Sampling Methods

Simple random sampling

For a simple random sample of fixed size $n$ without replacement, every possible subset of $n$ population units has the same chance of selection. Consequently, each unit has inclusion probability $n/N$, where $N$ is the population size.

From 100 listed learners, a simple random sample of 20 gives each learner probability $20/100=0.2$. Number the complete frame, select 20 distinct numbers randomly, and contact the corresponding learners. A genuine random-number procedure is different from asking a person to choose numbers that “look random.”

Equal individual inclusion probabilities are not enough to establish simple random sampling. Some other designs give every learner the same chance but allow only a restricted set of possible groups. That distinction matters for variance calculations.

Systematic sampling

Systematic sampling selects every $k$th unit after a random start. For an illustrative list of 100 learners and a sample of 25,

If the randomly chosen start is 3, select $3,7,11,\ldots,99$. There are 25 selected positions. The four possible starts produce only four possible samples, unlike a simple random sample of 25, which allows every 25-person subset.

Check the ordering of the list. If a repeating feature aligns with the interval, one realised sample can be very unbalanced. A list with a leader in every fourth position could produce a sample of only leaders or no leaders. A properly randomised start can preserve equal inclusion probabilities and an unbiased mean estimator, while this periodicity creates large sampling variability. It is not the same as inevitable selection bias.

Stratified sampling

A stratified design divides the population into non-overlapping groups and samples within every group. Groups might be year levels or regions, provided the necessary information is available on the frame before selection.

Suppose a synthetic population contains groups of 240, 180 and 180 learners, and a total sample of 60 is allocated proportionally. The allocations are

Each group then supplies a random sample of the allocated size. This protects against accidentally collecting too few observations from a group that needs separate description. A design can deliberately oversample a smaller group, but population estimates must then use appropriate weights.

Stratification can improve precision when the grouping is relevant to the outcome. It is not a guarantee that any arbitrary grouping will improve every estimate.

Cluster and multistage sampling

In one-stage cluster sampling, the population is divided into groups, some groups are selected randomly, and all eligible units in those selected groups are included. Selecting four of twelve classes and surveying every learner in those classes is an example.

Stratification takes some units from every stratum. Cluster sampling takes units from selected clusters. This is the central distinction, even though both begin with groups.

A multistage design adds selection within the chosen clusters. For example, select schools, then classes within those schools, then learners within those classes. This may reduce travel and administrative costs. It also changes the uncertainty calculation: learners in the same class may be more alike than learners selected independently from the whole population.

Do not treat 120 records from a few classes as automatically equivalent to 120 independently selected learners. The number and structure of clusters matter.

Convenience, voluntary and quota samples

A convenience sample uses readily accessible units. A voluntary-response sample relies on people deciding to respond, such as an open website poll. A quota sample fills predetermined category counts but may select people within each category non-randomly.

These methods can be useful for pilot testing, exploring a question or working under practical constraints. They do not automatically justify the same margin-of-error calculation as a probability sample. Matching a few demographic proportions also does not establish balance on unmeasured characteristics related to the outcome. Statistics Canada’s non-probability overview discusses these limits.

The right conclusion may be a description of respondents, not an estimate for all eligible people. Report the selection process rather than hiding it behind a large sample size.

Selection does not guarantee response

After drawing a random sample, keep a record of who was selected and who responded. Replacing a nonrespondent with the nearest available person changes the design. A systematic follow-up process, accessible response modes and clear questions can reduce missingness without pretending it has disappeared.

Where nonresponse adjustments are used, record the assumptions. A weight based on known year level cannot fully correct nonresponse caused by an unmeasured outcome unless the adjustment model is adequate.

Sampling also differs from experimental assignment. Randomly splitting volunteers between two learning conditions can support a comparison within those volunteers, but does not make the volunteer recruitment a random population sample.

Choose the design from the question

For a small, complete list and a general population summary, simple random sampling is often straightforward. If separate year-level estimates matter, stratification may be useful. If units are geographically dispersed, clusters may reduce cost, but the analysis must reflect the grouping.

Plan the target, frame, unit, selection rule, sample size, collection period, follow-up and analysis together. Choose a design that provides defensible evidence for the question within the available time and resources.

Related topics

Use Sampling Bias to test a design for systematic exclusions. Populations and Samples explains weighting and scope, and Confidence Intervals later connects design assumptions to uncertainty.