GlossaryStatistics and interpretation
Margin of error
A margin of error describes sampling uncertainty around an estimate at a stated confidence level.
A margin of error describes sampling uncertainty around an estimate at a stated confidence level. It is commonly shown with a plus-or-minus sign. Read it in the same units as the estimate: a margin around a percentage is usually expressed in percentage points, not as a percentage change.
Reading an estimate
Survey results describe a population using information from a sample. The Census Bureau's statistical-testing guidance explains why the margin of error matters when comparing American Community Survey estimates. A difference between two printed numbers can be smaller than the uncertainty involved in estimating them.
A margin of error is meaningful only with its estimate, confidence level, and method. It does not certify that a source has no reporting mistakes, missing groups, or biased questions. Those problems can require separate assessment.
Example
Hypothetical example: A survey estimates that 40% of residents have a specified concern, with a margin of error of five percentage points at the stated confidence level. The corresponding symmetric interval runs from 35% to 45%.
The interval is ten percentage points wide; the margin is five. It does not mean that the estimate is 5% larger or smaller in relative terms. Keep the confidence level beside the range when quoting it.
Common confusion
A confidence interval is the resulting range. The margin of error is the distance from the estimate to either endpoint when that range is symmetric. Not every interval is symmetric.
The number of responses is also not the margin of error. Survey design and weighting can affect uncertainty, so a sample count alone is insufficient for reconstructing a published margin.
Comparison scope
Use the source's recommended significance test when comparing estimates. Do not subtract two point estimates and call the difference established merely because the printed values differ.