Sampling

What is a population?

The complete set of items, individuals or events about which information is wanted.

What is a sample?

A subset of the population, selected and used to make inferences about the whole population.

Why do we use a sample instead of the whole population?

Studying the entire population is often too expensive, too slow, impractical or impossible (e.g. destructive testing, infinite populations).

What does it mean to make an informal inference about a population from a sample?

Using sample data (e.g. the sample mean or proportion) to draw a conclusion about the corresponding feature of the population, without a formal statistical test.

Can two different samples from the same population lead to different conclusions?

Yes — this is sampling variability, and it is why the choice of sample size and sampling method matters.

What is sampling without replacement?

Once an item is chosen for the sample it cannot be chosen again. For large populations, sampling without replacement is approximately equivalent to with replacement.

What is simple random sampling?

A method in which every member of the population has an equal chance of being selected and every possible sample of size n is equally likely.

How would you carry out a simple random sample of size n?

Number the population 1 to N, then use random numbers (RNG, random number tables, or a calculator) to select n distinct numbers; the corresponding members form the sample.

Advantage of simple random sampling

Unbiased; every member has equal chance, so the sample is representative on average.

Disadvantage of simple random sampling

Requires a full sampling frame (list of the population); can be impractical for large populations.

What is opportunity (convenience) sampling?

Choosing whoever is most easily available at the time of sampling.

Advantage of opportunity sampling

Quick, easy and cheap.

Disadvantage of opportunity sampling

Highly likely to be biased; sample is unlikely to be representative of the wider population.

What is systematic sampling?

After listing the population, choose a random start and then select every kth member, where k = N/n.

Disadvantage of systematic sampling

If the list has a hidden periodic pattern matching the interval k, the sample can be biased.

What is stratified sampling?

The population is split into distinct, non-overlapping groups (strata), and a simple random sample is taken from each stratum in proportion to its size.

Advantage of stratified sampling

Guarantees all key subgroups are represented, usually giving a more accurate estimate than simple random sampling.

Disadvantage of stratified sampling

Requires knowledge of the population structure and the strata; more complex to organise.

What is cluster sampling?

The population is divided into clusters (often by geography); whole clusters are randomly chosen and every member of those clusters is surveyed (or a sub-sample is taken).

Advantage of cluster sampling

Cheaper and more practical when the population is widely spread; no full sampling frame needed.

Disadvantage of cluster sampling

A cluster may not be representative of the whole population, increasing sampling error.

What is quota sampling?

The interviewer selects respondents (non-randomly) until preset quotas for each subgroup of the population are filled.

Advantage of quota sampling

Fast, cheap and ensures subgroups are represented.

Disadvantage of quota sampling

Non-random selection — interviewer bias can creep in and results may not be representative.

On OCR A H240, which two sampling methods must you be able to carry out?

Simple random sampling and opportunity sampling.

On OCR A H240, which sampling methods do you only need to be familiar with and critique (not carry out)?

Systematic, stratified, cluster and quota sampling.

What is a sampling frame?

A list of every member of the population from which a sample can be drawn (needed for simple random and systematic sampling).

What is sampling bias?

Any systematic tendency for a sample to misrepresent the population, caused by the sampling method or non-response.