Glossary

4.2 Methods of stratification

3 min read•august 9, 2024

Stratified sampling uses various methods to divide populations into groups. Geographic and demographic factors help create representative samples, while advanced techniques like cluster stratification and post-stratification improve efficiency and accuracy.

Allocation methods determine how to distribute samples across strata. Proportional allocation maintains population proportions, while optimal and Neyman allocation consider variability and costs. Proper stratification and allocation enhance survey precision and representativeness.

Stratification Techniques

Geographic and Demographic Stratification

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  • Geographic stratification divides population based on physical location (countries, states, cities)
  • Improves sampling efficiency by capturing regional variations
  • Demographic stratification uses population characteristics (age, gender, income)
  • Ensures representation of diverse subgroups within the sample
  • Combines geographic and demographic factors for more precise stratification
  • Utilizes census data or existing population databases to define strata

Advanced Stratification Methods

  • Cluster stratification groups similar units into clusters before sampling
  • Reduces costs and improves efficiency in large-scale surveys
  • Involves two-stage sampling: select clusters, then sample within clusters
  • Post-stratification adjusts sample data after collection to match population proportions
  • Corrects for under or overrepresentation of certain groups in the sample
  • Applies weights to observations based on known population characteristics

Allocation Methods

Proportional and Optimal Allocation

  • Proportional allocation assigns sample sizes to strata based on their proportion in the population
  • Ensures each is represented relative to its size in the overall population
  • Calculated as nh=n×(Nh/N)n_h = n \times (N_h / N) where nhn_h is stratum sample size, nn is total sample size, NhN_h is stratum population size, and NN is total population size
  • Optimal allocation minimizes variance for a given cost or minimizes cost for a given variance
  • Considers both stratum size and variability within each stratum
  • Allocates larger samples to strata with higher variability or lower sampling costs

Neyman and Sample Size Allocation

  • Neyman allocation optimizes sample allocation when costs are equal across strata
  • Assigns larger samples to strata with higher standard deviations
  • Calculated as nh=n×(NhSh/∑NiSi)n_h = n \times (N_h S_h / \sum N_i S_i) where ShS_h is the standard deviation of the stratum
  • Sample size allocation determines the overall sample size needed for desired precision
  • Considers factors such as confidence level, margin of error, and population variability
  • Uses formulas like n=(z2×s2)/e2n = (z^2 \times s^2) / e^2 where zz is the z-score, ss is the population standard deviation, and ee is the margin of error

Stratification Principles

Stratification Variable Selection and Homogeneity

  • Stratification variables strongly correlate with the study variable of interest
  • Choose variables that create homogeneous groups within strata
  • Reduces within-stratum variance and improves overall estimation precision
  • Common stratification variables include age, income, education level, or geographic region
  • within strata minimizes variation of the characteristic being measured
  • Increases precision of estimates by reducing within each stratum

Stratum Boundaries and Efficiency

  • between strata maximizes differences in the characteristic across groups
  • Enhances the ability to capture population diversity in the sample
  • Stratum boundaries define clear, non-overlapping divisions between groups
  • Use natural breaks, percentiles, or optimization techniques to determine boundaries
  • Stratification efficiency measures the improvement in precision compared to simple
  • Calculated as the ratio of the variances: Eff=VarSRS/VarStratifiedEff = Var_{SRS} / Var_{Stratified}
  • Higher efficiency ratios indicate greater benefits from stratification

Key Terms to Review (16)

