Sampling Weights: When and How to Use Survey Weights

What Is a Sampling Weight?

A sampling weight is a number attached to each respondent. It says how many people (or households) in the population that respondent represents. A weight of 50 means the respondent stands for about 50 population units.

The starting point is the base weight, which is 1 divided by the unit's probability of being selected. A household with a 1-in-50 chance of selection gets a base weight of 50. This only works when every in-scope unit had a known, positive chance of selection, which is the defining feature of random sampling. A convenience sample has no such probabilities, so weights cannot make it a probability sample.

Weights are not the same as the importance weights used to combine indicators; for those, see composite indicators.

When a Sample Needs Weights

• Disproportionate stratified sampling. You deliberately interview the same number in a small district and a large one so that each can be reported on its own.
• Unequal chances in multi-stage designs. Villages chosen with probability proportional to size, then a fixed number of households per village, give every household about the same chance only if the village size figures are accurate. Out-of-date sizes, or a varying number of households taken, leave households with different chances.
• Selecting one person per household. A person in a large household has a smaller chance of being picked than one in a small household.
• Differential response. Some groups answer more often than others.

If every unit had the same chance and nobody was missed, the weights are all equal and a weighted analysis returns the unweighted answer.

Three Layers of Weighting

Each layer adds assumptions. Document which were applied, the classes used and the source of any population totals.

A Worked Example

A fictional survey measures the share of households with a functioning latrine. District A has 10,000 households and District B has 2,000. The team interviews 200 households in each so that both districts can be reported separately. All numbers are made up.

The unweighted share across all 400 is 220 / 400 = 55%. That figure over-counts District B, which makes up one-sixth of the households but half of the sample.

The weighted share is (50 x 80 + 10 x 140) / (50 x 200 + 10 x 200) = 5,400 / 12,000 = 45%. This is the estimate for the 12,000 households in the two districts together, assuming the frame is complete and everyone answered.

Both district-level figures (40% and 70%) are right as they stand. Weights matter when you combine districts.

Suppose instead that 220 households were selected in District A and 200 responded. The base weight is 10,000 / 220 = 45.5. The nonresponse adjustment is 220 / 200 = 1.1, which gives an adjusted weight of 50. That adjustment assumes the 20 nonrespondents resemble the 200 respondents in that district. If this is doubtful, check it with nonresponse analysis rather than assuming it.

The Cost of Unequal Weights

Weights remove bias from unequal selection but add variance. A common approximation, due to Kish, is a weighting design effect of n x (sum of squared weights) / (sum of weights) squared. It is approximate, and it is closest when the weights are unrelated to the outcome. Here the weights and the outcome both differ by district, so a calculation that uses the district results gives a somewhat lower figure, about 1.39.

In the example: the sum of weights is 12,000, the sum of squared weights is 520,000, and n is 400. The factor is 400 x 520,000 / 12,000 squared = 1.44. The 400 interviews carry the information of about 277 equally weighted ones. This is a cost of the design, not an error, and it grows when a few respondents carry very large weights.

Very large weights can be capped ("trimmed") by a specialist, but trimming trades bias for variance and should be documented.

What Weights Cannot Do

• Create coverage. If a group is missing from the sampling frame, no weight represents it. Households in informal settlements missing from a list are not recovered by weighting the listed ones.
• Fix measurement error. Wrong answers are weighted as faithfully as right ones.
• Replace a design. Weighting a small, self-selected sample to match census totals does not make it a probability sample. Its estimates depend on a model that can fail.
• Give correct precision by themselves. Standard errors must also use the strata and clusters. Ignoring the clusters usually makes confidence intervals too narrow, and ignoring the strata can make them too wide.

Weights in Analysis

Use survey commands that accept the weight, the strata and the primary sampling units together. Report whether tables are weighted, and show the unweighted sample size beside weighted percentages. For regression, the question of whether to weight depends on the purpose; Gelman (2007) reviews the difficulties and an alternative, and a statistician's advice is worthwhile for complex cases. For a full case that carries weights through to an interval, see reading a survey estimate.

When an AI tool drafts survey analysis code or a results table, check that the weight variable is named in the call, that the design (strata, clusters) is declared, and that the output sample sizes match your records.

Frequently Asked Questions

Do I Need Weights if I Used Simple Random Sampling?

If every unit had the same selection chance and there was no differential nonresponse, the weights would all be equal. Many teams still apply nonresponse adjustments or calibrate to population totals, which changes the weights.

Should I Report Weighted or Unweighted Numbers?

For population estimates from a probability sample with unequal selection chances, report weighted estimates and the unweighted counts. Unweighted figures describe only the people interviewed.

Where Do the Selection Probabilities Come From?

From the sampling plan and field records: the number of units in each stratum, how clusters were chosen, and how many households were selected within them. Keep these records during fieldwork, because rebuilding them afterward is difficult.