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Margin of error, without false precision.
Estimate uncertainty for a proportion under simple random sampling—and see every assumption used in the calculation.
Model: z × √(p × (1 − p) × design effect ÷ n), multiplied by the finite-population correction √((N − n) ÷ (N − 1)) when a population is supplied. This estimates sampling variation; it does not correct selection bias, nonresponse, weighting instability, clustering not captured by the chosen design effect, multiple comparisons, or poor questions.
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How to read the result
A result of ±4.9 points means an observed 50% share would have an approximate 95% interval from 45.1% to 54.9% under the stated model assumptions. It is not a guarantee that the true population value lies there, and it does not make a nonprobability sample representative.
Why population and design effect matter
Sampling every member of a finite population leaves no sampling margin under this formula. Sampling only part of a population applies a finite-population correction when the population size is supplied. A design effect changes the nominal sample into an effective sample for the variance calculation; use a value other than one only when the actual design supports it.
What it cannot repair
Margin of error describes modeled random sampling variation. It does not measure coverage error, nonresponse, panel conditioning, fraudulent respondents, biased wording, weighting instability, multiple testing, or the gap between a convenience sample and the intended population.