Stratified sampling divides a population into non-overlapping groups, then selects a probability sample within each group. Every population member belongs to one stratum. It can support subgroup analysis when the sampling frame contains the information needed to form the groups.
Worked example: a campus study-space survey
Imagine an authorised list of 1,000 enrolled students: 600 undergraduates, 300 taught postgraduates and 100 research postgraduates. You plan to select 100 students. For this invented example, everyone appears once, programme type is known and the list covers the population you intend to discuss.
| Stratum | Population | Population share | Proportional sample |
|---|---|---|---|
| Undergraduate | 600 | 60% | 60 |
| Taught postgraduate | 300 | 30% | 30 |
| Research postgraduate | 100 | 10% | 10 |
| Total | 1,000 | 100% | 100 |
The proportional allocation is sample size × stratum population / total population. Here the undergraduate allocation is 100 × 600 / 1,000 = 60. Select those 60 randomly from the undergraduate list, then independently select 30 and 10 from the other lists. Approaching any 60 undergraduates who happen to be available would not implement this random selection plan.
Why choose a different allocation?
Ten research postgraduates may be too few for a useful subgroup comparison. You might plan a larger sample from that group while staying within your total budget. The decision should follow the question, expected variability and precision requirements, with appropriate statistical advice.
Consider a separate hypothetical design selecting 30 students from each group. The sample then contains equal group numbers although the population proportions are 60%, 30% and 10%. An unweighted overall average gives each group one-third of the influence.
A simple weighting illustration
Suppose all selected students respond and the observed proportions favouring longer opening hours are 50%, 60% and 80% respectively. Weighting those group estimates by population share gives 0.60 × 0.50 + 0.30 × 0.60 + 0.10 × 0.80 = 0.56, or 56%. The unweighted mean of the three group percentages is about 63.3%.
These invented values demonstrate why allocation matters. They are not a precision calculation or a complete survey-analysis recipe. Actual analysis must account for selection probabilities, non-response, coverage and the design when estimating uncertainty.
Stratified, quota or cluster?
A quota plan can also target group numbers but does not necessarily randomly select people within groups. In a cluster design, selected groups provide the sampled units, rather than independently sampling from every stratum. Describe the selection procedure rather than relying on the label alone.
Methods paragraph to adapt
The sampling frame was divided by programme type into mutually exclusive strata. A proportional allocation of 60, 30 and 10 students was selected using independent random draws within the three lists. Eligibility, frame coverage and response numbers are reported separately. Analysis followed the stated sampling design and considered non-response.
Use that paragraph only if it matches what you did. State the frame date, exclusions, randomisation procedure, invitations, responses and any weighting. Avoid calling the final respondent group automatically representative.
Method background: Statistics Canada: probability sampling. The campus allocation and numerical examples are original teaching material.
Compare convenience sampling, snowball recruitment and the sampling-methods guide.