📊Sampling Surveys Unit 4 – Stratified Sampling

What's Stratified Sampling?

• Stratified sampling divides a population into subgroups called strata based on shared characteristics or attributes
• Involves selecting a random sample from each stratum independently
• Ensures representation of key subgroups within the overall population
• Captures diversity within the population by sampling from each stratum separately
• Aims to reduce sampling error and increase precision compared to simple random sampling
• Requires identifying relevant stratification variables that are related to the characteristic of interest
• Can be proportionate (sample size of each stratum is proportional to population size) or disproportionate (equal sample sizes from each stratum regardless of population proportion)

Why Use Stratified Sampling?

• Ensures representation of all important subgroups or strata within the population
• Improves precision and reduces sampling error compared to simple random sampling
  • Sampling error is reduced because each stratum is more homogeneous than the entire population
• Guarantees sufficient sample sizes from minority groups or small but important subpopulations
• Enables separate estimates and comparisons between different strata
• Accommodates different sampling techniques, sample sizes, or costs for each stratum
• Can be more cost-effective and efficient than simple random sampling when strata are easily identifiable
• Provides better coverage of the population by ensuring all key segments are included in the sample

Key Concepts and Terms

• Stratification variables: The characteristics or attributes used to divide the population into strata (age groups, income levels, geographic regions)
• Stratum (plural: strata): A subgroup within the population that shares a common characteristic or attribute
• Stratification: The process of dividing a population into strata based on selected variables
• Sampling frame: A list of all units in the population from which the sample will be drawn
  • In stratified sampling, a separate sampling frame is created for each stratum
• Proportionate allocation: Sample size for each stratum is proportional to its size in the population
• Disproportionate allocation: Sample sizes are determined independently for each stratum, often to ensure sufficient representation of small but important subgroups
• Sampling weight: A weight assigned to each sampled unit to account for different probabilities of selection across strata

How to Do Stratified Sampling

• Define the population and identify the characteristic of interest to be estimated
• Determine relevant stratification variables that are related to the characteristic of interest
  • Stratification variables should create homogeneous subgroups with respect to the characteristic of interest
• Divide the population into mutually exclusive and exhaustive strata based on the selected stratification variables
• Create a separate sampling frame for each stratum
• Decide on the type of allocation (proportionate or disproportionate) based on research objectives and available resources
• Determine the desired sample size for each stratum based on the allocation method chosen
• Randomly select the required number of units from each stratum independently
• Collect data from the sampled units and compute estimates for each stratum and the overall population
  • Use sampling weights to account for different probabilities of selection across strata when computing overall estimates

Types of Stratified Sampling

• Proportionate stratified sampling: Sample size for each stratum is proportional to its size in the population
  • Ensures each stratum is represented in the sample according to its proportion in the population
• Disproportionate stratified sampling: Sample sizes are determined independently for each stratum, often to ensure sufficient representation of small but important subgroups
  • Useful when some strata are more variable or of greater interest than others
• Optimum allocation: Sample sizes are allocated to minimize variance for a fixed total sample size
  • Takes into account variability within strata and cost of sampling each stratum
• Post-stratification: Stratification is performed after data collection based on known population characteristics
  • Used to adjust for non-response or to ensure sample represents known population proportions

Pros and Cons

Pros:

• Ensures representation of all important subgroups or strata within the population
• Improves precision and reduces sampling error compared to simple random sampling
• Enables separate estimates and comparisons between different strata
• Can be more cost-effective and efficient than simple random sampling when strata are easily identifiable
• Provides better coverage of the population by ensuring all key segments are included in the sample

Cons:

• Requires accurate and complete information about the population to create strata
• Stratification variables must be related to the characteristic of interest for gains in precision
• Can be more complex and time-consuming to implement than simple random sampling
• Inappropriate stratification can lead to biased estimates if strata are not homogeneous or mutually exclusive
• Smaller sample sizes within each stratum may limit the ability to detect differences between strata

Real-World Examples

• Market research: Stratifying by age, gender, income, or geographic region to ensure representation of key customer segments
• Public health surveys: Stratifying by race, ethnicity, or socioeconomic status to assess health disparities and target interventions
• Educational research: Stratifying by school type (public, private, charter) or student characteristics (grade level, academic performance) to compare outcomes
• Agricultural studies: Stratifying by farm size, crop type, or soil characteristics to estimate crop yields or assess farming practices
• Political polls: Stratifying by political affiliation, likelihood to vote, or key demographic variables to predict election outcomes

Common Mistakes and How to Avoid Them

• Failing to ensure strata are mutually exclusive and exhaustive
  • Carefully define strata based on clear, non-overlapping categories that cover the entire population
• Using stratification variables that are not related to the characteristic of interest
  • Select variables based on prior knowledge or pilot studies to ensure they create homogeneous subgroups
• Allocating sample sizes inappropriately across strata
  • Use proportionate allocation unless there are specific reasons for disproportionate allocation (e.g., ensuring sufficient sample sizes for small but important subgroups)
• Ignoring sampling weights when computing overall estimates
  • Account for different probabilities of selection across strata by using sampling weights in analysis
• Overestimating the precision gains from stratification
  • Stratification is most effective when strata are homogeneous and the stratification variables are strongly related to the characteristic of interest