4.4(d) - Sampling, measurement and uncertainty

Population, sample and representativeness

The population is the complete set of cases to which a question refers; it does not have to mean people. For a beach investigation it might be every surface pebble in a defined beach sector at a particular time. A sample is a subset observed to learn about that population. Define the spatial boundary, time period and relevant cases before selecting the sample, otherwise “representative” has no clear reference.

A sampling frame is the practical list or spatial framework from which selection occurs. An address list can provide a frame for households, while a coordinate grid can provide one for beach quadrats. If the frame omits informal dwellings or inaccessible parts of a beach, random selection within it does not repair that omission. Likewise, surveying people currently using a square cannot directly represent residents who avoid it.

Sampling variation occurs because different samples contain different cases. Even fair selection may produce a sample mean above or below the population mean. Increasing a well-designed sample generally gives a more stable estimate, but repeatedly measuring only the easiest access point can produce a precise estimate of the wrong population. Systematic bias does not disappear just because the sample becomes larger.

Representativeness concerns the features relevant to the enquiry. An illustrative survey of attitudes to a bus route should consider users at different times and people with different mobility needs, not merely match the population's age distribution. No sample is automatically representative of every characteristic. State who or what was observed and the population to which the findings can reasonably apply.

The 2021 Census in England and Wales used 21 March 2021 as its reference date, with first population results published on 28 June 2022. These ONS milestones show why a population's time boundary and a dataset's publication date are different. A later field survey must account for movement and new housing before using an older frame as if it described the same residents.

Worked dataset limitation

Illustrative source: an online town survey invites responses through a local cycling club. The source reaches people already connected to that activity, so positive experiences of cycle access may be over-represented relative to all residents. The limitation follows from recruitment, even if every submitted answer is recorded accurately. Combining a wider address-based frame with deliberate coverage of non-cyclists would target the omitted population.

Random, systematic and stratified samples

Different designs balance comparability, spatial coverage, feasibility and the risk of bias. In a simple random sample, every eligible case in the frame has an equal chance of selection. A random-number procedure selects cases without choosing those that look typical. It reduces investigator selection bias, but a small spatial sample may cluster and fail to cover important zones. A nonresponse or an inaccessible selected site still needs a stated treatment; silently replacing it with a convenient case changes the design.

Systematic sampling takes observations at a regular interval, such as every tenth address after a random start or every five metres along a transect. It provides even coverage and can reveal a gradient. However, if the interval coincides with a repeating landscape feature, the sample may repeatedly hit the same kind of location. A transect across a beach also samples one line rather than every alongshore variation.

Stratified sampling divides a population into relevant subgroups, then samples within each. An urban survey could stratify by neighbourhood or housing type. Proportional allocation gives more observations to larger strata; equal allocation can help compare small and large strata but does not directly reproduce the whole population's proportions. Selection within strata can be random.

Worked proportional allocation

A district has 600 households in stratum A and 400 in B; the required sample is 50. Total the population, then apply each share:

The allocations sum to the required 50.

Worked unequal strata

A second frame contains 350 addresses in C and 650 in D, with a sample of 40. Calculate:

Equal groups of 20 would over-represent C in an unweighted population estimate. Proportional allocation still needs a fair within-stratum selection and a response strategy.

Worked spatial sampling limitation

Illustrative coastal design: a regular interval matches the spacing of groynes, so measurements repeatedly fall beside structures that trap sediment. Even coverage along the tape then samples one recurring setting disproportionately. Changing the start or interval and including positions between groynes targets this periodicity; merely doubling the same pattern would preserve it.

Opportunistic sampling selects available cases, which can be practical during exploratory work but often favours accessible sites or willing respondents. It should be described honestly rather than relabelled random. A justified design follows the geographical question: stratification can capture contrasting coastal substrates, while systematic sites can reveal change with distance from a river mouth. Actual field implementation must also account for permissions, safety and environmental protection; those performance decisions belong to the independent investigation.