Easy to use.
Open to inspection.
Sixteen people. One survey question. Follow every answer from the original response to the percentage, the test and its assumptions.
A small, synthetic teaching example. These people and weights are invented, so you can check the arithmetic by hand. They are not evidence about a real population.
Would you consider this service?
Two independent groups · A and BThe calculation records could not be loaded. Your choices are still here.
Loading the calculation records…
The people behind the percentages
Each tile is one person. The number below their answer is their contribution weight.
Same percentages.
Different uncertainty.
How you estimate uncertainty matters. Compare the method Velocity uses for this table with a design-based R reference.
Why don’t the p-values match?
Velocity’s ordinary independent-column comparison uses a pooled Pearson test without weights and a second-order Rao–Scott test with fixed weights. The weighted test uses the answers and squared weights to linearize a 2×2 association, with an F reference. Kish effective bases remain a weight-dispersion diagnostic. Neither method models a complete sampling design.
The R reference uses survey::svydesign, svymean, svyby and
svycontrast. Its Taylor linearization variance depends on the actual answers and their
weights. The two groups are declared as strata, with independent respondents, no clusters and no
finite-population correction. The design is formed on the selected contributing population.
R’s displayed test also uses a t distribution with the design degrees of freedom. The downloadable reference includes a normal-reference p-value as well, so you can separate the variance difference from the distribution difference.
The difference interval below is R’s pointwise 95% t interval. The bars above are Velocity’s per-group Wilson intervals on Kish effective bases. They answer different questions and are labelled separately.
What can this example tell me?
It verifies the displayed estimates against an independent implementation and shows how the declared methods differ. Sixteen invented observations cannot establish performance across all survey designs.
Neither calculation corrects selection or nonresponse bias, accounts for uncertainty in estimated weighting targets, or demonstrates a causal effect. The reference is conditional on the chosen contributing population. A real clustered, stratified or repeated-measures study needs its own design and method.
A p-value is not the probability that the finding is true. Look at the size of the difference, its uncertainty and the research design together. This lesson contains one comparison, with no multiple-testing correction.
Follow the calculation.
Open the exact contributions, check the bases, then reproduce the result outside Velocity.
1. From answers to weighted percentages
2. From weights to an effective base
Kish effective n = (sum of weights)² ÷ sum of squared weights. Equal weights give the raw number of people. Unequal weights reduce this dispersion-based effective base. Multiplying every weight by the same positive constant leaves it unchanged.
An effective base describes this approximation. It does not certify representativeness or substitute for a complete survey-design variance.
3. Inspect all sixteen original responses
| Person | Group | Raw answer | Label | Original weight | Current weight | In base? |
|---|
4. Reproduce and inspect the evidence
This page selects from 12 frozen calculation records. They were generated through Velocity’s production
crosstab pipeline and independently through R survey; the page does not run R or ask an AI
model to calculate numbers.
- Original data · CSV
- Independent reference · R script
- R survey results · JSON
- Production results, version and source hashes · JSON
- Production receipt generator · TypeScript (requires the Velocity checkout)
- Download this comparison · JSON
To reproduce the R results, put the CSV and R script together, install survey and
jsonlite, and run Rscript reference.R. Versions are recorded in the results.
How do Q and Displayr handle weights?
Their documentation describes Taylor series linearization for automatic table tests of means and proportions, and Kish-based methods for other calculations. Q also exposes an extra design-effect setting. Matching percentages does not guarantee matching tests.
Q’s weighting methodology · Displayr’s worked weighting example
Documentation checked 8 October 2026. The R reference here is a declared teaching design, not a captured Q or Displayr result. Product comparisons must also match bases, variance methods, test distributions and correction settings.