## Stratified Random Sampling

**Definition:**

Stratified random sampling is a type of probability sampling method that involves dividing a population into subgroups or strata based on certain characteristics and then selecting a random sample from each stratum.

This sampling technique is useful when the population being studied can be divided into distinct subgroups or strata, each with its own unique characteristics or attributes.

### Stratified Random Sampling Methods

There are two Stratified Random Sampling Methods:

**Proportional Stratified Random Sampling:**In this method, the sample size for each stratum is proportional to the size of that stratum in the population. For example, if a population has three strata with sizes of 1000, 2000, and 3000, and a total sample size of 1000 is desired, then the sample size for the first stratum would be 100, the sample size for the second stratum would be 200, and the sample size for the third stratum would be 300.**Disproportional Stratified Random Sampling:**In this method, the sample size for each stratum is not proportional to the size of that stratum in the population. This method is used when some strata have greater variability or are of greater interest than others. For example, if a population has three strata with sizes of 1000, 2000, and 3000, and a total sample size of 1000 is desired, the researcher may allocate more sample size to the stratum with the highest variability or greater interest.

### Stratified Random Sampling Formula

The formula for stratified random sampling is:

**n_h = (N_h / N) * n**

where:

- n_h is the sample size for the h-th stratum
- N_h is the size of the h-th stratum
- N is the size of the population
- n is the total sample size (i.e., the number of units to be sampled from the population)

In other words, the sample size for each stratum is proportional to the size of the stratum relative to the population size. The total sample size is the sum of the sample sizes for all strata. Once the sample sizes for each stratum are determined, a simple random sample can be drawn from each stratum.

### How to Conduct Stratified Random Sampling

Here are the steps for conducting stratified random sampling:

**Define the population:**Determine the population that you want to sample from and the characteristics that you want to stratify on.**Divide the population into strata:**Divide the population into strata based on the characteristics you identified in step 1. Each individual in the population should only be included in one stratum.**Determine the sample size:**Determine the desired sample size for each stratum. The sample size for each stratum should be proportional to the size of the stratum in the population.**Randomly select individuals from each stratum**: Using a random sampling method, select individuals from each stratum. The number of individuals selected from each stratum should be equal to the sample size determined in step 3.**Combine the samples:**Combine the samples from each stratum to create the final sample.**Analyze the data:**Analyze the data from the final sample using appropriate statistical methods.

### Examples of Stratified Random Sampling

Here are a few examples of stratified random sampling:

**A political poll**: A political pollster wants to conduct a survey to determine the public’s opinion on a particular political issue. The pollster divides the population into strata based on demographic factors such as age, gender, and income. They then randomly select individuals from each stratum in proportion to the size of the stratum in the population.**Quality control in a manufacturing plant**: A manufacturer wants to test the quality of its products. The manufacturer divides the production line into strata based on the time of day that the products were produced. They then randomly select a sample of products from each stratum and test them for quality.**Medical research:**A medical researcher wants to study the effectiveness of a new medication. The researcher divides the patient population into strata based on the severity of the illness. They then randomly assign patients to receive either the new medication or a placebo, with the number of patients in each stratum proportionate to the size of the stratum in the population.**College admissions**: A college wants to determine the effectiveness of its admissions policies. The college divides the applicant pool into strata based on factors such as GPA, standardized test scores, and extracurricular activities. They then randomly select applicants from each stratum to admit to the college, with the number of applicants in each stratum proportionate to the size of the stratum in the applicant pool.

**Stratified Random Sampling Example Situation**

Stratified Random Sampling Example Situation is as follows:

Let’s say you are conducting a survey to study the job satisfaction levels of employees in a large organization with 1000 employees. The organization has four departments: sales, marketing, human resources, and operations. You want to ensure that your sample is representative of the entire population, and you decide to use stratified random sampling.

First, you need to define your strata. In this case, you will use the department as the stratification variable, and you will have four strata: sales, marketing, human resources, and operations.

Next, you need to determine the sample size for each stratum. Let’s say you want to survey a total of 200 employees, with 50 employees from each department. You need to use the formula:

**n_h = (N_h / N) * n**

where n_h is the sample size for the h-th stratum, N_h is the size of the h-th stratum, N is the size of the population, and n is the total sample size.

For the sales department, you have 300 employees. Using the formula, you get:

n_sales = (300 / 1000) * 200 = 60

So you need to survey 60 employees from the sales department.

Similarly, for the marketing department, you have 200 employees, so:

n_marketing = (200 / 1000) * 200 = 40

For the human resources department, you have 250 employees, so:

n_hr = (250 / 1000) * 200 = 50

And for the operations department, you have 250 employees, so:

n_operations = (250 / 1000) * 200 = 50

Once you have determined the sample sizes for each stratum, you can draw a simple random sample from each stratum. For example, you can use a random number generator to select 60 employees from the sales department, 40 employees from the marketing department, 50 employees from the human resources department, and 50 employees from the operations department.

