Stratified random sampling is a technique used in statistics that ensures that specific subgroups. It is a simple and effective way to ensure that our survey or study results represent all parts of your population fairly. This method ensures every subgroup of our population gets represented, giving us a more clear picture. By carefully selecting samples from each subgroup, you get a balanced view, whether you’re studying opinions, behaviours, or characteristics.

In this article, we are going to learn what is stratified random sampling, its importance, the steps to select a stratified sample, the challenges in selecting a stratified random sample, and some practice questions based on it.

What is Stratified Random Sampling?

Stratified random sampling is a technique used in statistics that ensures that different subgroups of a population are represented proportionally within a sample. This is different from simple random sampling which treats the entire population as a single group. Stratified random sampling divides the population into mutually exclusive subgroups(strata) based on some specific characteristics. Stratified Random Sampling increases the accuracy of the sample estimates by reducing sampling error and ensuring the participation of each subgroup.

Importance of Stratified Sampling

• Improved Accuracy: By focusing on key subgroups, the accuracy of the sample can be increased.
• Enhanced Representation: It ensures that every significant subgroup within the population is represented, which is particularly useful when we are interested in any particular group.
• Efficiency: Stratified sampling can reduce differences within strata and increase the efficiency of the sample.

How to Perform Stratified Random Sampling

Step 1: Define the Population

The very first step in stratified random sampling is to clearly define the population for which we want to study. This includes many things such as the geographic location, the time frame, and the key characteristics of the population.

Example: If we want to study the effectiveness of a new educational program in a school district, we want a population of all students enrolled in that district.

Step 2: Identify Strata(Subgroups)

After the population is defined, the next step is to identify the strata. Strata are distinct subgroups within which the population share common characteristics. The choice of strata should be relevant.

Example: In a study of student performance, strata might include grade level, gender, or socio-economic status.

Step 3: Determine the Sample Size

Decide the size of overall sample we want for our study. This depends on various factors such as the desired level of accuracy, the variability within strata, and the available resources.

Example: If we determine that a total sample size of 300 students is needed, we will allocate this sample across the identified strata.

Step 4: Allocate Samples to Strata

We will allocate the total sample size to each stratum. This can be done proportionally or equally, depending on the study’s requirements. Sample size for each stratum is proportional to the stratum’s size in the population. Each stratum receives the same sample size regardless of its proportion in the population.

Example: If the population consists of 50% 9th graders and 50% 10th graders, and we are using proportional allocation with a total sample size of 300, then we would select 150 students from each grade level.

Step 5: Randomly Select Samples from Each Stratum

Within each stratum, we will use random sampling techniques to select the required number of samples. This can be done using different methods such as simple random sampling, systematic sampling, or any other appropriate techniques.

Example: We could choose 150 pupils at random using a random number generator or another randomization technique out of the 150 9th graders.

Case of Stratified Random Sampling

Case Study: Employee Satisfaction Survey

A company wants to check satisfaction of employees. The workforce is divided into different departments: Sales, Marketing, and Engineering.

Follow the steps

Step 1: Define Population: Deine all employees of the company.

Step 2: Identify Strata: Identify different groups/ departments of sales, marketing and engineering.

Step 3: Determine Sample Size: Take the total sample size of 150 employees.

Step 4: Allocate Samples: Proportionally allocates based on size of department.

Step 5: Random Selection: Use random sampling within each department to select employees.

Outcome: After using stratified random sampling, the company ensures representation from all departments, which will result in accurate insights into employee satisfaction across different areas.

Case Study2: National Health Survey

This national health survey aims to study different age groups and genders.

Follow the steps

Step 1: Define Population: Define the number of all residents living in the country.

Step 2: Identify Strata: Identify different age groups such as 0-18, 19-35, 36-60, 61+ and gender also.

Step 3: Determine Sample Size: Take the total sample size of 2000 individuals.

Step 4: Allocate Samples: Proportionally allocates based on age group and gender of individuals.

Step 5: Randomly Select: Use random sampling within each age group and gender to select participants.

Outcome: This survey provides a broad view of health trends across different demographics, ensuring accurate and representative data.

Challenges in Selecting a Stratified Random Sample

Various chalanges in selecting a stratified random sample includes:

Stratum Definition

It is difficult to define mutually exclusive and collectively exhaustive strata. The solution to this problem is to clearly define stratum characteristics and take suggestion from experts to ensure that all relevant subgroups are included.

Sample Size Allocation

It is difficult to determine how to allocate samples proportionally when the size of strata is different. The solution to this problem is to employ statistical formulae and calculate the sample numbers for each stratum of a given population and opt for an equal allocation method if there is no need for stratification.

Random Selection within Strata

For achieving an unbiased selection of samples within each subgroup, one should use random number generators or other randomization techniques. This ensures that each member of a stratum has an equal chance of being selected which reduce selection bias and improve the correctness of our result.

When to Use Stratified Random Sampling?

Heterogeneous Population: Use stratified random sampling when your population is heterogeneous, meaning it consists of distinct subgroups (strata) that are different from each other in some significant way.

For example, a study on student performance might stratify the population by grade level (freshman, sophomore, junior, senior) to ensure each group is represented.

When Subgroup Analysis is Important: If you are interested in making comparisons between different subgroups of the population, stratified sampling ensures that each subgroup is adequately represented.

For example, in a health study, you might stratify by age groups or gender to compare health outcomes across these strata.

When Resources Are Limited: If resources (time, money, etc.) are limited, stratified sampling can be more cost-effective. By focusing on key strata, you can achieve reliable results with fewer samples than if you were to sample randomly from the entire population.

Stratified Random Sampling vs. Simple Random Sampling

Differences between Stratified Random Sampling and Simple Random Sampling in tabular form is added below: