Why doubling your sample doesn't halve the error
The margin shrinks with the square root of n. Drag the sample size and watch the dot slide down a curve that flattens fast: going from 100 to 400 responses halves the margin, but going from 1,000 to 2,000 only trims it by about 0.9 points.
Reading a margin of error
If a survey of 400 finds 62% support with a ±4.9-point margin at 95% confidence, the interval 57.1% to 66.9% was produced by a method that captures the true population value in 95% of repeated samples. Two results whose intervals overlap slightly can still differ significantly; to compare two groups directly, use the two-proportion significance test.
Quick reference (95%, p = 50%)
| n | Margin of error |
|---|---|
| 100 | ±9.8 |
| 200 | ±6.9 |
| 400 | ±4.9 |
| 600 | ±4 |
| 1,000 | ±3.1 |
| 1,500 | ±2.5 |
| 2,500 | ±2 |
Frequently asked questions
How do I calculate the margin of error?
For a proportion: MOE = z × √(p(1 − p)/n). With 1,000 respondents, p = 0.5 and 95% confidence: 1.96 × √(0.25/1000) = 0.031, or ±3.1 percentage points.
What is a good margin of error?
Published national polls usually aim for ±3 points; organisational surveys commonly accept ±5; small pilot studies may accept ±10. What matters is whether the interval is narrow enough for the decision you need to make.
Does the margin of error apply to subgroups?
Each subgroup has its own, larger margin because it has fewer respondents. A national poll of 1,000 with ±3.1 overall has about ±6.9 among a subgroup of 200.
What does the margin of error not cover?
Only random sampling error. It does not account for non-response bias, poorly worded questions, or a sampling frame that misses part of the population.