Breaking down the question

The command is explain with examples, so this is an expository question that rewards clear definitions, a correct typology and concrete illustrations. The subject is probability sampling strategies — those methods in which every unit of the population has a known, non-zero chance of selection, which is what permits statistical generalisation from sample to population.

You must distinguish probability from non-probability sampling at the outset, then walk through the principal probability techniques — simple random, systematic, stratified and cluster — giving a worked example of each.

How to approach it

Open by defining probability sampling and stating why it matters — it minimises selection bias and allows the calculation of sampling error, making findings generalisable.

  • Simple random sampling: every unit has an equal chance; selection by lottery or random numbers.
  • Systematic sampling: select every kth unit from an ordered list after a random start.
  • Stratified sampling: divide the population into homogeneous strata and sample within each, proportionately or disproportionately.
  • Cluster and multi-stage sampling: sample whole groups, then units within them, useful for large, dispersed populations.

Close by noting the requirement of a complete sampling frame and the trade-offs of cost and precision. See Variables, sampling, reliability and validity for related material.

Model answer

Probability sampling refers to those selection strategies in which every element of the population has a known and non-zero probability of being chosen. Because selection is governed by chance rather than the researcher's discretion, probability sampling reduces bias, permits the estimation of sampling error, and allows valid generalisation from the sample to the wider population. It presupposes a complete and accurate sampling frame — a list of all units.

The simplest strategy is simple random sampling, in which every unit has an equal chance of selection, typically through a lottery method or a table of random numbers. For example, to survey 100 students from a college of 2,000, one might assign each a number and draw 100 at random.

Systematic sampling selects every kth unit from an ordered list after a random starting point. To draw 100 from 2,000, one picks every twentieth name after a random start between 1 and 20. It is convenient but can introduce bias if the list has a hidden periodic pattern.

Stratified sampling first divides the population into homogeneous sub-groups, or strata, such as gender, income or region, and then samples within each. If a village is 60 per cent farmers and 40 per cent labourers, a proportionate stratified sample preserves that ratio, improving precision when strata differ markedly.

Cluster sampling selects entire naturally occurring groups — schools, villages, city blocks — rather than individuals, and is economical for large, geographically dispersed populations. Multi-stage sampling extends this by sampling clusters, then sub-units within them, for instance selecting districts, then villages, then households.

Each strategy trades cost, convenience and precision differently, but all share the defining virtue emphasised by methodologists such as Goode and Hatt — that random selection makes the sample statistically representative and the findings generalisable.

Examiner's perspective

Examiners expect the opening distinction between probability and non-probability sampling and the key idea that a known, non-zero chance of selection is what underwrites generalisation. The discriminating feature of strong answers is a concrete numerical example for each method rather than bare definitions — the every-kth illustration for systematic sampling, proportionate strata for stratified. Candidates frequently confuse stratified with cluster sampling, so making the contrast explicit (homogeneous strata versus whole heterogeneous clusters) earns credit. A closing line on the sampling frame and the cost-precision trade-off signals methodological sophistication.