Describe and apply the main sampling methods, including simple random, systematic and stratified sampling, distinguish a sample from a population and a statistic from a parameter, and explain how a poor sampling method introduces bias.

What this dot point is asking

Inference is the art of learning about a whole population from a sample, and that only works if the sample is representative. The SQA wants you to know the standard sampling methods, to carry each out, to use the right language (population and sample, parameter and statistic), and to explain how a careless choice of method or frame lets bias creep in.

Population, sample, parameter and statistic

Getting this vocabulary exactly right is worth easy marks and keeps the later inference clear.

The whole point of inference is that we rarely measure the population; we measure a sample, compute a statistic, and use it to estimate the unknown parameter, attaching a measure of uncertainty.

Simple random sampling

Simple random sampling is the benchmark against which other methods are judged.

Its strength is that it is unbiased and underpins the probability theory of inference. Its drawbacks are practical: it needs a complete numbered list (sampling frame) of the population, which may not exist, and the chosen members can be widely scattered and costly to reach.

Systematic sampling

Systematic sampling is a quick, ordered alternative.

Systematic sampling is easy to administer, especially on a production line or a queue, but it becomes biased if the list has a periodic pattern whose period matches the interval $k$.

Stratified sampling

Stratified sampling guarantees that important subgroups are represented in proportion to their size.

Stratified sampling improves accuracy when the strata differ markedly, because it removes the chance that a simple random sample misses a subgroup. It needs the stratum sizes to be known in advance.

Try this

Q1. A population of $5000$ is to give a systematic sample of $250$. State the sampling interval. [1 mark]

• Cue. $k = \dfrac{5000}{250} = 20$, so take every $20$th member after a random start between $1$ and $20$.

Q2. Explain one advantage of stratified over simple random sampling when a population has very unequal subgroups. [1 mark]

• Cue. Stratified sampling guarantees each subgroup is represented in proportion, so a small but important stratum cannot be missed by chance, which a simple random sample could do.