Stratified sampling is a probability sampling technique in which the population is divided into distinct subgroups or strata, and a random sample is then selected from each stratum. This method ensures that the sample is representative of the overall population by capturing the diversity within the different strata.
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Stratified sampling is used to ensure that the sample is representative of the population, especially when the population is heterogeneous and consists of distinct subgroups.
The strata in stratified sampling are formed based on one or more characteristics of the population, such as age, gender, income level, or geographic location.
Stratified sampling can improve the precision of the estimates obtained from the sample, as it reduces the variability within the strata.
Proportional allocation is a common method of allocating the sample size to each stratum, where the sample size for each stratum is proportional to the size of the stratum in the population.
Stratified sampling is often used in experimental design and hypothesis testing, as it helps to control for confounding variables and improve the statistical power of the analysis.
Review Questions
Explain how stratified sampling ensures a representative sample of the population.
Stratified sampling ensures a representative sample by dividing the population into distinct subgroups or strata based on relevant characteristics, and then selecting a random sample from each stratum. This method ensures that the sample reflects the diversity and proportions of the different subgroups within the population, which is particularly important when the population is heterogeneous. By capturing the variation within the strata, stratified sampling can provide more precise estimates and improve the statistical power of the analysis.
Describe the role of stratified sampling in experimental design and hypothesis testing.
Stratified sampling is often used in experimental design and hypothesis testing to control for confounding variables and improve the statistical power of the analysis. By dividing the population into homogeneous strata, researchers can ensure that the experimental groups are balanced with respect to important characteristics, reducing the impact of potential confounding factors. Additionally, stratified sampling can increase the precision of the estimates obtained from the sample, leading to more robust statistical inferences and a higher likelihood of detecting significant effects, if they exist.
Evaluate the advantages and limitations of using proportional allocation in stratified sampling.
The primary advantage of using proportional allocation in stratified sampling is that it ensures the sample size for each stratum is proportional to the size of the stratum in the population. This helps to maintain the representativeness of the sample and can improve the precision of the estimates. However, a limitation of proportional allocation is that it may not be optimal for all research questions or study designs. In some cases, it may be more appropriate to use disproportionate allocation, where the sample size for each stratum is determined based on other factors, such as the expected variability within the stratum or the desired level of precision for the estimates. The choice of allocation method should be guided by the specific research objectives and the characteristics of the population.
A method of selecting a sample in which each individual in the population has an equal chance of being chosen, and the selection of one individual is independent of the selection of others.
A sampling technique in which the population is divided into clusters, and a random sample of clusters is selected, with all individuals within the selected clusters being included in the sample.
Proportional Allocation: A method of allocating the sample size to each stratum in stratified sampling, where the sample size for each stratum is proportional to the size of the stratum in the population.