Confidence interval
A confidence interval is a range, calculated from a sample, that is likely to contain the true value for the whole population. A 95 percent confidence interval means that the method would capture the true value in 95 of 100 samples.
How it works
Every sample estimate carries uncertainty, because a different sample would give a slightly different answer. The confidence interval expresses that uncertainty as the estimate plus or minus a margin of error. The margin has two parts: the standard error, which shrinks as the sample grows, and a multiplier set by the confidence level, 1.96 for 95 percent.
Three levers change its width. A larger sample narrows it; a higher confidence level widens it; and more variation in the population widens it. A confidence interval is read as a statement about the method: it does not mean there is a 95 percent chance the true value lies inside this particular interval, a common misreading.
For a proportion: CI = p ± z x √(p(1 - p) / n), where p is the sample proportion, n the sample size and z the multiplier for the confidence level (1.96 for 95 percent)
A worked example
Of 600 hotel guests surveyed, 42 percent say they would use a new mobile check-in. The margin of error is 1.96 x √(0.42 x 0.58 / 600) = 0.039, so the 95 percent confidence interval runs from 38.1 to 45.9 percent. Doubling the sample to 1,200 would narrow it to about plus or minus 2.8 points.
Related
Automate this in Pulse
The confidence interval around a small segment's share is wide, so a team reading a Pulse survey by segment can recruit more participants to the thinnest segment's profile until its interval is narrow enough to act on.