Sampling Methods

Sampling methods are techniques used to select a subset of individuals (a sample) from a population to represent the entire group. The goal is to gather data that can be used to make inferences about the population without surveying every member.

Random sampling

In random sampling, every individual in the population has an equal chance of being selected.

Example: Drawing names from a hat where every name has an equal probability of being picked. The probability of selecting an individual from a population of size \(N\) in a random sample of size \(n\) is:

\[P(\text{selection}) = \frac{1}{N}\]

This method is simple and unbiased, but it can be difficult to implement for very large populations.

Systematic sampling

In systematic sampling, members of the population are selected at regular intervals from a list or ordered group. For example, every \(k\)-th individual is chosen.

Example: Selecting every 10th person from a list of registered voters.

To calculate the sampling interval \(k\), use:

\[k = \frac{N}{n}\]

where \(N\) is the population size and \(n\) is the desired sample size.

Stratified sampling

In stratified sampling, the population is divided into distinct subgroups (strata) based on a characteristic such as age, gender, or income. A sample is then drawn from each stratum, either proportionally or equally.

Example: Dividing a population into age groups and selecting a sample from each group to ensure representation of all age categories.

The sample size from each stratum can be calculated using:

\[\text{Sample size from stratum} = \frac{\text{Stratum size}}{N} \times n\]

This ensures representation from all strata, making the sample more reflective of the population.