What you'll learn

• How to distinguish a population, census and sample.
• How to carry out simple random, systematic and stratified sampling.
• How opportunity and quota sampling work.
• How to compare sampling methods and identify possible sources of bias.

Populations and samples

Before choosing a sampling technique, you need to be clear about the group you want to investigate.

For example, if a college wants to investigate the journey times of all its students, the population is every student at that college. Each student is a sampling unit.

A census collects data from every member of the population. A sample collects data from only part of the population.

A census may give more complete information, but it can be expensive, slow or impractical. Sampling is usually quicker and cheaper, but conclusions based on a sample are subject to sampling variation: different samples may produce different results.

A large sample is not automatically representative. A badly chosen large sample can still be biased.

Sampling frames

Examples include a school register, an employee database or a list of customer account numbers.

A suitable sampling frame should be:

• relevant to the population being studied;
• complete, with no eligible sampling units missing;
• free from duplicates;
• up to date.

If the sampling frame is incomplete or inaccurate, the sample may suffer from selection bias, meaning some parts of the population are more likely to be selected than others.

Probability and non-probability sampling

Sampling techniques can be divided into two broad types.

Probability sampling

In probability sampling, selection is controlled by a random process. Each sampling unit has a known chance of being selected.

Examples include:

• simple random sampling;
• systematic sampling with a random start;
• stratified random sampling.

Random selection helps reduce conscious and unconscious selection bias.

Non-probability sampling

In non-probability sampling, selection is not completely random, so the chance of any particular sampling unit being chosen may be unknown.

Examples include:

• opportunity sampling;
• quota sampling.

These methods may be quicker and more practical, but they are generally more vulnerable to bias.

Simple random sampling

To select a simple random sample:

1. Give every member of the sampling frame a unique number.
2. Generate random numbers using a calculator, computer or random number table.
3. Select the corresponding members.
4. Ignore numbers outside the required range and repeated numbers if sampling is without replacement.

Sampling without replacement means that once a unit has been selected, it cannot be selected again. This is the usual approach when sampling people.

Strengths and limitations

A simple random sample:

• reduces the researcher's influence over who is chosen;
• gives each possible sample of the required size an equal chance;
• makes statistical analysis easier to justify.

However, it requires a complete sampling frame and may select a sample that is unbalanced purely by chance. It may also be inconvenient if selected people are widely dispersed or difficult to contact.

Systematic sampling

If the population size is $N$ and the required sample size is $n$, the approximate sampling interval is

$$k=\frac{N}{n}.$$

Choose a random starting position among the first $k$ units, then select every $k$th unit.

Systematic sampling is usually quicker to carry out than simple random sampling. However, it can be biased if the ordering of the sampling frame contains a repeating pattern that matches the sampling interval.

Stratified random sampling

Sometimes a population contains distinct groups whose representation matters. These groups are called strata; one group is a stratum.

For a proportional stratified sample,

$$number\; sampled\; from\; a\; stratum=\frac{size\; of\; stratum}{population\; size}\times sample\; size.$$

Stratified sampling ensures that relevant groups are represented in appropriate proportions. However, the population must be divided into suitable strata, and separate sampling frames may be needed.

Opportunity sampling

For example, a researcher investigating opinions about college catering might ask the first 30 students leaving the dining hall.

Opportunity sampling is:

• quick and inexpensive;
• easy to organise;
• useful when no sampling frame is available.

However, it is likely to be biased because availability is related to where and when the sample is collected. The dining-hall sample, for instance, excludes students who do not use the dining hall.

It may also involve voluntary response bias: people who agree to participate may have stronger opinions than those who refuse.

Quota sampling

Quota sampling resembles stratified sampling because both use population groups. The crucial difference is how individuals are selected:

• In stratified sampling, members are selected randomly within each stratum.
• In quota sampling, the interviewer chooses available individuals within each group.

Quota sampling does not require a complete sampling frame and can ensure that important groups are included. However, interviewer choice can introduce bias.

Choosing a suitable technique

The best method depends on the population, available information, time and cost.

• Use simple random sampling when a complete sampling frame exists and unbiased random selection is practical.
• Use systematic sampling for a long ordered list, provided its ordering does not create a periodic pattern.
• Use stratified sampling when particular population groups must be represented proportionally.
• Use opportunity sampling when speed and access matter more than strong representativeness.
• Use quota sampling when group representation is needed but no complete sampling frame is available.

When evaluating a method, do not merely state that it “may be biased”. Explain which people are more or less likely to be selected and how that could affect the variable being measured.