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Weighting

Adjusting how much each response counts, so the sample's composition matches known population figures.

If your sample is 70% women and the population is 51%, each woman's response can be down-weighted and each man's up-weighted so the totals reflect the population. Done well, it corrects a known imbalance on the variables you weighted by, using external figures such as a census.

It cannot correct an imbalance you did not measure, and it does not repair selection bias on anything that is not in the weighting scheme: the twenty-five men who did answer now stand in for everybody who did not, and if they are unusual, weighting amplifies them. Weights also cost precision, so your effective sample size falls even though the number of rows does not change.

If you weight, say which variables you used and what source supplied the targets. Unstated weights turn a number into something a reader cannot check.

Where it goes wrong

Heavy weights on small cells. When a handful of responses are asked to carry a whole demographic, the estimate becomes unstable rather than representative.

See also

Nonresponse bias
The error that arrives when the people who did not answer differ from the people who did, in a way that matters to your question.
Sampling frame
The actual list your sample is drawn from, which is rarely the same thing as the population you want to describe.
Cross-tabulation
A table that breaks down answers to one question by answers to another.

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