Block Sampling: Block sampling is a sampling technique where the population is divided into groups or blocks, and then whole blocks are selected for analysis rather than individual elements. This method can enhance efficiency and reduce costs, especially when certain blocks are more accessible or relevant to the study. By focusing on these blocks, researchers can achieve better representation of specific characteristics within the population.
Demographic Variables: Demographic variables are the statistical characteristics of a population that can be used to analyze and understand different groups within that population. These variables include age, gender, race, income level, education, and marital status, among others, and they help researchers identify patterns and trends within various segments of society.
Disproportional Stratified Sampling: Disproportional stratified sampling is a technique where the sample sizes from different strata (subgroups) do not reflect their proportions in the population. Instead, certain strata may be over-sampled or under-sampled to ensure adequate representation of specific groups or to improve the precision of estimates for those groups. This method helps to address the needs of analysis by allowing researchers to focus on particular segments of a population that are of interest, making it vital for effective analysis and estimation.
Heterogeneity: Heterogeneity refers to the presence of diverse or varied characteristics within a population or sample. In research, understanding heterogeneity is crucial because it influences how data is collected, analyzed, and interpreted. Different subgroups may respond differently to interventions or exhibit unique patterns, making it essential to account for these differences when designing sampling strategies and determining sample sizes.
Homogeneity: Homogeneity refers to the quality of being similar or uniform in nature within a particular group or population. In sampling, this concept plays a vital role in how samples are chosen, as it influences the stratification process, helps define clusters, and impacts the efficiency of sampling methods. When a population is homogeneous, it means that its members share similar characteristics, which can lead to more accurate and reliable data collection.
Increased Precision: Increased precision refers to the enhancement of the accuracy and reliability of estimates derived from a sample, particularly through stratification methods. It ensures that the sample closely represents the entire population by minimizing variability within subgroups, allowing for more accurate generalizations. Achieving increased precision is crucial for effective analysis and estimation as it leads to reduced sampling error and more trustworthy results.
Layering: Layering is a technique used in sampling surveys where the population is divided into distinct subgroups or strata to improve the accuracy and efficiency of the sample. This method helps ensure that each subgroup is represented appropriately, leading to more reliable results in data analysis. By organizing the population into layers, researchers can focus on specific characteristics and variations within each stratum, which enhances the overall understanding of the data collected.
Proportional Stratified Sampling: Proportional stratified sampling is a sampling method where the population is divided into distinct subgroups, or strata, and samples are drawn from each stratum in proportion to its size relative to the entire population. This approach ensures that each subgroup is adequately represented in the final sample, which enhances the accuracy of estimates and analysis. By using this technique, researchers can better understand the characteristics of different segments within a population and improve the reliability of their findings.
Random Sampling: Random sampling is a method used to select individuals from a larger population where each member has an equal chance of being chosen. This technique helps ensure that the sample represents the overall population, minimizing bias and allowing for valid generalizations from the sample to the larger group.
Reduced Bias: Reduced bias refers to the minimization of systematic errors that can affect the validity and reliability of survey results. It plays a critical role in enhancing the accuracy of data collection methods, ensuring that samples accurately reflect the population being studied. By addressing various sources of bias, such as selection bias or measurement bias, researchers can obtain more reliable insights and make better-informed decisions based on their findings.
Sampling error: Sampling error is the difference between the results obtained from a sample and the actual values in the entire population. This error arises because the sample may not perfectly represent the population, leading to inaccuracies in estimates such as means, proportions, or totals.
Sampling frame: A sampling frame is a list or database from which a sample is drawn for a study, serving as the foundation for selecting participants. It connects to the overall effectiveness of different sampling methods and is crucial for ensuring that every individual in the population has a known chance of being selected, thus minimizing bias and increasing representativeness.
Socioeconomic status: Socioeconomic status (SES) is an individual's or group's social and economic position relative to others, often measured by factors such as income, education, and occupation. It plays a critical role in understanding access to resources, health outcomes, and social mobility, influencing how populations are stratified and how demographic data is collected and analyzed.
Stratified Analysis: Stratified analysis is a statistical method used to examine the relationship between variables within different subgroups of a population. This technique helps to identify patterns and trends by segmenting data into strata, allowing for more precise insights and minimizing potential confounding factors. It emphasizes the importance of recognizing the heterogeneity within populations to draw more accurate conclusions.
Stratum: A stratum is a subset of a population that shares a specific characteristic, which is used in stratified sampling to ensure representation across different segments. Each stratum is formed based on key attributes like age, income, or education level, helping to provide a more accurate reflection of the population. This division allows for tailored sampling methods that enhance the precision of estimates and analyses.
Weighted analysis: Weighted analysis is a statistical method used to give different levels of importance to various observations or strata in a sample. This technique adjusts the results based on the representation of each stratum in the overall population, ensuring that the analysis reflects the true characteristics of the entire group rather than just the sample. By using weights, researchers can improve the accuracy and validity of their findings, especially when certain segments of a population are underrepresented or overrepresented.
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