Community medicine chapters
Sampling techniques and sample size
Why we sample, the probability methods (simple random, systematic, stratified, cluster, multistage) and non-probability methods (convenience, purposive, quota, snowball), sampling error and bias, and how to calculate sample size for a prevalence or a mean, with worked examples.
- Probability sampling gives every member a known, non-zero chance of selection (simple random, systematic, stratified, cluster, multistage) and allows results to be generalised; non-probability methods (convenience, purposive, quota, snowball) are easier but prone to bias.
- Stratified sampling divides the population into similar subgroups and samples each; cluster sampling randomly selects whole groups (villages, schools) and is cheaper but less precise (design effect).
- Sample size for a prevalence: n = Z² × p × q ÷ d²; for a mean: n = Z² × σ² ÷ d² (Z = 1.96 for 95% confidence).
On this page
Overview
We usually cannot study everyone. A sample is a part of the population chosen to represent it. Good sampling lets us draw valid conclusions about the whole population at a fraction of the cost.
Key terms
- Population (universe): all the units of interest (for example all children under 5 in a district).
- Sampling unit: the unit being selected (a person, household, village).
- Sampling frame: a list of all the units from which the sample is drawn (for example a household register or voter list).
- Sampling error: the difference between the sample result and the true population value that arises by chance; it falls as sample size increases.
- Sampling (selection) bias: a systematic difference because the sample is not representative; a bigger sample does not fix it.
Probability (random) sampling
Each unit has a known, non-zero chance of being selected. Results can be generalised and sampling error can be calculated.
| Method | How it works | Strengths and uses |
|---|---|---|
| Simple random sampling | Every unit has an equal chance; select by lottery, random number tables or computer | Simple, unbiased; needs a full sampling frame; fine for small, uniform populations |
| Systematic random sampling | Select every k-th unit after a random start, where k = N ÷ n (the sampling interval) | Easy in the field (houses on a street, patients in a register); risk of bias if the list has a repeating pattern |
| Stratified random sampling | Divide the population into homogeneous strata (age, sex, urban/rural, province), then sample randomly within each | Ensures all subgroups are represented; improves precision; can compare strata |
| Cluster sampling | Randomly select whole groups (clusters) such as villages, schools or blocks, and study all or some units in them | Cheaper and practical when no list of individuals exists; less precise (people in a cluster are alike), so a larger sample is needed |
| Multistage sampling | Sampling in stages: for example districts → villages → households → individuals | Used in large national surveys (PDHS, National Nutrition Survey) |
Stratified sampling: strata are similar inside, and you sample from every stratum. Cluster sampling: clusters are mixed inside (like mini-populations), and you sample only some clusters.
The WHO EPI coverage survey classically uses cluster sampling with 30 clusters of 7 children (the "30 × 7" method), chosen with probability proportional to size.
Population list N = 1,000 households; sample needed n = 100
Sampling interval k = N ÷ n = 1,000 ÷ 100 = 10
Pick a random start between 1 and 10, say 7
Households chosen: 7, 17, 27, 37 … 997 (100 households)
Non-probability sampling
The chance of selection is unknown. Easier and cheaper but more open to bias; results cannot be reliably generalised. Common in qualitative research and pilot studies.
| Method | How it works |
|---|---|
| Convenience | Whoever is easiest to reach (patients in today's OPD) |
| Purposive (judgmental) | Deliberately chosen for their knowledge or experience (key informants) |
| Quota | Fill set numbers in categories (for example 50 men and 50 women), but not randomly |
| Snowball | Participants recruit others; for hidden or hard-to-reach groups (drug users, sex workers) |
Sample size
The sample must be large enough to give a precise estimate or to detect a real difference (adequate power), but not wastefully large.
What increases the required sample size?
- Smaller margin of error (more precision): smaller d.
- Higher confidence level (99% instead of 95%).
- For prevalence, p near 50% (p × q is largest at 0.5).
- More variability (larger SD) for means.
- Smaller differences to detect; higher power wanted.
- Cluster sampling (multiply by the design effect).
- Expected non-response or loss to follow-up.
Formula for estimating a prevalence (proportion)
n = Z² × p × q ÷ d²
- Z = 1.96 for 95% confidence.
- p = expected prevalence (from earlier studies or a pilot); q = 1 − p.
- d = absolute precision (margin of error), for example 0.05.
Expected prevalence of anaemia p = 30% = 0.3 → q = 0.7
Absolute precision d = 5% = 0.05; 95% confidence → Z = 1.96
n = Z² × p × q ÷ d²
= (1.96)² × 0.3 × 0.7 ÷ (0.05)²
= 3.8416 × 0.21 ÷ 0.0025
= 0.8067 ÷ 0.0025 = 322.7 → 323
Allow 10% non-response: 323 ÷ 0.9 = 358.9 → 359
If cluster sampling with design effect 2: 323 × 2 = 646 (before non-response)
Formula for estimating a mean
n = Z² × σ² ÷ d²
- σ = expected standard deviation; d = acceptable error in the units of measurement.
Estimate mean systolic BP; expected SD σ = 10 mmHg; want precision d = 2 mmHg; 95% confidence
n = (1.96)² × 10² ÷ 2²
= 3.8416 × 100 ÷ 4 = 96.04 → 97 (always round up)
Always round up sample size calculations; rounding down gives slightly less precision than planned.
Sample size for comparing groups
Studies that compare two groups (trials, cohort and case-control studies) also need the significance level (α), the power (1 − β), usually 80% or 90%, and the smallest difference worth detecting. Software such as OpenEpi or G*Power is used.
Choosing a method in practice
- Have a full list and a uniform population → simple random or systematic.
- Important subgroups must be represented → stratified.
- Large, spread-out population with no list → cluster or multistage.
- Exploring experiences in depth → purposive (qualitative).
- Hidden population → snowball.
Expect: definitions (population, sampling frame, sampling error vs bias), each probability method with an example, stratified vs cluster sampling, the EPI 30 × 7 cluster survey, the systematic sampling interval, non-probability methods (especially snowball and purposive), the sample size formula for a proportion and a mean with a calculation, and what increases sample size.
Quick revision
- Probability: simple random, systematic (k = N ÷ n), stratified, cluster, multistage.
- Stratified: similar strata, sample each; improves precision.
- Cluster: whole groups; cheaper, less precise; EPI 30 × 7.
- Non-probability: convenience, purposive, quota, snowball.
- Sampling error falls with sample size; bias does not.
- Prevalence: n = Z² p q ÷ d². Mean: n = Z² σ² ÷ d². Round up; add for non-response and design effect.
Written by The House Job from Excel Community Medicine and Park's Textbook of Preventive and Social Medicine (named in the UHS PGET syllabus).
FAQ
What is a sampling frame?
A complete list of all the units in the population from which a sample is drawn.
What is the difference between stratified and cluster sampling?
In stratified sampling the population is divided into similar subgroups and a sample is taken from each; in cluster sampling whole groups are selected at random and only those groups are studied.
What is the formula for sample size to estimate a prevalence?
n = Z² × p × q ÷ d², where Z is 1.96 for 95% confidence, p is the expected prevalence, q = 1 − p and d is the margin of error.
Which sampling method is used to reach hidden populations?
Snowball sampling.