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Sample size

Also called n

The number of responses in your analysis. It affects the precision of your estimates.

Sample size is usually written as n. For a completed-response analysis, it counts the responses you use, excluding invitations and unfinished responses. It is one of the factors that determines precision.

Under the usual sampling assumptions, the margin of error shrinks in proportion to the square root of n. Increasing a sample from 100 to 400 roughly halves that margin. Further precision requires progressively more responses.

Population size matters much less than people expect. Estimating something about a country of 60 million and about a town of 60,000 needs roughly the same number of responses, unless your sample is a large share of the population, in which case the finite-population correction narrows the margin.

Worked example

At 95% confidence and a margin of ±5 percentage points, a large population needs 385 completed responses. At a 20% response rate, that means inviting about 1,925 people.

Where it goes wrong

Sizing the whole survey and then reporting subgroups. If you need to say something about first-year students specifically, it is their n that decides the margin, not the survey's.

See also

Margin of error
An estimate of sampling uncertainty around a survey percentage, stated at a chosen confidence level.
Response rate
The share of invited people who completed the survey.
Confidence interval
The range your result is consistent with, and the confidence level is how often that kind of range would contain the truth.

All 35 terms

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Put it into practice in your next survey.