Sampling Methods

Sampling methods determine how units enter a study and therefore how credibly sample results can represent a population.

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Question → sample → inference. A population question leads to a sampling design, a data summary, and a conclusion with uncertainty. The return arrow requires revisiting earlier choices whenever verification exposes a design or interpretation problem.

A large sample is not automatically representative; the selection process matters more than size alone.

Census versus sample

A census attempts to measure every population member. A sample measures a subset to save time, cost, or effort.

A census can still suffer nonresponse, measurement error, outdated coverage, and processing mistakes. Sampling introduces sampling variability but can sometimes produce higher-quality measurements with available resources.

Sampling frame

The sampling frame is the practical list or mechanism from which units are selected. If it omits parts of the target population, undercoverage occurs.

Compare the frame with the population definition before drawing the sample.

Simple random sample

In a simple random sample (SRS) of size $n$, every possible sample of that size has an equal chance of selection. Assign identifiers and use a genuine random mechanism.

Choosing whoever is easiest or “randomly looking around” is not an SRS.

Worked example: school survey

A convenience sample from one lunch period would miss students with different schedules.

Common mistakes

Calling any varied sample random. Random selection requires a defined chance mechanism.

Assuming a census has no error. Nonresponse and measurement error remain.

Confusing stratified and cluster sampling. Stratified samples from every stratum; cluster samples selected clusters.

Believing size fixes convenience bias. It does not.

Ignoring frame and nonresponse coverage. Selection continues beyond the initial draw.

Quick self-check

What exact population and sampling frame are used?
Does every target unit have a known chance of selection?
Is simple random, stratified, cluster, systematic, or multistage design appropriate?
Could list order, undercoverage, or self-selection distort results?
Is sample size sufficient for desired precision without pretending to fix bias?
Are response rate, weights, and design limitations reported?