What is stratified random sampling?
Stratified random sampling is a sampling method that divides a population into smaller subgroups called strata. In stratified random sampling, or stratification, strata are formed based on common attributes or characteristics of members, such as: B. Income or level of education. Stratified random sampling has numerous applications and benefits, such as: B. the study of population demography andLife expectancy.
Stratified random sampling is also known as proportional sampling or quota sampling.
The central theses
- Stratified random sampling allows researchers to obtain a sample population that best represents the entire population studied.
- Sampling is a statistical inference made using a subset of a population.
- In stratified random sampling, the entire population is divided into homogeneous groups, called strata.
- Proportional stratified random sampling draws samples from groups stratified with respect to the population. With disproportionate sampling, the strata are not proportional to the occurrence of the population.
- Stratified random sampling differs from simple random sampling, which involves the random selection of data from an entire population so that each possible sample occurs with the same probability.
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Stratified random sample
This is how stratified random sampling works
When conducting analysis or research on a group of entities with similar characteristics, a researcher may discover that thepopulationit is too big to complete the investigation about it. To save time and money, an analyst can take a more practical approach by selecting a small group of the population. The small group is denoted as asample size, which is a subset of the population that is used to represent the entire population. A sample can be selected from a population in several ways, one of which is the stratified random sampling method.
Stratified random sampling divides the entire population into homogeneous groups called strata (plural of stratum). Random samples are then taken from each layer.For example, imagine an academic researcher who wants to know how many MBA students were offered a job in 2021 within three months of graduation.
The researcher will soon discover that there were about 200,000 MBA graduates that year. He may decide to take a random sample of 50,000 graduates and conduct a survey. Even better, they could classify the population into strata and draw a random sample from the strata. To do this, they would create population groups based on gender, age group, race, country of nationality, and work experience. A random sample is drawn from each stratum in a number proportional to the size of the stratum in relation to the population. These strata subsets are then combined into a random sample.
Stratified sampling is used to highlight differences between groups in a population, as opposed to simple random sampling, which treats all members of a population as equals with the same probability of being sampled.
Example of a stratified random sample
Suppose a research team wants to determine the grade point average (GPA) of college students in the United States. The research team struggles to collect data from all 21 million college students; You decide to draw a random sample from the population using 4000 students.
Now suppose the team looks at the different characteristics of the sample participants and asks if there are differences in the averages and majors of the students. Suppose you find that 560 students are majoring in English, 1,135 are majoring in science, 800 are majoring in computer science, 1,090 are majoring in engineering, and 415 are majoring in mathematics. The team wants to use a proportionally stratified random sample, where the stratification of the sample is proportional to the random sample in the population.
Suppose the team searches for thedemographic dataof college students in the US and find the percentage of what students study: 12% English, 28% Science, 24% Computer Science, 21% Engineering, and 15% Mathematics. Thus five strata are formed from the stratified random sample.
The team must then confirm that the population class is proportional to the sample class; However, you notice that the proportions are not the same. The team must then retest 4,000 students from the general population, randomly selecting 480 English, 1,120 science, 960 computer science, 840 engineering, and 600 math students.
With these groups, you have a proportionally stratified random sample of college students, providing a better representation of US college degrees. Researchers can then select specific strata, look at different types of studies conducted by US college students and look at different GPAs.
Simple x Stratified Random Sampling
simple random samplesand stratified samples are statistical measures. A simple random sample is used to represent the entire data population.A stratified random sample divides the population into smaller groups, or strata, based on common characteristics. However, stratified sampling is more complicated, time-consuming, and potentially more expensive to perform than simplified random sampling.
Simple random sampling is generally used when there is too little information available about the data population, when the data population has too many differences to separate it into different subsets, or when there is only one characteristic in the data population.
For example, a candy company might want to study the buying habits of its customers to determine the future of its product line. If there are 10,000 customers, you can select 100 of those customers as a random sample. You can then apply what you find from those 100 customers to the rest of your base.Unlike the stratification, 100 members are sampled purely at random, without taking into account their individual characteristics.
Proportional and disproportionate stratification
Stratified random sampling ensures that each subgroup of a given population is adequately represented in the overall population sample of a research study. Stratification can be proportional or disproportionate. In a proportionally stratified method, the sample size of each stratum is proportional to the population size of the stratum. This type of stratified random sampling is generally a more accurate metric because it better represents the general population.
