Population, Sample and Sampling

Overview

Medical research rarely measures every person to whom the research question applies. Instead, investigators select a sample, collect data from that sample and use the findings to learn about a defined population.

Sampling is not merely a practical step for reducing workload. It determines who had an opportunity to enter the study, which population the findings can describe and how uncertainty should be calculated. Probability-sampling theory provides a formal connection between selected observations and a finite population when selection probabilities are known [1].

A large sample does not automatically represent a population. A smaller, carefully selected probability sample may support more credible population estimates than a much larger convenience sample. Sample selection, nonresponse, measurement quality and analysis must therefore be planned together.

Why this matters

Suppose a clinic surveys 2,000 people who respond to a social-media link about hypertension. The sample is large, but adults without internet access, people who do not follow the clinic and those uninterested in hypertension may have little or no opportunity to participate. The resulting percentage may be precise for the respondents yet systematically different from the percentage in the intended population.

Sampling error is only one part of possible survey error. Coverage, nonresponse, measurement and data-processing errors can also affect the result [2]. Increasing sample size can reduce random sampling variability, but it does not automatically correct a poor sampling frame, selective participation or inaccurate measurements.

Defining the population and sample

Target population

The target population is the group to which the investigators intend the study findings to apply.

In the scenario, the target population is:

all adults with diagnosed hypertension who meet the active-care definition in the district’s public primary-care clinics on 1 June 2026.

The target population does not include adults receiving care only from private clinics, adults with undiagnosed hypertension or residents who have not attended a participating public clinic during the stated period. Findings should not be silently generalised to those groups.

The population should be defined by people or units, place, eligibility conditions and time. Epidemiological interpretation depends on making that target explicit [3].

Source or study population

The source population, sometimes called the study population before sampling, is the practical population from which eligible participants can be identified.

Ideally, it corresponds closely to the target population. In this study, it consists of eligible patients recorded across the participating public-clinic information systems.

Differences between the intended target population and the accessible source population may restrict applicability. For example, a clinic without an electronic register might be omitted from the practical study population even though its patients belong to the intended target population.

Sampling frame

A sampling frame is the operational list or system used to identify sampling units.

The deduplicated electronic register is the sampling frame. A good frame should:

• include eligible members of the source population;
• exclude ineligible records;
• avoid duplicate entries;
• contain sufficient information for selection; and
• reflect the study’s reference period.

A frame can be imperfect. Missing patients create undercoverage. Ineligible or outdated records create overcoverage. Duplicate records may give some people more than one chance of selection.

Sampling unit and unit of analysis

A sampling unit is the unit selected at a particular stage of sampling. In the scenario, the individual patient is selected directly from each stratum.

The unit of analysis is the entity represented by each contribution to the main analysis. It is also the patient because each selected patient contributes one study assessment.

These units need not always be the same. A household survey may first select neighbourhoods, then households and finally one adult within each household. The sampling units change across stages, while the final unit of analysis may be the individual adult.

Selected sample, participants and analysis sample

The selected sample consists of all units chosen by the sampling procedure.

The participant sample consists of selected units from whom data are obtained.

The analysis sample consists of participants included in a particular analysis after accounting for missing or unusable data.

These numbers should not be used interchangeably. A report should state how many units were selected, eligible, contacted, enrolled, measured and analysed.

Census and sample

A census attempts to collect information from every unit in the defined population. A census may appear to remove sampling variability, but it can still contain coverage, nonresponse, measurement and processing errors.

A sample survey measures only part of the population. Sampling is often preferable when:

• the population is large;
• data collection is expensive or burdensome;
• measurements require specialised staff;
• faster results are needed; or
• closer quality control is possible with fewer observations.

Studying the entire available database is not automatically a census of the target population. It is a census only of the population represented by that database at the relevant time.

Probability sampling

In a probability sample, every eligible unit on the sampling frame has a known probability greater than zero of selection, and random selection is used [1]. The probabilities need not be equal.

Known selection probabilities allow investigators to calculate sampling weights and estimate sampling variability under the design. This does not guarantee absence of bias: the frame, response process and measurements must also be credible.

Simple random sampling

In simple random sampling, every unit on the frame has an equal chance of selection, and every possible sample of the specified size is selected through the same random mechanism.

It is conceptually straightforward but requires a suitable list of eligible units.

Systematic sampling

Systematic sampling selects a random starting point and then every $k$th unit on an ordered list.

For example, if 2,000 records are listed and 200 are required, the sampling interval is 10. A random start from 1 to 10 is chosen, followed by every tenth record.

Systematic sampling can be efficient, but the list should be checked for repeating patterns related to the outcome. Always starting with the first record is not random systematic sampling.

