Sampling methods: random, systematic, stratified, quota and cluster

Choosing a fair sample

How a sample is chosen decides whether it represents the population. This lesson covers simple random, systematic, stratified, quota and cluster sampling, how to carry out each one, and when each is the right choice.

Simple random sampling

In a simple random sample, every member of the population has an equal chance of being chosen, and so does every possible sample of that size. Number the population, for example 001 to 360, and generate random three-digit numbers from tables or a calculator. Ignore numbers above 360, and ignore repeats, until the sample is complete.

Systematic sampling

Systematic sampling takes every kth member of a list, where k is the population size divided by the sample size. For 1,200 items and a sample of 40, k is 30. Choose a random start from 1 to 30, then take every 30th item. It is quick and spreads the sample evenly, but it can be biased if the list has a repeating pattern that matches k.

Stratified sampling

Stratified sampling splits the population into groups, called strata, and samples each group in proportion to its size. 600 lamps: 150 small, 300 medium and 150 large. A sample of 40 takes 150 over 600 times 40, which is 10 small, then 20 medium and 10 large. Within each stratum, the members are chosen at random, so the sample represents every group.

Quota and cluster sampling

In quota sampling, an interviewer chooses people to fill set numbers in each group, such as 20 men and 20 women. No sampling frame is needed. But the choice is not random, so the interviewer may pick people who are easy to reach, which causes bias. In cluster sampling, the population is split into groups such as areas; some groups are chosen at random, and members within them are sampled.

Representative samples

A representative sample has the same features as the population, in the same proportions. Taking the first 30 customers of the day is not random: early customers may differ from those who come later. Stratifying by the groups that matter, such as age, size or type, makes a sample more representative.

Which method when?

Simple random: there is a full sampling frame and no important subgroups. Systematic: there is a long list, such as items coming off a production line. Stratified: the groups may differ. Quota: there is no sampling frame and a quick result is needed.

Sampling methods compared

The sampling methods compared.

Mistakes that lose marks

Mistake one: in stratified sampling, taking equal numbers from each group instead of numbers in proportion. Mistake two: describing random sampling without saying what happens to repeats and out-of-range numbers. Mistake three: forgetting the random start in systematic sampling. The fix: describe each step, as if someone else will carry it out.

The full-marks tip

The full-marks tip: describe the method in steps: number the population, choose, and deal with repeats. For a stratified sample, show the group size over the population size, times the sample size.

On one card

So, on one card: sampling methods. Keep it for revision.