For example, if the researcher wants a sample of 50,000 graduates by age group, the proportional stratified random sample is obtained using this formula: (sample size/population size) × stratum size. The following table assumes a population size of 180,000 MBA graduates per year.
| age group | 24–28 | 29–33 | 34–37 | no totals |
|---|---|---|---|---|
| Number of people in shift | 90.000 | 60.000 | 30.000 | 180.000 |
| Strata sample size | 25.000 | 16.667 | 8.333 | 50.000 |
The sample size of the strata forMaster of Business Administration Graduatesin the 24-28 age group it is calculated as (50,000/180,000) × 90,000 = 25,000. The same method is used for the other age groups. Now that the sample sizes of the strata are known, the researcher can use simple random sampling in each stratum to select their respondents. In other words, 25,000 graduates between the ages of 24 and 28 are randomly selected from the total population, 16,667 graduates between the ages of 29 and 33 are randomly selected from the population, and so on.
In a disproportionately stratified sample, the size of each stratum is not proportional to its size in the population. The researcher may choose to sample half of the graduates in the 34-37 age group and one-third of the graduates in the 29-33 age group.
It is important to note that one person cannot accommodate multiple shifts. Each feature can only fit on one layer. Having overlapping subgroups means that some people are more likely to be selected for the survey, which completely negates the concept of stratified sampling as a type of probability sampling.
Portfolio managers can use stratified random sampling to build portfolios by tracking an index, such as a bond index.
Advantages of Stratified Random Sampling
The most importantAdvantage of Stratified Random Samplingis that it captures important characteristics of the population in the sample. Similar to a weighted average, this sampling method produces characteristics in the sample that are proportional to the total population. Stratified random sampling works well for populations with a wide range of characteristics, but is ineffective when it is not possible to form subgroups.
Stratification gives a lowerestimation errorand higher precision than the simple sampling method. The greater the differences between the slices, the greater the gain in precision.
Disadvantages of Stratified Random Sampling
Unfortunately, this research method cannot be used in all studies. The downside of the method is that several conditions must be met for it to be used correctly. Researchers must identify each member of a population under study and classify each member into one and only one subpopulation. As a result, stratified random sampling is disadvantageous when researchers cannot reliably assign each member of the population to a subgroup. You will also find a complete and definitive list of an entirePopulationit can be challenging.
Overlap can be a problem when there are topics that fall into multiple subgroups. When simple random sampling is done, those in more than one subgroup are more likely to be selected. The result can be a misrepresentation or an inaccurate representation of the population.
The examples above make it easy: Graduate, Graduate, Male, and Female are clearly defined groups. In other situations, however, it can be much more difficult. Imagine including characteristics like race, ethnicity, or religion. The classification process becomes more difficult, making stratified random sampling an ineffective and suboptimal method.
When would you use stratified random sampling?
Stratified random sampling is often used when researchers want to know about different subgroups or strata based on the entire population being studied, for example, when one is interested in differences between groups based on race, gender or education.
Which sampling method is better?
The best sampling method to use depends on the type of analysis and the data used. In general, a simple random sample is usually the easiest and cheapest, but a stratified sample can produce a more accurate sample relative to the population being studied.
What are the two types of stratified random sampling?
In proportional sampling, each stratum in the sample is taken proportionally to the population size of the stratum. In disproportionate sampling, the analyst will overestimate or underestimate certain strata depending on the research question or study design used. For example, those interested in early childhood education outcomes may oversample school-age children and children in their first working years, while undersampling the younger and older strata.
How are strata selected for stratified random sampling?
The strata depend on the subgroups of interest found in your population. These subgroups are based on shared differences between participant characteristics, such as gender, race, education level, geographic location, or age group.
Article sources
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University of Arizona, College of Agriculture and Life Sciences. "Chapter 4: Stratified Random Sample," Page 1.
(Video) Stratified SamplingYale University, Department of Statistics and Data Science. "sampling.“
Just psychology. "This is how stratified random sampling works.“
FAQs
How stratified random sampling works, with examples? ›
But the most common type is probably proportional stratified random sampling, where a population divides into strata, and then the random sample is taken from each stratum in proportion to its size. For example, if the entire population is 60% female and 40% male, then the sample would be 60% female and 40% male.
What is stratified random sampling with example? ›But the most common type is probably proportional stratified random sampling, where a population divides into strata, and then the random sample is taken from each stratum in proportion to its size. For example, if the entire population is 60% female and 40% male, then the sample would be 60% female and 40% male.
How does stratified random sampling work? ›Stratified sampling is a method of random sampling where researchers first divide a population into smaller subgroups, or strata, based on shared characteristics of the members and then randomly select among these groups to form the final sample.
How do you solve stratified random sampling examples? ›For example, if the researcher wanted a sample of 50,000 graduates using age range, the proportionate stratified random sample will be obtained using this formula: (sample size/population size) × stratum size. The table below assumes a population size of 180,000 MBA graduates per year.
How is a simple random sample different from a stratified random sample example? ›A simple random sample is used to represent the entire data population and randomly selects individuals from the population without any other consideration. A stratified random sample, on the other hand, first divides the population into smaller groups, or strata, based on shared characteristics.