### Applications of Stratified Random Sampling

Stratified random sampling is a widely used method in many fields, as it allows for a more representative and accurate sample than simple random sampling. Here are some examples of its applications in different fields:

**Healthcare**: In healthcare, stratified random sampling can be used to study the prevalence of diseases or health conditions in a population. Researchers can divide the population into strata based on age, sex, socioeconomic status, or other relevant factors, and then randomly select individuals from each stratum to participate in the study.**Education**: In education, stratified random sampling can be used to evaluate the effectiveness of educational programs or policies. Researchers can divide the student population into strata based on academic performance, socioeconomic status, or other relevant factors, and then randomly select students from each stratum to participate in the study.**Market research**: In market research, stratified random sampling can be used to study consumer behavior and preferences. Researchers can divide the population into strata based on age, income, geographic location, or other relevant factors, and then randomly select individuals from each stratum to participate in the study.**Environmental science:**In environmental science, stratified random sampling can be used to study the distribution and abundance of plant or animal species in a given ecosystem. Researchers can divide the ecosystem into strata based on vegetation type, topography, or other relevant factors, and then randomly select sampling sites from each stratum to conduct their surveys.**Finance**: In finance, stratified random sampling can be used to evaluate the performance of investment portfolios. Researchers can divide the portfolio into strata based on asset type, sector, or other relevant factors, and then randomly select investments from each stratum to evaluate their performance.

### Purpose of Stratified Random Sampling

The purpose of stratified random sampling is to improve the accuracy and precision of estimates of population parameters by ensuring that the sample is representative of the population with respect to certain characteristics. Stratified random sampling is particularly useful when the population has a high degree of variability with respect to these characteristics.

By dividing the population into strata based on these characteristics, and then randomly selecting individuals from each stratum, we can ensure that the sample includes individuals from each subgroup in proportion to their representation in the population. This can help to reduce sampling bias and increase the efficiency of our estimates.

Stratified random sampling can also help to increase the precision of our estimates by reducing the variance within each stratum. This is because individuals within each stratum are likely to be more similar to each other with respect to the characteristic being stratified on than individuals from different strata.

### Characteristics of Stratified Random Sampling

The main characteristics of stratified random sampling are:

**Population division into subgroups or strata:**In stratified random sampling, the population is divided into non-overlapping subgroups or strata based on some relevant characteristics such as age, gender, income, education, or other relevant factors.**Random selection of individuals within each stratum**: Once the population is divided into strata, a random sample of individuals is selected from each stratum. This ensures that the sample includes individuals from each subgroup in proportion to their representation in the population.**Proportional representation:**Each stratum is represented in the sample in proportion to its size in the population. This ensures that the sample accurately represents the population with respect to the characteristic being stratified on.**Reduced sampling bias:**By ensuring that each stratum is represented in the sample, stratified random sampling can help to reduce sampling bias, which is a type of error that can occur when the sample is not representative of the population.**Increased precision**: Stratified random sampling can also increase the precision of estimates by reducing the variance within each stratum. This is because individuals within each stratum are likely to be more similar to each other with respect to the characteristic being stratified on than individuals from different strata.

### Advantages of Stratified Random Sampling

Stratified random sampling has several advantages over other sampling methods, including:

**Increased representativeness**: Stratified random sampling ensures that each stratum of the population is represented in the sample in proportion to its size in the population. This makes the sample more representative of the population and reduces the risk of sampling bias.**Increased precision**: Stratified random sampling can increase the precision of estimates by reducing the variance within each stratum. This is because individuals within each stratum are likely to be more similar to each other with respect to the characteristic being stratified on than individuals from different strata.**Efficient use of resources:**Stratified random sampling can be more efficient than other sampling methods because it allows researchers to focus their resources on the subgroups of the population that are of most interest, rather than sampling randomly across the entire population.**Better estimation of subgroups**: Stratified random sampling can provide better estimates of subgroups within the population, as it ensures that each subgroup is represented in the sample in proportion to its size in the population.**Flexibility**: Stratified random sampling can be used in a variety of settings and can be adapted to different populations and characteristics.

### Disadvantages of Stratified Random Sampling

Some Disadvantages of Stratified Random Sampling are as follows:

**Selection of relevant stratification factors**: Stratified random sampling requires prior knowledge of the relevant characteristics of the population and the factors that should be used to stratify the population. If the stratification factors are not correctly chosen, the sample may not be representative of the population.**Additional time and resources:**Stratified random sampling requires additional time and resources to identify and select individuals from each stratum. This can increase the cost and time required for sampling.**Complexity**: Stratified random sampling can be more complex than other sampling methods, especially when dealing with large and diverse populations. This can lead to difficulties in implementing and interpreting the sampling results.**Difficulty in identifying strata**: Identifying meaningful and relevant strata can be difficult, especially when dealing with complex populations that have multiple relevant characteristics.**Increased sample size**: Stratified random sampling requires a larger sample size than other sampling methods to ensure that each stratum is represented adequately. This can increase the cost and complexity of the study.