A sample is a subset of the population. When a sample is taken, it is important that it is representative of the population. There are six different sampling methods you need to know, as well as the advantages and disadvantages of each type.

Random sampling

Random sampling means that each member of the population has an equal chance of being selected. Random sampling helps to remove any bias from the sampling process, and in turn this should ensure that the sample is representative of the population.

type	description	advantages	disadvantages
Simple random sampling	Every individual item from the sample size $n$ has an equal chance of being selected.	Free of bias. Easy and cheap for small samples. Each sample unit has a known and equal chance of selection.	Not suitable for large samples and populations. Sampling frame is needed.
Systematic sampling	The individual items are chosen at regular intervals from an ordered list.	Simple and quick to use. Suitable for large samples and populations.	Sampling frame or ordered list is required. Bias would be introduced if the ordered list is not random.
Stratified sampling	A population is divided into 'strata' or groups, then a simple random sample is taken from each. The size of the group for the sample should be proportional to the size of the group in the population.	The sample would have an accurate representation of the population structure. Proportional representation of each group from the population.	It must be possible to divide the population into separate strata. Same disadvantages as simple random sampling within each group.
Cluster sampling	A population is split into clusters based on convenience, then a simple random sample is taken from each. The clusters are not necessarily representative of the population.	Cheaper and easier than other random methods like stratified sampling.	Less accurate than other methods of random sampling. Clusters may not be representative of the whole population.

Non-random sampling

Sometimes, ensuring a random sample is difficult. Part of this difficulty is due to the fact that it may not be possible to obtain a list of all the members of a population to which you can then apply a sampling procedure. In this case, there are two non-random sampling methods that can be used.

type	description	advantages	disadvantages
Quota sampling	The population is divided into groups according to a particular characteristic. The size of the group determines the proportion of the sample that should have that characteristic.	Allows a small sample to be representative of the population. No sampling frame required. Quick, easy and inexpensive. Easy comparison between groups.	Non random sampling can introduce bias. Splitting the population into groups can be inaccurate. Non responses would not be recorded.
Opportunity sampling	Take a sample from people who are available at the time of study, who fit the required criteria.	Easy and inexpensive.	Sample is unlikely to be representative. The sample would be dependent on the researcher.

Example 1

A large company has $5000$ full-time staff and $3000$ part-time staff. A manager wants to investigate their opinions on company policy and wants to take a sample of $40$ members of staff. What type of sampling method should she use? Describe the sampling method.

The total population size is known and there are two distinct groups to sample from. Therefore, the best type of sampling to use is stratified sampling.

Use a table to calculate the size of the groups in the sample, the ratio of the sample size to the population size is $1:200$ . Therefore, use a scale factor of $200$ to work out the size of the groups in the sample.

	Full-time	Part-time	total
Population	$5000$	$3000$	$8000$
Sample	$\dfrac {5000}{200} = 25$	$\dfrac{3000}{200}=15$	$40$

The manager should choose $\underline{25}$ full-time staff and $\underline{15}$ part-time staff.

Learn with Basics

Length:

Unit 1

Collecting data: types and classes of data

Unit 2

Sampling and bias

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Optional

Unit 3