## 2.3 Types of sampling

One key to obtaining accurate estimates about the population is to ensure that the sample studied is representative of the population of interest (that is, to ensure the study is externally valid).

So, how can a representative sample of the population be found? Whenever a sample is taken, only some of the population is selected. The selected individuals can be chosen using either random sampling or non-random sampling.

The word random here has a specific meaning that is different than how it is often used in everyday use.

Definition 2.3 (Random) In research and statistics, random means "determined completely by chance".

### 2.3.1 Random sampling methods

In a random sample, each individual in the population can be selected on the basis of impersonal chance. (Remember that random means that the sample is determined completly by chance!) Some examples of random sampling methods appear in the following sections (Table 2.2).

The results obtained from a random sample probably generalise to the population from which the sample is drawn; that is, random samples are likely to produce externally valid studies.
Table 2.2: Comparing four types of random sampling
Type Stage 1 Stage 2 Reference
Systematic Start at a random location Take every $$n$$th element thereafter Sect. 2.5
Stratified Split into a few large groups ('strata') Select simple random sample from every stratum Sect. 2.6
Cluster Split into many small groups ('clusters'); select simple random sample of clusters Select all in the chosen clusters Sect. 2.7
Multistage Select simple random sample from the larger stage Select simple random sample from those chosen in Stage 1; etc. Sect. 2.8

Consider testing a pot of soup by 'sampling'. If the soup is stirred, we don't need to taste the whole pot of soup to see how the soup tastes.

The same principle applies in research: If we use a random sample (analagous to the stirring the soup), we don't need to study every member of the population. If we don't use a random sample (that is, we don't stir the soup), we do not get an overall impression of the population (or the soup).

### 2.3.2 Non-random sampling methods

A non-random sample requires some kind personal input. Examples of non-random samples include:

• Judgement sample: Individuals are selected, based on the researchers' judgement, depending on whether the researcher thinks they are likely to be agreeable or helpful. For example, researchers may decided to survey people who are not in a hurry.
• Convenience sample: Individuals are selected because they are convenient for the researcher. For example, researchers may gather data from their family and friends.
• Voluntary response (self-selecting) sample: Individuals participate if they wish to. For example, a voluntary response survey, or a TV station call-in survey.

In non-random sampling, those who are in the study may be different than those who are not in the study. That is, non-random samples are not likely to be externally valid.

Using a non-random sample means that the results may not generalise to the intended population: they probably do not produce externally valid studies.

Example 2.3 (Different ways to sample) During the COVID-19 (coronavirus) pandemic in 2020, a Facebook poll asked the question:

Do you think a Coronavirus vaccine should be compulsory?

The result was reported as '79 per cent of Australians oppose a compulsory vaccination', from a sample of over 53,000 responses.

However, this sample was a voluntary response sample, not a random sample, so the results may not be accurate. For example, many anti-vaccination groups instructed their members to flood the poll with 'No' responses (including celebrity chef Pete Evans), and the poll could have been completed by non-Australians as well as Australians.

The Federal Government's 'No Jab, No Pay' policy withholds certain benefits and payments from families who don't fully vaccinate their children. Do you agree with this policy?

In the sample of 1809 respondents, 83.7% either agreed or strongly agreed with this statement.

While this study did not use a random sample, the researchers made efforts to sample a representative cross-section of Australians:

Researchers recruited Australian adults aged 18-years and older to participate in the study through a large, well-established online panel provider. While not a random sample of the Australian population, researchers made efforts to ensure the sample included individuals representing a wide range of demographics (e.g., age, gender, location, income, political preferences, religiosity).

--- , p. 194

Further more, 'respondents were paid small token sum for their participation in the study' to encourage all selected respondents to provide an answer.

In Sect. 2.11, random and non-random samples are compared using an example.

### References

Smith, David T., Katie Attwell, and Uwana Evers. 2020. “Majority Acceptance of Vaccination and Mandates Across the Political Spectrum in Australia.” Politics 40 (2): 189–206.