Stratified sampling is a probability sampling technique where the population is divided into distinct, non-overlapping subgroups or strata based on one or more characteristics, and then a random sample is selected from each stratum. The purpose is to ensure that the sample is representative of the overall population and to potentially increase the precision of estimates.
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Stratified sampling ensures that the sample is representative of the population by including individuals from all relevant subgroups or strata.
Stratification can be based on any characteristic of the population, such as age, gender, income level, or geographic location.
Stratified sampling can improve the precision of estimates compared to simple random sampling, especially when the variability within strata is lower than the variability between strata.
Proportional allocation is a common method of assigning sample sizes to each stratum, where the sample size for each stratum is proportional to the size of that stratum in the population.
Stratified sampling can be used in both data collection experiments and sampling experiments to ensure that the sample is representative of the population.
Review Questions
Explain how stratified sampling can be used to ensure a representative sample in a data collection experiment.
In a data collection experiment, stratified sampling can be used to ensure that the sample is representative of the population by dividing the population into distinct subgroups or strata based on relevant characteristics, such as age, gender, or income level. A random sample is then selected from each stratum, with the sample size for each stratum proportional to the size of that stratum in the population. This ensures that the sample includes individuals from all relevant subgroups, allowing the researcher to make more accurate inferences about the population.
Describe how stratified sampling can be used to increase the precision of estimates in a sampling experiment.
In a sampling experiment, stratified sampling can be used to increase the precision of estimates by reducing the variability within the sample. By dividing the population into distinct, homogeneous strata based on relevant characteristics, the variability within each stratum is typically lower than the variability in the overall population. This allows the researcher to obtain more precise estimates of population parameters, such as the mean or proportion, by combining the estimates from each stratum. The increased precision can be particularly useful when the researcher is interested in making inferences about specific subgroups within the population.
Analyze how stratified sampling can be applied in the context of independent and mutually exclusive events, and how it might impact the calculation of a population proportion.
In the context of independent and mutually exclusive events, stratified sampling can be used to ensure that the sample accurately represents the different subgroups or strata within the population. For example, if the population can be divided into mutually exclusive strata based on a characteristic like gender, stratified sampling can be used to obtain a sample that includes the appropriate proportions of males and females. This can be particularly important when calculating a population proportion, as the proportion may vary significantly between the different strata. By using stratified sampling, the researcher can obtain a more accurate estimate of the overall population proportion by combining the estimates from each stratum, weighted by the relative size of each stratum in the population.
A sampling method where each member of the population has an equal chance of being selected for the sample.
Proportional Allocation: A method of allocating the sample size to each stratum in proportion to the size of the stratum relative to the total population.