Sample size and margin of error explained
How sample size, the response proportion and confidence level shape a poll's margin of error, and why quadrupling the sample only halves the margin.
The square-root rule
Sample size drives the margin of error, but not in a straight line. Because n sits under a square root in MOE = z times the square root of p(1-p)/n, the margin shrinks with the square root of the sample rather than in proportion to it. Doubling the respondents divides the margin by about 1.41, and to cut the margin in half you need roughly four times as many people. That is why a national poll of 1,000 lands near a 3.1% margin at 95% confidence, while pushing to a 1.5% margin demands close to 4,000 interviews and far more cost.
Confidence level versus margin
The confidence level sets how often the interval should capture the true value across repeated samples, and it enters the formula only through the z-value. At 95% confidence z is 1.959964; raising the bar to 99% swaps in 2.575829, which widens the same result by about 31%, while dropping to 90% uses 1.644854 and tightens it. Nothing about your data changes when you move the slider, only the price you pay in width for extra certainty. Most published polls settle on 95% as a working compromise between confidence and a usably narrow band.
When the population size matters
The basic formula quietly assumes you are drawing from an effectively infinite population. When the group is small and your sample covers a big fraction of it, that assumption overstates the uncertainty, and the finite-population correction fixes it by multiplying the margin by the square root of (N - n) / (N - 1). Surveying 500 of a 2,000-person company, for example, pulls a 95% margin from about 4.38% down to roughly 3.8%. Once the population is many times the sample, the correction is close to 1 and safely ignored, which is why national polls leave the population field blank.
What the margin does not capture
Margin of error only measures sampling error, the noise from surveying a subset rather than everyone. It says nothing about biased question wording, respondents who lie or drop out, coverage gaps in the frame, or a poorly weighted sample. Two polls can share the same 3% margin yet disagree by more than that because their non-sampling errors differ. Read the margin as the best case under perfect random sampling, and judge the rest of the survey on its methodology.