Sampling
What the exam tests
Sampling covers how a sample is selected, types of sampling, sampling and non-sampling errors, and basic sample-size ideas. Expect definitions, comparisons and simple counting or allocation problems.
Core rules
- Population = complete set of units; sample = selected subset; sampling frame = list from which the sample is drawn.
- Probability sampling gives every unit a known non-zero chance of selection. Types: simple random sampling (SRS), stratified, systematic, cluster and multistage.
- SRS without replacement: number of samples of size n from N is NCn; with replacement it is N^n.
- Stratified sampling divides the population into homogeneous strata, then samples within each stratum. Proportional allocation uses nh = n(Nh/N).
- Systematic sampling selects every kth unit after a random start, with k = N/n.
- Cluster sampling selects whole groups; multistage sampling combines stages.
- Non-probability sampling includes quota, convenience, purposive and judgement sampling; selection probabilities are unknown.
- Sampling error arises because a sample is used and generally falls as n increases. Non-sampling errors - frame defects, non-response, measurement and recording - can grow with survey size.
Worked example
A college has 60 science and 40 arts students; a sample of 20 is needed. Proportional stratified allocation gives science 20 × 60/100 = 12 and arts 20 × 40/100 = 8. From 100 students, the number of SRS samples of size 2 without replacement is 100C2 = 4950.
Traps
Calling quota sampling random; using N^n when sampling is without replacement; allocating strata equally instead of proportionally; assuming a larger sample removes non-sampling error; ignoring an incomplete sampling frame.