Maths - Sampling methods

Simple random sampling

Randomly selects a sample from the population.

Every possible sample of size n has an equal chance of being chosen.

Reduces systematic bias.

Requires the whole population to be known and identifiable

Best method for making reliable inferences about the population (with a large enough sample).

Larger sample sizes reduce the chance of a biased sample.

Stratified sampling

Used when the population has clear subgroups (strata).

Ensures each subgroup is represented proportionally in the sample.

Number selected from each subgroup: (subgroup size/population size) x sample size.

Individuals within each subgroup are selected randomly.

Requires detailed information about the population before sampling.

Quota sampling

Population is divided into subgroups.

A set quota is taken from each subgroup (not necessarily proportion).

Individuals are not selected randomly.

High risk of bias due to non-random selection.

Systematic sampling

Population is listed in an ordered way (e.g. alphabetically).

Selects every nth person/item from the list.

Simple and quick to carry out.

Can be biased if the ordering of the list follows a pattern.

Opportunity (convenience) sampling

Selects the most accessible or available individuals.

Can be used even when the population size is unknown.

Quick, easy, and inexpensive.

Often uses the first n people/items available. High risk of bias because some groups are more likely to be included than others.

Cluster sampling

Population is divided into representative groups (clusters).

A sample is taken from only a few clusters.

Useful when clusters are similar to the whole population.

Appropriate only if the characteristic being studied is unlikely to differ between clusters.

Self-selected sampling

Individuals choose to take part in the sample.

Example: online public surveys.

Easy to collect responses.

High risk of bias because volunteers may not represent the whole population.