Poll Lead Significance Calculator
Test whether one candidate's lead over another in the same poll is statistically significant, accounting for the correlation between the two shares.
How it works
SE = √((pₐ + p_b − (pₐ − p_b)²) ÷ n) · z = (pₐ − p_b) ÷ SE
Comparing two candidates in the same poll is not the same as comparing two independent numbers, because a vote for one is a vote away from the other — their shares are negatively correlated. The correct standard error for the lead uses the multinomial variance formula, which is larger than a single-number margin but smaller than treating the two as independent. The result is that a lead must exceed roughly 1.7 times the headline margin of error before it is significant.
Worked example
48% versus 45% on n = 1,000: lead = 3 points. SE = √((0.48 + 0.45 − 0.03²) ÷ 1000) = √(0.000929) = 0.0305. z = 0.03 ÷ 0.0305 = 0.98, p = 0.33 — the lead is within the margin.
Sources: Margin of error — Wikipedia
Frequently asked questions
Why is the lead margin bigger than the poll margin of error?
The headline margin applies to a single percentage. The gap between two candidates involves the uncertainty of both, so its margin is larger — a common rule of thumb is about 1.7 times the single-number margin.
Does this handle undecided voters?
Yes, implicitly. As long as A% and B% are shares of the full sample (with the remainder undecided or other), the multinomial formula accounts for that third category through the (pₐ + p_b) term.
What if the poll is weighted?
Weighting inflates the effective margin via the design effect. Divide your sample size by the design effect first, then use that effective n here for a more honest significance test.
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This calculator is for educational purposes. Double-check important results before acting on them.