What is Stratified Sampling in Mathematics?
Stratified sampling is a method of sampling that involves dividing a population into distinct subgroups, or 'strata,' that are different from each other. This technique ensures that each subgroup is adequately represented within the overall sample, which helps to improve the accuracy and reliability of the results.
How is Stratified Sampling Performed?
To perform stratified sampling, follow these steps:
1. Identify the Strata: Divide the entire population into different subgroups, or strata. These strata should be mutually exclusive, meaning no individual can belong to more than one stratum. The division is usually based on specific characteristics, such as age, gender, income level, etc.
2. Determine the Sample Size for Each Stratum: Decide how many individuals you want to sample from each stratum. This can be proportional to the size of each stratum relative to the overall population, or it can be an equal number of samples from each stratum, depending on the study’s requirements.
3. Random Sampling Within Each Stratum: Perform a random sampling within each stratum. This ensures that every individual within each stratum has an equal chance of being selected. This random selection can be done using simple random sampling techniques like drawing lots, using random number generators, etc.
4. Combine the Sampled Units: Once you have sampled units from each stratum, combine them to form your overall sample. This aggregated sample should reflect the population’s structure more accurately than a simple random sample.
Example of Stratified Sampling:
Suppose you want to study the dietary habits of a city's population, which consists of 60% adults and 40% children. A simple random sample may, by chance, include fewer children or more adults, leading to biased results. In stratified sampling:
1. Identify the Strata: - Stratum 1: Adults - Stratum 2: Children
2. Determine the Sample Size: If you decide to sample 100 individuals: - 60% of 100 = 60 adults - 40% of 100 = 40 children
3. Random Sampling Within Each Stratum: Randomly select 60 individuals from the adult population and 40 individuals from the child population.
4. Combine the Sampled Units: Combine the selected adults and children to form your sample of 100 individuals.
By ensuring that each subgroup is proportionally represented, this technique mitigates the risk of bias and enhances the study’s reliability.
Why Use Stratified Sampling?
Stratified sampling is particularly useful when:
- The population is heterogeneous and can be easily subdivided into non-overlapping subgroups.- Researchers aim to understand differences between subgroups.- There's a need to ensure representation of distinct subgroups within the sample.- You want to increase statistical efficiency by reducing sampling error.
Conclusion
Stratified sampling is a robust sampling method that can significantly improve the accuracy of your data by ensuring all relevant subgroups are represented. By dividing the population into distinct strata and performing random sampling within each, researchers can better capture the diversity within the population, leading to more reliable and generalisable results.
Sample Design The city of Naperville is considering the construction of a new commuter rail station. The city wishes to survey the residents of the c…
Sample Design A marketing executive for Coca-Cola, Inc., wants to identify television shows that people in the Boston area who typically drink Coke a…
Putting It Together: Comparing Sampling Methods Suppose a political strategist wants to get a sense of how American adults aged 18 years or older fee…
Putting It Together: Thinking about Randomness What is random sampling? Why is it necessary for a sample to be obtained randomly rather than convenie…
Watch the video solution with this free unlock.
EMAIL
PASSWORD