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Uniform sampling fraction
Definition
A uniform sampling fraction means that the same proportion of units is selected from each stratum of a stratified population. If a stratum contains Nh units and contributes nh sampled units, the fractions nh/Nh are equal across strata. This corresponds to allocating the sample in proportion to stratum sizes. It does not mean taking the same number from every stratum, unless the strata themselves have equal sizes.
What it means
Suppose one group contains twice as many population units as another. Under a uniform sampling fraction, it contributes twice as many sampled units, apart from practical rounding. The sample therefore preserves the population's stratum proportions by design. With simple random sampling within each stratum and complete response, all units have the same inclusion probability and the same basic design weight. More complex selection within strata can change that conclusion, so the fraction alone is not a complete description of the sampling design.
How it works
Choose the overall sample size n and identify stratum population sizes Nh, which sum to N. Proportional allocation sets nh approximately equal to n times Nh/N, giving a common fraction n/N when integer counts permit exact allocation. Select units using the specified probability method within each stratum. If rounding is needed, document the resulting fractions and weights. For inference, retain stratum information and use a variance estimator appropriate to the design. Equal basic weights do not remove the value of stratification or make every survey analysis identical to simple random sampling.
Three practical examples
Example 1: An employee survey samples 10% of staff within each department. Example 2: A business audit samples the same percentage of records from each product category. Example 3: An AI adoption survey allocates interviews proportionally across company-size strata. These examples describe uniform fractions only if the stated populations and selection counts are accurate. Equal interview quotas without probability selection do not automatically provide the same design-based properties.
Think of it this way
Think of taking one scoop from every ten scoops in several containers of different sizes. Larger containers contribute more scoops, but the share removed is the same. Taking one scoop from every container would instead give smaller containers a larger sampling fraction. The distinction is between matching proportions and matching counts.
Worked example
Consider three strata containing 120, 280 and 600 units, for a total of 1,000. A 100-unit sample with a uniform fraction of 0.10 selects 12, 28 and 60 units respectively. Under simple random sampling within each stratum, every unit has inclusion probability 0.10 and basic weight ten. Suppose the observed success proportions are 0.25, 0.50 and 0.60. The estimated overall proportion is 0.12 times 0.25 plus 0.28 times 0.50 plus 0.60 times 0.60, equal to 0.53. The corresponding sample success counts are three, fourteen and thirty-six, so the unweighted overall sample proportion is also 53/100. This equality follows from proportional allocation and equal within-stratum weights; it need not survive unequal response or different selection probabilities.
Illustrative case study
In this fictional case study, Willow Workforce plans an employee survey across divisions of very different sizes. A first proposal assigns the same number of invitations to every division. Analysts explain that this creates different sampling fractions. The team chooses proportional allocation for its main company-wide estimate and records the division sizes used. It also recognizes that the smallest division may have too few respondents for a precise separate estimate, prompting a discussion of whether deliberate oversampling would better serve that additional objective.
Common misconceptions and mistakes
Common mistakes include confusing equal sample counts with equal fractions, calling a sample self-weighting without checking within-stratum selection, and ignoring nonresponse. Uniform selection fractions do not imply equal final respondent fractions when response rates differ. Another mistake is assuming proportional allocation is always the most statistically efficient choice. Different within-stratum variability, costs or priorities for subgroup estimates can justify other allocations. Those designs require suitable weighting rather than being inherently invalid.
Business use
Businesses can use uniform fractions when an overall population summary is a central goal and proportional representation is operationally convenient. Verify the stratum counts and decide whether subgroup reporting needs more observations than proportional allocation provides. Preserve design weights even when they are initially equal, because adjustments may be required later. Report selection and response separately. A design that is simple to explain still needs appropriate analysis of stratification, finite population sampling and any changes between the planned sample and achieved responses.
People also ask
Does uniform fraction mean equal numbers from every stratum?
No.
When are those equivalent?
When stratum sizes are equal.
Does a common fraction guarantee equal weights in every possible design?
No; the within-stratum selection method matters.
Can nonresponse disturb equal weighting?
Yes.
Is proportional allocation always optimal?
No; efficiency, cost and subgroup precision may favor another allocation.
Check your understanding
What sample comes from the 280-unit stratum at a 10% fraction?
Answer: Twenty-eight units.
What is the basic weight under the stated simple random design?
Answer: Ten.
Why does the overall unweighted sample proportion equal 0.53?
Answer: The sample proportions across strata match the population proportions.
Would selecting twenty from each stratum preserve a uniform fraction?
Answer: No, because the stratum sizes differ.
Related terms
- Stratified sampling
- Sampling fraction
- Related terms include proportional allocation
- design weight
- self-weighting sample and disproportionate allocation
Learn next
Learn next how Neyman allocation balances stratum size and variability, and how unequal fractions affect weighted estimates. Compare designs that prioritize an overall mean with designs that prioritize small subgroups. Then examine why the appropriate variance calculation retains the stratification structure even when basic weights are equal.
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Sources
Source: OECD, Glossary of Statistical Terms, Uniform sampling fraction, https://www.oecd.org/content/dam/oecd/en/publications/reports/2008/09/oecd-glossary-of-statistical-terms_g1gh9ad7/9789264055087-en.pdf. This primary institutional glossary defines proportional selection across strata. The three-stratum allocation, weights and success-rate calculation are original and independently checked. The employee-survey case is fictional and does not claim measured results.
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