Sampling

Why does sample size matter in experimental design? (Sx1)

Too small a sample gives unreliable estimates and large sampling variability; too large can be wasteful or destructive. Sample size affects how meaningfully an effect size can be interpreted.

Why might sampling be necessary instead of a full census? (Sx2)

The population may be too large or too expensive to census; the sampling process may be destructive (e.g. testing tins for strength); or a full census may simply be impractical.

What are the desirable features of a sample? (Sx2)

The sample should be unbiased, representative of the population, and the data should be relevant and not changed by the act of sampling.

Why is a random sample better when inferring properties of a population? (Sx3)

Because the probability basis on which the sample was selected is known, proper statistical inference (e.g. hypothesis tests, confidence intervals) can be carried out.

Why might it be wrong to test only the final 30 items produced in a batch?

The sample is not random and likely not representative - items produced at the end may differ systematically from earlier ones (e.g. tooling wear, fatigue), introducing bias.

Why might a sample size of 5 be too small for batch testing?

With only 5 items, sampling variability is huge and the test could easily miss a faulty batch; the conclusion about the batch is unreliable.

Why might a sample size of 1000 be inappropriate for destructive batch testing?

Destructive testing destroys those items; 1000 may be too costly, wasteful, or even larger than the number you can afford to spare.

What does it mean for data to be "changed by the act of sampling"?

When the process of measuring or selecting alters the items themselves (e.g. destructive testing, or a survey question that changes attitudes) — this can bias the sample.

What does "representative" mean for a sample?

The sample reflects the structure and characteristics of the population, so inferences drawn from it are likely to apply to the whole population.

What is the link between an effect size and sample size?

Larger samples make it easier to detect even small effects as statistically significant; the effect size itself measures the practical (not just statistical) importance of a result.

What additional sampling methods are assumed knowledge from A-level Maths for Y432?

Simple random sampling and opportunity sampling (use), plus familiarity with systematic, stratified, cluster and quota sampling (critique only).