A margin of error is a promise, not a shrug
“Within the margin of error” is the most misused phrase in election coverage. Here is what ±3.4 points actually commits us to.
Integrity Polling research staff · Methods
· 3 min read
Sample data. This article is a demonstration of our analysis format. The figures it discusses are illustrative unless a source is cited.
Our demonstration gubernatorial release shows Delgado at 44 and Reed at 40 with a margin of sampling error of ±3.4 percentage points. Three different headlines could be written from those numbers, and two of them are wrong.
Wrong: “Delgado leads by four.” A four-point lead is a point estimate, not a finding. It describes the sample we drew, not the population we drew it from.
Also wrong: “The race is a statistical tie.” Nothing about a 44–40 result says the candidates are tied. It says the data cannot rule out a tie. Those are different claims. The most likely state of the world, given this poll, is still that Delgado is ahead.
Right: “Delgado narrowly ahead, within the range where a different sample could show a tie.” Less quotable. Correct.
What the number means
The margin of sampling error says: if we drew a hundred samples the same way, in about ninety-five of them each candidate’s measured share would land within 3.4 points of their true share. It applies to each share separately. It does not apply to the gap between two shares, because the gap combines two uncertain numbers, and their errors are negatively correlated (a respondent who moves from Delgado to Reed changes both at once).
As a rule of thumb, the margin on the difference between two candidates is a little under twice the margin on a single share. For this poll, call it ±6.5 points. Delgado’s four-point lead sits comfortably inside that range, which is why we describe it as narrow rather than as a lead.
Each candidate's share with its ±3.4-point margin
Demonstration data. The whiskers are the 95% interval for each candidate individually. Where two intervals overlap, a different sample could plausibly have reversed the order.
Whiskers show ±3.4 percentage points, the margin of sampling error.
Integrity Polling demonstration release, Sept. 14–18, 2026 (illustrative). n = 1,012 likely voters.
What the number does not cover
The margin of sampling error covers exactly one source of error: the luck of the draw. It says nothing about the other sources, which are usually larger:
- Non-response. When fewer than five in a hundred people answer the phone, the four who do are different from the ninety-six who do not. Weighting corrects for the differences we can measure (age, education, region) and not for the ones we cannot (interest in politics, trust in strangers).
- Likely-voter screening. Who counts as “likely” is a judgment call. Change the screen and the toplines move, sometimes by more than the stated margin.
- Question wording and order. A ballot question that names every candidate yields different numbers from one that does not. Neither has a sampling error problem. They are measuring different things.
- Late movement. A poll is a photograph of the week it was fielded, not a forecast.
This is why the methodology box on every release reports the design effect, the response rate, the screening rule, and the exact wording, and why the Scorecard grades us on the total error after the election, not just the part the margin was supposed to cover.
The promise
When we print ±3.4, we are making a testable claim: that across all the races we poll, roughly 95 percent of our final numbers should fall within the stated margin of the certified result. If, over enough elections, far fewer than 95 percent do, our margins are too small and we will say so. If far more than 95 percent do, our margins are too wide and we will say that too.
A margin of error that is never checked against outcomes is decoration. Ours is a promise with a due date.