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# 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.

Updated Nov 13, 2026

## Key points

- Simple random: every unit has the same chance; it needs a complete frame.
- Systematic: every k-th unit (k = N / n) from a random start; it fails if the list has a periodic pattern.
- Stratified: sampling within groups (strata) defined by a variable; it improves precision and secures small groups.
- Cluster: whole groups are drawn (villages, schools); cheap but less precise (design effect).
- Multistage: several stages (towns → blocks → households); used by large health surveys.
- Consecutive sampling is the most used non-probability method in clinical research and the least biased of them.

On this page

- The basics Key points
- What it is
- Key facts
- Worked example
- Comparison of sampling methods
- Markers
- In practice
- Common pitfalls
- Memory aid

- Study Test yourself

- Connections Connections

## 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.

## Memory aid

‘List, leap, layer, lump’: simple, systematic, stratified and cluster, from least to most field savings.

## 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).

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## Connections

## Related 5

- [Sample size](https://durgical.com/en/epidemiology/sample-size/)
- [Standard error](https://durgical.com/en/epidemiology/standard-error/)
- [Study population and selection criteria](https://durgical.com/en/epidemiology/study-population-and-selection-criteria/)
- [Cross-sectional study](https://durgical.com/en/epidemiology/cross-sectional-study/)
- [Selection bias](https://durgical.com/en/epidemiology/selection-bias/)

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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](https://www.who.int/publications/i/item/WHO-IVB-18.09) (World Health Organization, 2018); [Collecting Data](https://www.cdc.gov/field-epi-manual/php/chapters/collecting-data.html) (Centers for Disease Control and Prevention (The CDC Field Epidemiology Manual), 2024).

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Representative model, for educational purposes only.

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