Key takeaway
An oversampled group should not silently represent the same number of population units as every other row. Keep the selection design and estimation weights with the claim.
Ask what each sampled record represents
A company selects the same number of jobs from a small specialist team and a much larger general-service team. The combined sample is convenient to review, but its raw positive fraction describes the selected rows. Before using that fraction to describe the full archive, establish the target population, sampling frame, unit and actual inclusion mechanism. A balanced inspection workload can create an unbalanced representation of the population.
Statistics Canada explains design weights in probability surveys as the inverse of a unit’s inclusion probability. It also distinguishes later estimation-weight adjustments, including those for nonresponse and auxiliary information. Those principles supply a sampling question, not a claim that an arbitrary business archive is a probability sample. If records were chosen because they were memorable or easy to obtain, an analyst cannot invent the missing selection probabilities afterward.
A complete illustrative two-stratum calculation
This hypothetical audit has a known frame of 1,000 distinct eligible jobs: 100 specialist jobs and 900 general jobs. Within each stratum, 50 jobs are selected by simple random sampling without replacement, with complete response and no duplicates. The invented sample contains 40 positives in the specialist stratum and 10 in general service. A positive has the same predefined meaning in both groups.
The inclusion probabilities are 50/100 and 50/900, giving design weights of 2 and 18. Estimated positive totals are 40 × 2 = 80 and 10 × 18 = 180. Their sum is 260; dividing by the known frame total of 1,000 gives a 26% estimated population proportion. It is an estimate under the stipulated design, not an observed count of 260 positives in the full archive.
| Hypothetical stratum | Frame / selected jobs | Selected positives | Design weight | Estimated positive total |
|---|---|---|---|---|
| Specialist | 100 / 50 | 40 | 2 | 80 |
| General service | 900 / 50 | 10 | 18 | 180 |
| Combined | 1,000 / 100 | 50 | Weights differ | 260; estimated proportion 26% |
Reconcile the estimate with the unweighted result
The selected-row fraction is (40 + 10) / (50 + 50) = 50%. Both 50% and 26% can be calculated correctly while answering different questions. In this example, the first describes the selected sample and the second estimates a defined frame quantity using the stipulated sampling design. The discrepancy is not evidence of a parser error or a reason to choose whichever percentage favors the proposed deal.
NumPy’s average documentation gives the weighted-average calculation as the sum of weighted values divided by the sum of weights. Encoding each selected job’s outcome as zero or one reproduces 260/1,000 here. Software can execute that arithmetic without establishing that the weights are appropriate. Retain the source of each weight and the design specification, rather than labeling every numeric weight column as interchangeable.
Do not turn weighted totals into an invented sample size
The audit actually inspected 100 jobs, not 1,000. A weighted total can describe represented units while uncertainty still depends on the sampling design and observations. Keep the actual selected counts and relevant design information beside the estimate. A responsible statistical reviewer must choose an uncertainty method appropriate to that design; this teaching calculation supplies no confidence interval or effective sample size.
Statistics Canada describes adjustments for nonresponse and external information separately from initial design weights. The example assumes complete response precisely to avoid pretending those adjustments were performed. In an actual audit, identify missing responses, excluded units, strata or clusters and the analyst-approved final weight version. A missing weight is an unresolved estimation input, not an instruction to replace it with zero or one.
Publish a claim with the sampling boundary attached
The completed hypothetical conclusion is an estimated 26% positive proportion for the stated 1,000-job frame under the stated two-stratum design, alongside the actual sample of 100 and its 50% selected-row fraction. It does not describe future jobs, unresolved records outside the frame or a new recipient’s workload. The design assumptions and absence of an uncertainty interval remain visible.
This decision differs from choosing case-weighted versus equal-site summaries of a held-out model test. Here the question is how selection probabilities connect an inspected sample to its population frame. Keep the frame version, selection procedure, inclusion probabilities, final weights and outcome definition with the evaluation package. If those facts are unavailable, restrict the result to the observed sample instead of manufacturing a population claim.