Stratified sampling

In stratified sampling, the frame is divided into non-overlapping groups called strata, and a probability sample is selected independently within each stratum.

The simulated hypertension study uses urban and rural strata. Stratification can:

• ensure representation of important subgroups;
• permit planned subgroup estimates;
• improve precision when units within strata are relatively similar; and
• allow different sampling fractions across strata.

When sampling fractions differ, population estimates usually require weights.

Cluster and multistage sampling

A cluster is a naturally occurring group such as a village, school, clinic or household. Cluster sampling selects groups rather than sampling individuals directly from one complete list.

In multistage sampling, investigators may select districts, then clinics and then patients. This can reduce travel and listing costs.

However, people within the same cluster may be more similar to each other than people in different clusters. The analysis must account for clustering. Treating all individuals as independent can produce confidence intervals that are too narrow.

Table 1. Common probability-sampling approaches

Non-probability sampling

In non-probability sampling, selection probabilities are unknown or some eligible units have no practical opportunity to be selected. Standard design-based margins of sampling error cannot be derived from the selection mechanism alone.

Convenience sampling

A convenience sample includes readily available participants, such as people attending one clinic during the investigator’s available sessions.

It may be useful for feasibility work, instrument testing or early exploration. It should not automatically be described as representative of a wider population.

Consecutive sampling

Consecutive sampling attempts to include every eligible patient encountered over a defined period until the required sample is reached.

It reduces discretionary selection compared with choosing whichever patients seem convenient. However, the probability of selection is usually unknown, and the sample may reflect referral patterns, season, clinic schedules or changes in service use.

Purposive sampling

Purposive sampling selects participants because they possess characteristics relevant to the study. It is common in qualitative research and investigations seeking particular experiences or expertise.

Its value should be judged against that purpose rather than against probability-sampling criteria.

Quota sampling

Quota sampling recruits specified numbers from selected categories, such as age groups or sexes, without probability selection within those categories.

Meeting quotas does not ensure that participants represent the broader population within each category.

Snowball or respondent-driven recruitment

Initial participants refer other potential participants. This may help reach populations without an accessible sampling frame.

Network structure and recruitment patterns influence who enters the sample. Specialised methods and assumptions are needed before making population estimates.

Table 2. Probability and non-probability sampling

Sampling variability and other errors

Sampling variability

Different probability samples from the same population will usually produce different estimates. This random variation is sampling variability.

A standard error describes the expected sampling variability of an estimator under the sampling design and analysis assumptions. Increasing the sample size usually reduces the standard error, although clustering and unequal weights can alter the amount of information obtained.

Coverage error

Coverage error occurs when the sampling frame does not correspond adequately to the target or source population.

Examples include:

• eligible patients missing from the register;
• people appearing more than once;
• outdated contact information;
• ineligible records remaining on the frame; and
• omission of an entire clinic.

Nonresponse error

Unit nonresponse occurs when no study data are obtained from a selected eligible unit. Item nonresponse occurs when a participant provides some data but not a particular variable.

Nonresponse bias depends on whether respondents and nonrespondents differ in ways relevant to the study estimate, not merely on the response percentage. A high response rate is desirable but does not prove absence of bias, while a lower response rate does not by itself quantify the direction or size of bias.

Response rates should be calculated using a stated definition. The American Association for Public Opinion Research provides standard case dispositions and outcome-rate definitions for surveys [4].

Measurement and processing error

A well-selected sample can still produce misleading findings if blood pressure is measured inconsistently, eligibility is misclassified, data are entered incorrectly or variable definitions differ between clinics.

Sampling quality cannot compensate for poor measurement quality.

Random sampling is not random allocation

Random sampling selects units from a population. Its main purpose is to support population description and generalisation under the sampling design.

Random allocation assigns enrolled participants to intervention groups. Its main purpose is to create comparable groups for estimating an intervention effect under the trial design.

A randomised trial may use a convenience sample of eligible patients and then randomly allocate them. Randomisation can strengthen the internal treatment comparison, but it does not make the participants a random sample of every patient with the condition.

Conversely, a probability health survey may randomly sample residents but does not randomly assign their exposures. Random sampling alone does not remove confounding or establish causal effects.

Data structure

Simulated stratified hypertension sample

simulated data

Table 3. Population and sample by stratum

Stratum	Population size	Sample size	Patients with uncontrolled blood pressure	Sample prevalence
Urban clinics	40,000	300	90	30.0%
Rural clinics	10,000	200	90	45.0%
Total	50,000	500	180	36.0% unweighted

Note: Each selected patient contributes one standardised assessment. The rural stratum forms 20% of the population but 40% of the sample.

