Sampling Methods
Choose a sampling design, identify coverage and nonresponse bias, and distinguish stratified, cluster, systematic and convenience samples.
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Define the population and the sampling frame
The target population is whom the conclusion is about. The sampling frame is the list or mechanism from which units can actually be selected. A survey of registered accounts excludes visitors without an account even if its selections are random.
A probability sample uses a random selection mechanism with known inclusion probabilities for covered units. They need not all be equal. A simple random sample of fixed size makes every subset of that size equally likely. The design determines appropriate weights and uncertainty calculations.
Compare designs by how people enter
| Design | Selection process | Main consideration |
|---|---|---|
| Simple random | Randomly select units from a frame | Needs a suitable frame; nonresponse remains |
| Stratified | Sample within every defined stratum | Allocation may require weights |
| Cluster | Sample groups, then units in selected groups | Within-group similarity affects precision |
| Systematic | Random start, then every kth unit | Periodicity can align with the interval |
| Convenience/voluntary | Available or self-selected participants | Inclusion probabilities generally unknown |
Selecting all units in randomly chosen schools is cluster sampling. Sampling students from each school is stratification by school. These designs are not interchangeable. Treating correlated pupils as independent can understate uncertainty.
Worked example: unequal stratum allocation
A hypothetical organization has 800 standard and 200 premium accounts. Survey 100 randomly selected accounts from each tier, with complete response. Suppose 60 standard and 80 premium respondents are satisfied.
The tier estimates are 60% and 80%. Pooling respondents gives 140/200 = 70%, but it weights the tiers equally. Weighting by population shares gives:
The estimated overall satisfaction is 64%, assuming the within-tier samples and response process support those estimates. A sampled standard account represents eight accounts and a premium account two. Design-aware standard errors also need to respect the stratum allocation; an ordinary pooled-binomial calculation is not the whole analysis.
Larger samples do not remove systematic bias
Coverage error excludes relevant units. Nonresponse can distort estimates when response differs with the outcome. Measurement error comes from how the question or instrument records the value. Random sampling error concerns variation from selecting a sample rather than a census.
Increasing sample size usually reduces random variability under a sound design. It does not repair an unsuitable frame, misleading question or voluntary participation. Random selection may still yield imbalance in one realized sample.
For sampling without replacement, the finite population correction can reduce a simple-random-sample standard error when the sampled fraction is substantial. It does not correct convenience sampling or attrition.
Practice
A researcher selects three offices at random and surveys everyone in those offices. Is this stratified or cluster sampling?
Show the explanation
Cluster sampling: only selected offices contribute respondents. Stratified sampling would sample within every defined office stratum. Office-level similarity needs consideration when calculating uncertainty.
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Read sampling distributions and study design. OpenStax explains probability sampling and sources of variation.
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