Populations, samples and data collection
Populations, samples and sampling methods
A population is every item that could be studied; a sample is a subset chosen to represent it. A census measures the whole population - accurate but slow and expensive - while a sample is cheaper but introduces sampling error. A sampling frame is the list from which a sample is drawn; if the frame is incomplete or out of date, the sample is biased however carefully it is selected.
Random sampling gives every member of the population an equal chance of selection. Systematic sampling takes every kth item from a frame, where k = population size ÷ sample size. Stratified sampling splits the population into groups (strata) and samples each in proportion to its size. Quota sampling is non-random: an interviewer fills set quotas.
Also know primary data (collected first-hand) versus secondary data (already published), and the difference between qualitative and quantitative data. In questionnaires, avoid leading questions, offer 'don't know' options where sensible, use closed questions for numerical analysis and pilot the survey first.
Trap: 'random' does not mean haphazard. Interviewing people in a shopping centre is opportunity (convenience) sampling and is likely to be biased. Keep bias (systematic distortion) separate from reliability (repeatability and precision); a bigger sample is usually more reliable but not automatically less biased.
Worked example (stratified sample). A college has 480 first-year and 320 second-year students; a stratified sample of 50 is required. Total = 800, so the sampling fraction is 50 ÷ 800 = 1/16. First-years: 480 ÷ 16 = 30. Second-years: 320 ÷ 16 = 20. Always check the parts add to the required sample size.