### Types of Sampling

#### Random Sampling

Random sampling can also be thought of as a 'pick a name out of the hat' technique. Samples are chosen from a population either by using a random number table or a random number generator. Each member of the population has an equal, independent and known chance of being selected.

• Easy to implement.
• Each member of the population has an equal chance of being chosen.
• Free from bias.
• If the sampling frame is large random sampling may be impractical.
• A complete list of the population may not be available.
• Minority subgroups within the population may not be present in sample.

#### Stratified Sampling

The population is divided into subgroups (strata) based on specific characteristics, such as age, gender or race. Within the strata random sampling is used to choose the sample.

• Strata can be proportionally represented in the final sample.
• It is easy to compare subgroups.
• Information must be gathered before being able to divide the population into subgroups.

#### Worked Example

###### Worked Example

A school of $1000$ students are classified as follows:

• $57$% Brunette,
• $29$% Redhead,
• $14$% Blonde.

Find a stratified sample of $200$ students for this population.

###### Solution

Suppose we are interested in how each of these groups will react to this statement: everyone in this school has an equal chance of success. Relying on a random sample may under-represent the minority populations of the school (people with blonde hair). By grouping our population by hair colour, we can choose a sample ensuring each group is represented according to its proportion of the population. So $57$% of the sample should be brunette, $29$% should be redhead and $14$% blonde. Within each group (strata) you select your sample randomly. As our sample consists of $200$ people, $114$ should be brunette, $58$ should be redhead and $28$ should be blonde.

#### Cluster Sampling

Data is divided into clusters and random sampling is used to select whole clusters. The sample will be obtained from a collection of entire cluster groups. It is usually used with naturally occurring groups of individuals for example classrooms, city blocks or postcodes.

• Cuts down the cost and time by collecting data from only a limited number of groups.
• Can show grouped variations.
• It is not a genuine random sample.
• The sample size is smaller and from thus the sample is likely to be less representative of the population.
###### Illustrative Example

The children in a classroom are divided up depending on which table they sit at. A sample can be obtained from this classroom by choosing $n$ number of tables to represent the class.

#### Systematic Sampling

All data is sequentially numbered and every $n$th piece of data is chosen. The number $n$ is chosen by $\displaystyle n=\frac{\text{size of population}}{\text{desired population size}}.$

• Easy to select.
• Identified easily.
• Evenly spread over the entire population.
• May be biased where the pattern used for the samples coincides with a pattern in the population.
###### Illustrative Example

In a class of 14 students, 4 names are chosen out of the hat for an assignment. Systematically sampling them would mean choosing every 3rd student in the class.

#### Convenience Sampling

Data is chosen based on convenience.

• Cuts down the cost of preparing a sampling frame as it is less time-consuming.
• Bias, as it is does not represent the population well.
###### Illustrative Example

A sample is chosen from a classroom by the $n$ number of children sat nearest the teacher.

#### Multistage Sampling

Multistage sampling is where a combination of sampling techniques is used. For example cluster sampling and random sampling.