Sampling and inference

WJEC introduces sampling in Foundation contexts (one-mark vocabulary recall) and tests it more rigorously at Intermediate/Higher with capture-recapture and bias analysis.

Population vs sample

• Population — every member of the group you want to draw conclusions about.
• Sample — a subset selected from the population, used because the population is too large or expensive to survey.
• The sample must be representative — its mix should match the population's.

Common sampling methods

1. Random sample — every member of the population has an equal chance of being selected (e.g. names from a hat, random number generator).
2. Stratified sample — the population is split into strata (groups), then the sample takes from each stratum in proportion. Used when sub-groups differ noticeably (e.g. by age, by Welsh-medium vs English-medium school).
3. Systematic sample — every k-th item is taken (e.g. every 5th visitor). Quick but biased if the population has periodicity.

Bias

Bias is anything that makes the sample unrepresentative.

• Selection bias — only people from one place/time of day surveyed.
• Self-selection bias — only those who volunteer respond.
• Question bias — leading or loaded wording.

Capture-recapture (Higher only)

Used to estimate animal populations. Catch n_1, tag them, release. Later catch n_2; suppose m of them are tagged.

Estimate: N ≈ (n_1 × n_2) ÷ m.

Sampling exam tip

WJEC marks one B1 for naming a sampling method, and a separate B1 for explaining why it might still be biased ("only surveyed at lunchtime — students who eat off-site are missed"). Always quote a reason in the context of the question, not generically.