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Stratified Random Sampling: Everything you need to know

  • Yashoda Gandhi
  • May 11, 2022
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When it comes to conducting statistical surveys and gathering data, there is no shortage of sampling techniques to choose from. There are numerous methods for designing a sample to represent your population of interest, including simple sampling, systematic sampling, quota sampling, and cluster sampling.


Of course, each differs in terms of accuracy, dependability, and efficiency. There are no two methods that are alike, and some are more complicated than others.


This article will concentrate on one in particular: stratified random sampling. We'll go over what it is, how you can use it to your advantage, and a few best-practice tips to get you started.



What is Stratified Random Sampling?


Stratified random sampling (also known as proportional random sampling and quota random sampling) is a probability sampling technique in which the entire population is divided into homogeneous groups (strata) to complete the sampling process.


Each stratum (plural for strata) is formed based on shared attributes or characteristics, such as level of education, income, and/or gender.


Random samples are then drawn from each stratum and compared to one another to arrive at specific conclusions. For example, if a researcher wants to know the relationship between income and education, they could use stratified random sampling to divide the population into strata and take a random sample from each.


Stratified random sampling is commonly used by researchers when attempting to evaluate data from various subgroups or strata. Stratified random sampling is one of four probability sampling techniques: simple random sampling, systematic sampling, stratified sampling, and cluster sampling.


Of course, the sampling technique you use will be determined by your objectives, budget, and desired level of accuracy. With this in mind, make sure to clearly outline what you want to accomplish and experiment with various methods to see which work best for your research.


Also Read | What is Sampling Distribution?



Types of Stratified Sampling


There are mainly two types of Stratified Random Sampling.These are their identifiers:


  1. Stratified Proportionate Sampling


The sample size drawn from each stratum is proportionate to the stratum's size in relation to the total population in proportionate stratified sampling. Once the sample size is determined, researchers compute the percentage or proportion of each stratum in relation to the size of the target population.

 Once the relative size of each stratum is known, a sample size for each stratum can be calculated. Following this, simple random sampling can be used to select random elements from each stratum. This sampling method is simpler, faster, and more straightforward than disproportionate stratified sampling.


This method is used because larger strata, or subpopulations, have larger standard deviations (in terms of the characteristics of the stratified variables chosen), and thus larger sampling sizes must be chosen from these strata to increase the precision of the research.


Proportionate Stratified Random Sampling Formula: nh = ( Nh / N ) * n


Example Proportionate Stratified Sampling in Action


As part of a study to determine how many students wish to pursue a career in the sciences. To begin, the population of interest is divided into two strata based on gender, resulting in 4,000 male students and 6,000 female students.


800 male students and 1,200 female students are then chosen for the sample population, using 15 as the sampling fraction.


  1. Stratified Disproportionate Sampling


In disproportionate stratified sampling, the sample size chosen from each stratum is proportional to the relative size of the stratum and the standard deviation in the distribution of the characteristics among the elements in that stratum. The researcher and the rationale for their study determine the sample units from each stratum.


Example of Disproportionate Stratified Sampling in Action


A researcher divides a population of interest into three subsets based on age:


120,000 in Subset A (16–25).


80,000 in Subset B (26–35).


100,000 in Subset C (36–45).


Disproportionate stratified sampling entails the researcher selecting members of the sample at random from each group. As a result, the first group could have 60,000 participants, while the other groups could have 20,000 and 17,000 participants, respectively. There is no clear method for selecting variables for the research sample.


One key advantage of disproportionate sampling is that it allows you to collect responses from minority subsets where the sample size would otherwise be too small to draw statistical conclusions.


Also Read | What is Statistics?



How does Stratified Random Sampling Work?


When conducting analysis or research on a group of entities with similar characteristics, a researcher may discover that the population size is too large to conduct research on. An analyst may take a more feasible approach by selecting a small group from the population to save time and money. 


The sample size is a small subset of the population that is used to represent the entire population. A sample can be drawn from a population in a variety of ways, one of which is stratified random sampling.


A stratified random sampling procedure entails dividing the entire population into homogeneous groups known as strata (plural for stratum). After that, random samples are drawn from each stratum. Consider an academic researcher who wants to know the number of MBA students who received a job offer within three months of graduation in 2007.


The researcher will soon discover that nearly 200,000 MBA graduates graduated during the year. They may decide to conduct a survey of 50,000 graduates using a simple random sample. Even better, they could stratify the population and draw a random sample from each stratum. 


To accomplish this, they would divide the population into groups based on gender, age range, race, country of nationality, and work history. When compared to the population, a random sample from each stratum is taken in a number proportional to its size. These strata subsets are then combined to create a random sample.


When should Stratified Random Sampling be used?


In situations where the researcher intends to focus only on specific strata from the available population data, stratified random sampling is an extremely productive method of sampling. In this manner, the desired strata characteristics can be found in the survey sample.


This sampling method is used by researchers when they want to establish a relationship between two or more different strata. If this comparison is conducted using simple random sampling, the target groups are more likely to be unequally represented.


