Drawing a sample: probability sampling

The sample lies at the heart of survey research. It’s often called a miniature of the population, and the process of drawing a sample should maximise the similarity between the sample and the population under study. So how do we achieve this goal? There are two approaches to drawing a sample, non-probability and probability sampling. Probability sampling gives all units in the target population a chance of being selected to be in the study, and the probability is known. For example, if you have a list of 10,000 members of your target population, and you randomly draw 500 people for an interview, each member of the population has a 5% chance of being selected for the survey sample.

Let’s look at how to draw a probability sample and why it matters that a sample is drawn randomly. Let’s imagine that this is a population, and each of these dots represents an individual and the colours represent a measure of sociodemographic diversity of people, like ethnicity or age group. To obtain a good survey sample, first, you must determine a target population, and to do that you have to define spatial and temporal boundaries. So a geographic area and a time period. For example, it could be that we’re interested in studying people living in Sheffield who have visited a cinema in the last six months. The second step is to find the most suitable sampling frame.

This is a list of all the individuals in your target population. Now, having clearly defined the population you want to study, you can proceed to drawing a sample. The basic principle you follow is to obtain a representative sample, which means getting a smaller group, which would be a mini version of the population you study. Why is it so important that the sample resembles the whole population? Only when your sample and target population have similar characteristics can you generalise the results of your survey to the whole population.

So you want to end up with similar percentages of people with different demographic traits, such as gender, age and place of residence, as well as different preferences, opinions and attitudes within your chosen area. The best way of achieving this representativeness is to select individuals randomly. Random sampling gives each object an equal chance of being selected. If you followed any non-random pattern, like asking your friends or designing a quota, your sample would not represent the population well, and your estimates based on the sample would be biased. We could compare this procedure to the process of tasting soup. If you want to try soup to check whether it tastes good, you don’t need to eat the whole bowl.

If it’s well mixed, a random try of just a spoonful will tell you whether it’s tasty or not. Random sampling approaches work best when you have to make conclusions about the whole population, such as finding out how many of the dots in population are blue? If you want to investigate differences between specific groups that you know are different sizes, you should take a different approach. Let’s say that we want to compare differences in political attitudes across different ethnic groups. Each colour here represents a different ethnic group. And one of the groups is much smaller.

Random selection from the whole population would mean that we will receive a very small number of people represented by the blue dots, and this group is unlikely to be internally diverse enough in terms of other traits, like age or geographic coverage. Instead you could draw a stratified sample, which means that you have to divide the population into subgroups, each representing the ethnic groups. Since you want to measure differences to the same degree of precision, subsamples drawn from each subgroup should be of the same size. Now you randomly select your individuals from within these subgroups. Your sample is stratified, and should be highly representative for each subsample thanks to the random selection.

So in this example, it would allow you to precisely investigate differences in political attitudes between ethnic groups using a survey method. In summary, we have explained a few crucial steps that should be undertaken in designing a sample for a representative survey. If your population is clearly defined - you know who, what, where and when you want to study - then you can select the best sampling frame for your target population, and randomly draw a sample. And that is sampling, something relatively simple, which can have a profound effect on the reliability of a study.