5.2 One-stage and two-stage cluster sampling

Cluster sampling is a key technique in survey research, allowing for efficient data collection from groups of population elements. One-stage and two-stage methods offer different approaches, balancing precision and practicality in sample selection.

Understanding primary and secondary sampling units is crucial for implementing cluster sampling effectively. These concepts form the foundation for designing surveys that capture population characteristics while managing resources and logistical constraints.

Cluster Sampling Basics

Primary and Secondary Sampling Units

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• Cluster represents a group of population elements serving as the sampling unit
• Primary sampling unit (PSU) denotes the initial unit selected in cluster sampling
  • Often corresponds to naturally occurring groups (schools, hospitals, neighborhoods)
  • Forms the basis for the first stage of selection in cluster sampling
• Secondary sampling unit (SSU) refers to the elements or subgroups within the selected PSUs
  • Selected in the second stage of two-stage cluster sampling
  • Can be individual elements or smaller subgroups within the PSU

One-Stage and Two-Stage Cluster Sampling

• One-stage cluster sampling involves selecting PSUs and including all elements within chosen clusters
  • Simplifies data collection by focusing on fewer, larger units
  • Reduces travel and administrative costs compared to simple random sampling
• Two-stage cluster sampling selects PSUs first, then samples SSUs within chosen clusters
  • Offers more flexibility in sample size and allocation
  • Allows for more precise estimates when clusters are large or heterogeneous
• Sampling frame lists all clusters or PSUs in the population
  • Crucial for the proper implementation of cluster sampling
  • May be easier to construct than a complete list of individual elements

Cluster Characteristics

Intraclass Correlation and Homogeneity

• Intraclass correlation measures the similarity of elements within clusters
  • Ranges from 0 (no correlation) to 1 (perfect correlation)
  • Higher values indicate greater homogeneity within clusters
• Homogeneity within clusters refers to the similarity of elements in the same cluster
  • Affects the efficiency of cluster sampling
  • Can lead to less precise estimates compared to simple random sampling
• Heterogeneity between clusters indicates differences among clusters
  • Desirable for cluster sampling to capture population variability
  • Improves the representativeness of the sample

Cluster Size Considerations

• Cluster size impacts sampling efficiency and logistics
  • Larger clusters may reduce travel costs but increase intraclass correlation
  • Smaller clusters often provide more precise estimates but may increase overall sample size
• Optimal cluster size balances statistical efficiency and practical considerations
  • Depends on the specific study objectives and resource constraints
  • May vary depending on the population structure and research question

Efficiency and Cost

Design Effect and Sampling Efficiency

• Design effect measures the efficiency of cluster sampling relative to simple random sampling
  • Calculated as the ratio of the variance of the cluster sample to that of a simple random sample
  • Values greater than 1 indicate a loss in precision due to clustering
• Sampling efficiency compares the precision of different sampling designs
  • Influenced by cluster characteristics, sample size, and allocation methods
  • Helps researchers choose the most appropriate sampling strategy for their study

Cost-Effectiveness and Practical Considerations

• Cost-effectiveness balances statistical precision with resource constraints
  • Cluster sampling often reduces travel and administrative costs
  • May require larger sample sizes to achieve the same precision as simple random sampling
• Practical considerations include:
  • Ease of accessing and enumerating clusters
  • Availability of sampling frames at different levels
  • Logistical constraints in data collection and analysis
• Trade-offs between cost, precision, and feasibility guide the choice of sampling design
  • Researchers must weigh these factors to optimize their sampling strategy
  • May involve compromises between ideal statistical properties and practical limitations