How to Read Election Polls: What the Margin of Error Really Covers

A new poll shows one candidate at 48% and the other at 45%, with a margin of error of ±3 points. Headlines call it a lead. Is it? The answer depends on what the margin of error covers, and many readers apply it to the wrong number.

What the margin of error measures

The margin of error describes sampling error: how far a result could stray from the true value simply because only a sample of people was asked. For 1,000 respondents and a result near 50%, the 95% margin is about ±3.1 points (1.96 × √(0.25 ÷ 1,000)). With 400 respondents it is about ±4.9, and with 2,000 about ±2.2. Pew Research Center gives the same rule of thumb: a typical election poll of about 1,000 people carries roughly ±3 points. Enter your own numbers in the confidence interval calculator for a single proportion.

A lead needs about double the margin

The margin applies to each candidate's share separately. The gap between two candidates in the same poll is more uncertain, because one candidate's gain is partly the other's loss. For 48% against 45% with 1,000 respondents, the standard error of the gap is about 3.0 points, so the 95% interval for the 3-point lead runs from roughly −3 to +9. Zero lies inside it, so this poll cannot separate the race from a tie.

A margin of ±3 on each candidate becomes roughly ±6 on the lead.

Did opinion really change?

Say last month's poll had a candidate at 46% and this month's shows 49%, each with 1,000 respondents. The rise looks like momentum, but the standard error of the difference is about 2.2 points. The 95% interval runs from about −1.4 to +7.4 points and the p-value is about 0.18, so nothing here separates a real shift from noise. Pew cautions that the margin for the difference between two polls is larger than most people expect. Try your own figures in the difference of two proportions calculator or the confidence interval calculator for two proportions.

Is the candidate really above 50%?

A one-sample test compares support with a benchmark. If 520 of 1,000 respondents back a candidate, the 95% interval is about 48.9% to 55.1%. The test statistic is z ≈ 1.27 and the two-sided p-value about 0.21, so 50% remains plausible. The one-sample proportion test calculator does this in seconds.

What the margin does not cover

Sampling error is only one source of error. Non-response, question wording, the definition of a likely voter and the weighting of the sample can matter as much, and Pew's methodologists note that these other errors can be as large as sampling error or larger. Subgroups are noisier still: a subgroup of 100 respondents carries a margin of about ±9.8 points.

How to read the next poll

Ask how many people were interviewed, who was sampled (all adults, registered or likely voters), and whether the quoted margin applies to the whole sample or to a subgroup. Treat a change smaller than about twice the margin with caution, and prefer averages of several polls to any single one. For planning your own survey, ±3 points needs about 1,068 respondents and ±2 points about 2,401, as our sample size guide explains.