Sampling methods
- Concept
How a part of the population is chosen for study so that it stands for the whole and the error can be calculated.
What it is
Sampling selects the individuals to be studied from a sampling frame, the list or map of all the units in the population. In probability sampling (simple random, systematic, stratified, cluster and multistage) every unit has a known chance of being chosen, which lets the sampling error be estimated. Non-probability sampling (consecutive, convenience, quota, snowball) is cheaper but does not guarantee representativeness.
Key facts
- Systematic sampling interval: k = N / n.
- Design effect of cluster sampling: DEFF = 1 + (m − 1) × ICC, with m people per cluster and ICC the intracluster correlation.
- With m = 30 and ICC = 0.02: DEFF = 1 + 29 × 0.02 = 1.58; 90 pupils by clusters are worth about 90 / 1.58 ≈ 57 by simple random sampling.
Worked example
- Data: a sampling frame of 1 200 pupils at a school (complete list); a sample of 80 is wanted.
- Systematic sampling: k = 1 200 / 80 = 15. A random start between 1 and 15 is drawn: 7.
- Numbers 7, 22, 37, 52… are chosen. The last is 7 + 15 × 79 = 1 192. Total: 80 pupils.
- Proportional stratified by shift: morning 600, afternoon 400, evening 200; sampling fraction 80 / 1 200 = 1/15.
- Per stratum: 600/15 = 40; 400/15 = 26.7 → 27; 200/15 = 13.3 → 13 (rounded). Sum 80; each stratum is drawn at random.
- Cluster: 40 classes of 30 pupils; 3 whole classes are drawn, 90 pupils. Cheaper, but less precise.
- Reading: all three are probability methods; interviewing the first 80 pupils to arrive at school would be a convenience sample.
Comparison of sampling methods
| Method | How it is done | Advantage | Limitation |
|---|---|---|---|
| Simple random | Units drawn from a complete list | Simple to analyse | Needs a complete frame; may miss small groups |
| Systematic | Every k-th unit from a random start | Easy in the field | Bias if the list is periodic |
| Stratified | Drawn within each stratum | More precise; secures subgroups | Requires knowing each unit's stratum |
| Cluster | Whole groups drawn | Cheap; no list of individuals needed | Less precise (design effect) |
| Multistage | Drawn in several successive stages | Workable in large populations | More complex analysis |
| Non-probability | Consecutive, convenience, quota, snowball | Quick and cheap | No guarantee of representativeness |
Markers
- N
- n
- k
- DEFF
- ICC
In practice
- National health surveys and vaccination coverage surveys use multistage cluster sampling.
- In a clinical trial the sample is usually consecutive and non-probability; what is random is the allocation, not the selection.
Common pitfalls
- Confusing random sampling (who is studied) with random allocation (which group each person gets).
- Analysing a cluster sample as if it were simple random: the confidence intervals come out too narrow.
- Using an out-of-date or incomplete sampling frame.
Test yourself
Think of the answer, then tap the question to see it.
There are 2 000 records and a systematic sample of 100 is wanted. What is the interval?
k = 2 000 / 100 = 20: one record in every 20 from a random start between 1 and 20.
What is the advantage of stratified sampling?
It improves precision and ensures the subgroups defined by the stratifying variable are represented.
Why is cluster sampling less precise?
Because people in the same cluster resemble each other; the design effect measures this.
Is random sampling the same as random allocation?
No: sampling decides who is studied (external validity); allocation decides which group each person gets (internal validity).
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: World Health Organization Vaccination Coverage Cluster Surveys: Reference Manual (World Health Organization, 2018); Collecting Data (Centers for Disease Control and Prevention (The CDC Field Epidemiology Manual), 2024).
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Representative model, for educational purposes only.