Random, Systematic, and Quota Sampling

Suppose students want to investigate opinions about school uniform. Their population is all the students in the school, and their sample is the smaller group they interview. An up-to-date list of all students could provide their sampling frame.

The way they choose students matters. Interviewing only their friends could favour particular opinions and leave other views out. This is selection bias: the selection process tends to favour some members of the population over others.

Random, systematic and quota sampling offer different ways to select people. The appropriate choice depends on whether a complete list is available, the size of the population and which groups need to be represented. None guarantees that the sample will perfectly reflect the population.

Random sampling: removing personal choice

Random sampling uses chance to select members rather than allowing the researcher to choose them. In a simple random sample, every member of the population has an equal chance of selection.

For a school uniform survey, the students could number everyone on the school list and use randomly selected, distinct numbers to choose whom to interview. Choosing from the whole list avoids deliberately favouring friends, particular classes or students who are easiest to approach.

This is suitable when a complete sampling frame is available and it is practical to contact the selected members. It is harder to use when the population cannot easily be listed, such as all the fish in a lake.

Random selection reduces selection bias, but chance can still produce an unbalanced sample. A small random sample might contain very few students from one year group. Also, if selected students refuse to respond, the people who actually answer may differ from those who do not.

Systematic sampling: selecting at regular intervals

Systematic sampling selects members at regular intervals through a population list. It can make selection straightforward when working with a large sampling frame.

When the population size divides exactly by the required sample size, calculate the interval using:

For a school with 480 students and a required sample of 30, the interval is $480 \div 30 = 16$. Choose a starting number randomly from 1 to 16, then select every 16th student after it.

If the starting number is 7, the selected positions are:

This gives 30 students spread through the list. The random start prevents the researcher from choosing a convenient first person, but after that start the rest of the selections are fixed. This is not the same procedure as choosing every member independently at random.

Checking the order of a systematic sampling frame

Regular selection can be a problem if it matches a repeating pattern in the list.

Imagine a list arranged in five-person teams, with each team captain listed first. Selecting every fifth person would select the same position in every team. Depending on the starting point, the sample would contain either only captains or no captains.

A random starting point does not remove this problem. If captains have different views from other team members, the sample could give a misleading picture. Before using systematic sampling, check how the list is arranged. Randomising the order, or choosing a different sampling method, can avoid selecting the same type of member repeatedly.

Quota sampling: ensuring specified groups are included

Quota sampling sets a required number of respondents from each group. The researcher selects people until each quota is filled; the people within a group do not have to be chosen randomly.

For example, a class contains 12 boys and 18 girls, giving 30 pupils altogether. A proportional quota sample of 10 would contain:

• $\frac{12}{30} \times 10 = 4$ boys;
• $\frac{18}{30} \times 10 = 6$ girls.

The researcher would collect responses until four boys and six girls had taken part. If someone declined, another person from the same group could be approached.

Proportional quotas preserve the population proportions for the chosen categories. More generally:

Quota sampling is useful for opinion surveys when a complete list of individuals is unavailable, but information about the population's group proportions is known. It also prevents an easily reached group from filling the entire sample.

Representation is not the same as freedom from bias

A quota sample can match the required group proportions and still be biased. A teacher choosing favourite pupils could meet the quotas of four boys and six girls without representing the class's range of views. Similarly, interviewing passers-by at only one place and time may exclude people who are elsewhere.

Quotas control how many people come from each specified group, not which people are chosen within it. They therefore improve representation of those categories without guaranteeing an unbiased sample.

When choosing a method, connect its strengths and limitations to the investigation: random selection reduces personal choice, systematic selection is efficient with a suitable list, and quota sampling secures specified group numbers without requiring a complete sampling frame.