Multi random sampling, often referred to as multistage sampling, is a complex probability sampling technique that involves random selection at multiple stages or levels. It is an extension of cluster sampling.
At its core, multistage sampling allows researchers to draw a sample from a large population spread over a wide geographic area without having to sample every individual or even every subgroup directly.
Understanding Multistage Sampling
Based on the provided reference, multistage sampling works by:
- First, clusters are randomly selected. Clusters are naturally occurring groups or segments within the population (e.g., geographic areas, schools, hospitals).
- Second, sample units within the selected clusters are randomly selected. Once the initial clusters are chosen, individuals or smaller units within only those selected clusters are randomly sampled.
This process highlights that random selection occurs at both the cluster or group level and at the sample unit level.
How it Differs from Cluster Sampling
While similar to cluster sampling, which involves randomly selecting clusters and then including all units within those selected clusters, multistage sampling adds another layer of random selection. In multistage sampling, you don't necessarily include everyone in the selected clusters; you randomly sample from within them.
Think of it like this:
- Cluster Sampling: Randomly pick a few classrooms in a school, then survey every student in those chosen classrooms.
- Multistage Sampling: Randomly pick a few schools in a city, then randomly pick a few classrooms within each selected school, and finally, randomly pick a few students within each selected classroom to survey. (This would be a three-stage process).
Key Stages of Multistage Sampling
The number of stages can vary depending on the research design. A common multistage process involves at least two stages:
- Stage 1: Randomly select primary sampling units (PSUs), which are the large clusters.
- Stage 2: Within each selected PSU, randomly select secondary sampling units (SSUs), which could be sub-clusters or individual elements.
More stages can be added (e.g., selecting tertiary units within SSUs), making it three-stage, four-stage sampling, and so on.
| Stage | Action | What is Randomly Selected? |
|---|---|---|
| Stage 1 | Randomly select clusters | Primary Sampling Units |
| Stage 2 | Randomly select units | Within selected clusters |
| Stage 3+ | (Optional) Randomly select | Within selected units |
Practical Example
Imagine a study on health habits across a large country.
- Stage 1: Randomly select a certain number of states (primary clusters).
- Stage 2: Within each selected state, randomly select a certain number of counties (secondary clusters).
- Stage 3: Within each selected county, randomly select a certain number of households (tertiary units).
- Stage 4: Within each selected household, randomly select one adult to survey (final sampling unit).
This saves resources compared to trying to create a list of every household or county in the entire country initially.
Benefits and Considerations
- Efficiency: Reduces the cost and effort associated with creating a comprehensive sampling frame for the entire population.
- Practicality: Allows for sampling over wide geographic areas when simple random sampling or stratified sampling would be impractical.
- Flexibility: Can be adapted to various population structures and research needs.
However, it's important to note that multistage sampling can be more complex to design and analyze than simpler methods, and requires careful consideration at each stage to ensure representativeness.