Using the stratified random sampling technique, samples from a population that is difficult to access or contact can be easily included in the research process. The accuracy of statistical results is higher than that of simple random sampling because the sample elements are drawn from relevant strata. 


The stratification within the strata will be much less diverse than the stratification within the target population. Because of the accuracy involved, it is highly likely that the required sample size will be much smaller, allowing researchers to save time and effort.


Also Read | Types of Statistical Data Distribution Models

8 Steps to select a Stratified Random Sampling :1. Define the Target 2. Recognize the stratification variable 3. Create a sample 4. Evaluate the sample 5. Define the target 6. Assign a number to each element 7. Size each stratum 8. Select random elements

8 Steps to select a Stratified Random Sampling

Below are the steps required to select a stratified random sampling :


  1. Define the intended audience.


  1. Determine the number of strata to be used by recognizing the stratification variable or variables. These stratification variables should be consistent with the researcher's goal. Every additional piece of information influences the stratification variables. 


For example, if the goal of the research is to understand all of the subgroups, the variables will be related to the subgroups, and all of the information about these subgroups will have an impact on the variables. 


In general, no more than 4-6 stratification variables and no more than 6 strata should be used in a sample because increasing the number of stratification variables increases the likelihood of some variables canceling out the impact of others.


  1. Use an existing sampling frame or create one that includes all of the stratification variable information for all elements in the target audience.


  1. After evaluating the sampling frame for lack of coverage, over-coverage, or grouping, make changes.


  1. Taking the entire population into account, each stratum should be distinct and cover each and every member of the population. Differences within the stratum should be minimal, whereas each stratum should be vastly different from the others. Each member of the population should be assigned to only one stratum.


  1. Assign a random, one-of-a-kind number to each element.


  1. Determine the size of each stratum based on your needs. The type of sampling to be used will be determined by the numerical distribution of all elements across all strata. Stratified sampling can be proportional or disproportional.


  1. The sample can then be formed by selecting random elements from each stratum by the researcher. A minimum of one element from each stratum must be chosen so that there is representation from each stratum, but if two elements from each stratum are chosen, the error margins of the calculated data can be easily calculated.


Advantages of Stratified Random Sampling


When you believe that subgroups will have different mean values for the variable(s) you're studying, stratified sampling is the best method to use. There are several potential benefits of Stratified Random Sampling


  1. Allowing for a wide range of data collection methods


You may need to use different methods to collect data from different subgroups at times. For example, to reduce the cost and difficulty of your study, you may want to sample urban subjects door-to-door while sampling rural subjects via mail.


  1. Ensure that your sample is diverse


A stratified sample includes subjects from each subgroup, ensuring that it is representative of your population's diversity. It is theoretically possible (though unlikely) that this would not occur if other sampling methods, such as simple random sampling, were used.


  1. Reducing the population's overall variance


Although your overall population may be quite heterogeneous, certain subgroups may be more homogeneous. 


For example, if you're researching how a new schooling program affects children's test scores, both their initial scores and any changes in scores will almost certainly be highly correlated with family income. The scores are most likely to be organized by family income level.


In this case, stratified sampling allows for more precise measurements of the variables you want to study, with the lower variance within each subgroup and thus for the entire population.


Limitations of Stratified Random Sampling


  1. Planning


Researchers must ensure that each member of the population belongs to only one stratum and that all stata collectively contain every member of the larger population. This necessitates additional planning and information gathering that simple random sampling does not necessitate.


  1. Errors in sampling


Sampling errors occur when a sample fails to accurately represent the population as a whole. If this occurs, the researcher must restart the sampling procedure.


  1. There are far too many differences among people


If there are too many differences within a population or there is insufficient information about the population at hand, it cannot be organized into subgroups.


Cluster Sampling Vs Stratified Random Sampling


The distinctions between stratified and cluster sampling are clear on the following grounds:


  1. Stratified Sampling is a probability sampling procedure in which the population is divided into different homogeneous segments called ‘strata,' and then the sample is drawn at random from each stratum. Cluster sampling is a sampling technique in which units of the population are chosen at random from pre-existing groups known as 'clusters.'


  1. Individuals are drawn at random from all strata to form the sample in stratified sampling. Cluster sampling, on the other hand, is formed when all of the individuals are drawn at random from randomly selected clusters.


  1. Cluster sampling selects population elements in aggregates, whereas stratified sampling selects population elements individually from each stratum.


  1. In stratified sampling, homogeneity exists within the group, whereas in cluster sampling, homogeneity exists between groups.


  1. In stratified sampling, there is heterogeneity between groups. In cluster sampling, however, the members of the group are heterogeneous.


  1. When the researcher uses a stratified sampling method, the categories are imposed by him. In contrast, the categories in cluster sampling are already existing groups.


  1. The goal of stratified sampling is to improve precision and representation. In contrast to cluster sampling, which aims to improve cost-effectiveness and operational efficiency.


Also Read | Vital Statistics


To summarize the discussion, we can say that a preferable situation for stratified sampling is when the identicalness within an individual stratum and the strata mean to differ from each other. If between-group differences between strata are increased, stratified sampling errors can be reduced.

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