Survey methodology
Survey Weighting and Raking for Crosstabs
In a weighted crosstab, each eligible respondent contributes their positive numeric weight to the cell instead of contributing one. Use weighted percentages for the estimate, keep the unweighted respondent base beside them, and treat ordinary p-values or significance letters as approximate unless the weights are genuine frequency weights. Raking creates calibration weights by iteratively matching trusted population margins.
Published by crosstabs.com · Named statistical review pending · Last updated
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Open the workspace →First identify what your weight means
A design weight reflects unequal selection probabilities. A calibration or raking weightadjusts a starting weight until selected sample margins align with external targets. A frequency weightsays that one record represents repeated identical records. These can all produce weighted counts, but they do not justify the same variance or significance calculation.
Crosstabs accepts a prepared positive numeric weight column for descriptive tables. It does not currently create raked weights in the workspace or implement strata, clusters, finite-population corrections, replicate-weight variance, or Rao–Scott tests. For complex-sample inference, calculate design-aware standard errors and tests in specialist survey software.
A defensible weighting workflow
- Document the sampling design, starting weight, target source, target date, variables, category mappings, and missing-value rules.
- Check that every positive target category has observed cases. Sparse or empty cells cannot be repaired by an extreme weight.
- Rake outside the current Crosstabs workspace, inspect convergence, weight spread and any trimming, then save the validated result as a numeric column.
- Open the Crosstabs workspace and select that column under Weight. Compare weighted and unweighted output before reporting.
- Publish the weighted estimate, unweighted base, exclusions, weight method, targets, trim rule, and the correct design-aware uncertainty calculation.
How raking changes the weights
For one target margin at a time, raking multiplies every case in category g by the target total for gdivided by its current weighted total. It cycles through all target variables until the largest margin error is within the chosen tolerance or the iteration limit is reached.
Always inspect convergence and the minimum, maximum and spread of the resulting weights. Trimming extreme weights can reduce variance, but it also moves the achieved margins away from their targets; document both the rule and the post-trim discrepancy.
Formula
Definition
weighted cell = Σ wᵢ I(rowᵢ = r, columnᵢ = c)
weighted column % = weighted cell / Σ wᵢ in column c
weight-spread effective n = (Σ wᵢ)² / Σ wᵢ²
- wᵢ
- = the positive finite weight for respondent i
- I(·)
- = 1 when the record belongs in the cell, otherwise 0
- effective n
- = a weight-dispersion diagnostic—not a replacement for a full design-based effective sample size
Worked example
Worked example
When to use it
Use it when
- Estimating survey percentages after a documented weighting process.
- Comparing weighted and unweighted crosstabs to diagnose material shifts.
- Applying a validated positive numeric frequency, design, or calibration weight.
Not the right tool when
- Using weights to conceal coverage gaps or empty target categories.
- Calling ordinary weighted-count p-values design-corrected inference.
- Reporting a weighted total as the number of respondents interviewed.
How to interpret it
Rule of thumb
Weighting changes who contributes how much to an estimate; it does not create new respondents or automatically fix bias. A useful release table shows the weighted result, the unweighted base, the weight specification, and design-appropriate uncertainty together.
What Crosstabs does—and does not claim
The workspace multiplies eligible rows by the selected weight, calculates weighted counts and percentages, retains unweighted diagnostics, and excludes invalid weights with a visible warning. Fisher's exact test is hidden for weighted 2×2 tables because it requires unweighted integer frequencies.
The displayed chi-square, p-values, residuals, effect sizes and significance letters use weighted counts and carry an approximation warning. They are not a complex-survey variance estimator. See the full statistical methods and limitations before publishing inferential claims.
Frequently asked questions
- Should a weighted crosstab show weighted or unweighted bases?
- Keep both. Report weighted counts or percentages for the estimate, and retain the unweighted respondent base for sample-size and data-quality diagnostics. A weighted total is not the number of people interviewed.
- What is raking in survey weighting?
- Raking, also called iterative proportional fitting, repeatedly adjusts case weights so weighted marginal distributions match known population targets for variables such as age, region, and gender. It matches the specified margins; it does not guarantee every joint subgroup is represented well.
- Can I run chi-square and significance letters on weighted data?
- Only with care. Ordinary chi-square and column-proportion tests treat weighted cell totals like frequency counts. That is appropriate for genuine frequency weights, but only approximate for design or calibration weights. Complex samples need design-aware variance estimation, such as methods that account for strata, clusters, replicate weights, or Rao–Scott corrections.
- Does Crosstabs create raked weights?
- Not in the current workspace. Create and validate the weight in a survey-weighting package or your research workflow, add it as a positive numeric column, then select that prepared column as the weight in Crosstabs.
- What happens to zero, negative, missing, or non-numeric weights?
- Crosstabs excludes those rows from the weighted table and reports how many were excluded. The selected weight must be finite and greater than zero.
References & further reading
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