Sampling and Sampling Distributions
What you must understand
Know the main sampling methods: simple random sampling (every member of a numbered list equally likely, e.g. using random numbers), systematic sampling (every kth item from a list), stratified sampling (split the population into strata and sample proportionally), quota sampling (fixed numbers per group chosen by the interviewer), and cluster sampling (sample whole groups).
Understand sampling frames (the list from which a sample is drawn), sampling error (difference between sample and population values, unavoidable), and non-sampling errors (bias, poor questions, non-response, recording errors). Explain why a random sample is preferred: it reduces bias and allows probability statements about accuracy.
The sampling distribution of a statistic is the distribution of values it takes across all possible samples. Know the idea of the standard error (standard deviation of a sample mean, σ ÷ √n) and why larger samples give more precise estimates. If the population is normal, or n is large, sample means are approximately normally distributed.
Traps that appear in questions
- Calling stratified sampling "random" without saying selection within each stratum is random.
- Confusing sampling error with bias; bias does not shrink as the sample grows.
- Forgetting that a larger sample reduces sampling error but not non-response bias.
- Choosing a sampling method that cannot be applied because no sampling frame exists.
Worked example
A school has 400 boys and 600 girls. A stratified sample of 50 is needed.
Answer: Total = 1000. Boys: (400 ÷ 1000) × 50 = 20. Girls: (600 ÷ 1000) × 50 = 30. Select each group randomly within its stratum.
Rule of thumb: stratified sampling needs a known, proportional structure; systematic sampling needs an ordered list and a random start.