(Calculations for the stratum percentages shown in Table 3 are not shown here.)

Table 4. Example participant-level records

patient_id	stratum	base_weight	systolic_bp	diastolic_bp	uncontrolled_bp
HT001	Urban	133.33	146 mmHg	84 mmHg	Yes
HT002	Urban	133.33	132 mmHg	78 mmHg	No
HT003	Rural	50.00	138 mmHg	94 mmHg	Yes
HT004	Rural	50.00	126 mmHg	76 mmHg	No

Note: The base weight is the inverse of the probability of selection within the stratum. Values are rounded for display.

(Calculations for the base weights shown in Table 4 are not shown here.)

Worked example

Weights, stratification, clustering and design effects MMed extension

A base sampling weight is commonly defined as:

$$w_i = \frac{1}{\pi_i}$$

where $w_i$ is the weight for sampled unit $i$ and $\pi_i$ is that unit’s probability of selection.

Weights may later be adjusted for nonresponse or calibrated to reliable population totals. Those adjustments require assumptions; weighting does not automatically remove all selection bias.

Complex-survey analysis should retain the variables identifying weights, strata and clusters. National health surveys such as the National Health and Nutrition Examination Survey use multistage probability designs, oversampling and survey weights, and their analytic guidance emphasises design-aware variance estimation [5].

A design effect compares the variance under the actual sampling design with the variance that would arise from a simple random sample of the same nominal size. Clustering often increases variance because observations within a cluster tend to be similar. Effective stratification can reduce variance. Unequal weights may also reduce precision.

Suggested reporting

Reports of observational studies should state eligibility criteria, sources and methods of participant selection, numbers at relevant stages and the handling of missing data. The Strengthening the Reporting of Observational Studies in Epidemiology statement provides reporting recommendations for cross-sectional, cohort and case-control studies [6].

The wording identifies the population, reference period, frame, selection method, stratum sample sizes, analysis weights, denominators and population estimate.

Common mistakes

Knowledge check

What is the target population in the simulated hypertension study?

Answer and reasoning

It is all adults with diagnosed hypertension who meet the active-care definition in the district’s public primary-care clinics on the reference date. It is not every adult resident of the district and does not include patients receiving only private care.

Why is the electronic register called a sampling frame rather than the population itself?

Answer and reasoning

The register is the operational system used to identify and select eligible patients. It may differ from the intended population because records can be missing, duplicated, outdated or ineligible. The quality of that correspondence must be assessed.

Why is the unweighted prevalence of 36.0% not the preferred district estimate?

Answer and reasoning

Rural patients form 20% of the population but 40% of the sample, and their observed prevalence is higher. The unweighted calculation therefore gives the rural stratum too much influence. Weighting each stratum according to its population share gives an estimate of 33.0%.

Does random allocation in a clinical trial make its participants a random sample of all patients with the disease?

Answer and reasoning

No. Random allocation governs assignment among enrolled participants and supports the internal treatment comparison. It does not determine how those participants were recruited from the wider patient population.

Can increasing the sample size correct an incomplete sampling frame?

Answer and reasoning

Not by itself. A larger sample from the same incomplete frame may estimate the framed population more precisely while remaining systematically different from the intended target population. Coverage must be addressed through frame construction, supplementary sources or a narrower interpretation of the target population.

Key take-home messages

References

1. Lohr SL. Sampling: design and analysis. 3rd ed. New York: Chapman and Hall/CRC; 2021. https://doi.org/10.1201/9780429298899
2. Groves RM, Fowler FJ Jr, Couper MP, Lepkowski JM, Singer E, Tourangeau R. Survey methodology. 2nd ed. Hoboken (NJ): Wiley; 2009.
3. Lash TL, VanderWeele TJ, Haneuse S, Rothman KJ. Modern epidemiology. 4th ed. Philadelphia: Wolters Kluwer; 2021.
4. American Association for Public Opinion Research. Standard definitions: final dispositions of case codes and outcome rates for surveys. 10th ed. AAPOR; 2023. https://aapor.org/wp-content/uploads/2023/05/Standards-Definitions-10th-edition.pdf
5. Johnson CL, Paulose-Ram R, Ogden CL, Carroll MD, Kruszon-Moran D, Dohrmann SM, et al. National Health and Nutrition Examination Survey: analytic guidelines, 1999–2010. Vital Health Stat 2. 2013;(161):1–24. https://stacks.cdc.gov/view/cdc/255108
6. von Elm E, Altman DG, Egger M, Pocock SJ, Gøtzsche PC, Vandenbroucke JP, et al. The Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement: guidelines for reporting observational studies. PLoS Med. 2007;4(10):e296. https://doi.org/10.1371/journal.pmed.0040296