true value is 50 percentage points, and the statistic has a confidence interval radius of 5 percentage points, then we say the margin of error is 5 percentage points. As another example, if the true value is 50 people, and the statistic has a confidence interval radius of 5 people, then we might say the margin of error is 5 people.
In some cases, the margin of error is not expressed as an "absolute" quantity; rather it is expressed as a "relative" quantity. For example, suppose the true value is 50 people, and the statistic has a confidence interval radius of 5 people. If we use the "absolute" definition, the margin of error would be 5 people. If we use the "relative" definition, then we express this absolute margin of error as a percent of the true value. So in this case, the absolute margin of error is 5 people, but the "percent relative" margin of error is 10% (because 5 people are ten percent of 50 people). Often, however, the distinction is not explicitly made, yet usually is apparent from context.
Like confidence intervals, the margin of error can be defined for any desired confidence level, but usually a level of 90%, 95% or 99% is chosen (typically 95%). This level is the probability that a margin of error around the reported percentage would include the "true" percentage. Along with the confidence level, the sample design for a survey, and in particular its sample size, determines the magnitude of the margin of error. A larger sample size produces a smaller margin of error, all else remaining equal.
If the exact confidence intervals are used, then the margin of error takes into account both sampling error and non-sampling error. If an approximate confidence interval is used (for example, by assuming the distribution is normal and then modeling the confidence interval accordingly), then the margin of error may only take random sampling error into account. It does not represent other potential sources of error or bias such as a non-representative sample-design, poorly phrased questions, people lying or refusing to respond, the exclusion of people who could not be contacted, or miscounts and miscalculations.
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