Population, sampling frame and sample; simple random, systematic, stratified, quota, cluster, judgement and opportunity sampling; selecting random members; calculating strata sizes.

What this dot point is asking

Edexcel codes 1c.01 to 1c.06 require you to define a population, sampling frame and sample; to know when and why judgement (purposive) and opportunity (convenience) sampling are used and the bias risks they carry; to understand random, systematic, quota and cluster sampling with their advantages and disadvantages; to describe how random members are selected (including handling repeats and out-of-range numbers); and to use stratification, including calculating strata sizes. The stratified sample calculation is one of the most common calculation questions in the qualification.

Population, sampling frame and sample

Edexcel notes that "population" depends on context: it might mean all employees in an office, all females in the UK, or all items produced in a factory. A census surveys the whole population (accurate but slow and costly); a sample surveys a part (faster and cheaper, but introduces sampling error and the risk of bias). The quality of a sample depends on a good sampling frame: if the frame misses part of the population, no method can remove the resulting bias.

Simple random sampling

You select by numbering the frame and using a random device: dice, cards, random number lists, or calculator and spreadsheet functions. Edexcel expects you to deal with practical issues: ignore repeated random numbers and out-of-range numbers, and keep selecting until you have enough distinct members. Random sampling is free of selection bias, but it needs a complete frame and can, by chance, under-represent a group.

Systematic sampling

In systematic sampling you choose a random starting point and then take every $n$th member of the frame. For a population of $800$ and a sample of $40$, the interval is $\frac{800}{40} = 20$, so you pick a random start between $1$ and $20$ and take every $20$th member after it. It is quick and spreads the sample through the list, but Edexcel warns that it is generally non-random and can fail if the list has a repeating pattern (period) that coincides with the interval.

Stratified sampling

Stratified sampling guarantees each group is represented in proportion to its size, then selects at random within each group. Edexcel favours it for populations split into obvious strata (year groups, age bands, gender). At Higher tier you may stratify by more than one category.

Quota, cluster, judgement and opportunity sampling

• Quota sampling sets target numbers per group (for example $15$ men and $15$ women); the interviewer fills the quotas. No frame is needed, but it is non-random and can be biased by who the interviewer approaches.
• Cluster sampling divides the population into clusters (schools, towns), picks some clusters at random, and surveys everyone in them. It is cheap when the population is spread out, but chosen clusters may not represent the whole.
• Judgement (purposive) sampling chooses members the investigator believes are representative. It is quick but relies on opinion and risks bias.
• Opportunity (convenience) sampling takes whoever is easiest to reach (the first 20 people who pass). It is the quickest but the most biased, because it ignores the rest of the population.