A poll says '52% support, ±3%'. That ± is a confidence interval — an admission that the true number could be anywhere from 49% to 55%, and a measure of how much to trust the estimate.
A confidence interval is a range around an estimate that, with a stated confidence level (often 95%), is believed to contain the true population value.
Polls, drug trials, A/B tests, scientific measurements, economic forecasts — an estimate without an interval is half an answer. The interval quantifies uncertainty.
Wider interval = more confidence OR less data. For a 95% CI of a mean: x̄ ± 1.96·(σ/√n). Quadrupling the sample size halves the margin.
A poll of 1,000 people gives 50% support with a 95% margin of ±3 points. What does '95% confidence' actually mean?
Why does a bigger sample give a narrower interval?
The margin shrinks like 1/√n. 1,000 people → ±3%. 4,000 people → ±1.5%. To halve the margin you need *four times* the data — diminishing returns, which is why polls rarely exceed a few thousand.
'95% confidence' is not 'a 95% probability the true value is in this interval'. In the standard (frequentist) view the true value is fixed — it's either in or out. The 95% describes the long-run success rate of the *method*.
When two confidence intervals overlap a lot, the difference between the estimates probably isn't statistically significant. Barely-touching or non-overlapping intervals suggest a real difference.
- A CI = estimate ± margin of error, with a stated confidence level.
- Margin shrinks like 1/√n — quadruple the data to halve it.
- '95% confidence' describes the method's long-run hit rate, not this one interval.