Sampling and sampling variability
Populations and samples
- A population is the whole group a study is about (e.g. all NZ voters).
- A sample is the smaller group actually surveyed, used because studying everyone is usually impractical.
- A parameter is a true value for the whole population; a statistic (estimate) is calculated from the sample.
Sampling methods
- Simple random sample — everyone has an equal chance of being chosen; the fairest method.
- Stratified sample — the population is split into groups (strata, e.g. age bands) and sampled in proportion, so each group is fairly represented.
- Systematic sample — pick every -th person from a list.
- Cluster sample — split into clusters (e.g. schools), then survey whole clusters.
- A good sample is representative — it looks like the population.
Sampling variability
- Sampling variability is the fact that different random samples give different estimates, purely by chance.
- Larger samples vary less, so they give more reliable estimates.
A researcher surveys 500 students chosen at random from a university of 20,000 to estimate the proportion who cycle to campus. Identify the population, the sample, and one source of possible bias to watch for.
Step 1 — Name the population and sample
- Population: all 20,000 students at the university.
- Sample: the 500 students actually surveyed.
Step 2 — Consider a source of bias
Even with random selection, non-response bias can occur: if cyclists are more likely to reply (because the topic interests them), the estimate would be too high. A high response rate helps guard against this.
Test yourself
Practice by grade
One question each at Achieved, Merit and Excellence. Have a go, then compare with the model answer.
A poll surveys 800 people chosen at random from the electoral roll. Name the population and the sample.
Explain what 'sampling variability' means and why a larger sample is generally better.
A radio station asks listeners to phone in to vote on a question, and 3000 people respond. Explain why this large sample may still give a biased estimate of public opinion.