stratified sampling vs random assignment

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Statistics and probability

Course: statistics and probability   >   unit 6.

• Picking fairly
• Using probability to make fair decisions
• Techniques for generating a simple random sample
• Simple random samples
• Techniques for random sampling and avoiding bias
• Sampling methods

Sampling methods review

• Samples and surveys

What are sampling methods?

Bad ways to sample.

• (Choice A)   Convenience sampling A Convenience sampling
• (Choice B)   Voluntary response sampling B Voluntary response sampling

Good ways to sample

• (Choice A)   Simple random sampling A Simple random sampling
• (Choice B)   Stratified random sampling B Stratified random sampling
• (Choice C)   Cluster random sampling C Cluster random sampling
• (Choice D)   Systematic random sampling D Systematic random sampling

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• An Overview

Simple Random Sampling

Stratified random sampling, key differences, advantages and disadvantages, the bottom line.

• Marketing Essentials

Simple Random Sample vs. Stratified Random Sample: What’s the Difference?

Thomas J Catalano is a CFP and Registered Investment Adviser with the state of South Carolina, where he launched his own financial advisory firm in 2018. Thomas' experience gives him expertise in a variety of areas including investments, retirement, insurance, and financial planning.

Simple Random Sample vs. Stratified Random Sample: An Overview

In statistical analysis, the population is the total set of observations or data that exists. However, it is often unfeasible to measure every individual or data point in a population.

Instead, researchers rely on samples. A sample is a set of observations from the population. The sampling method is the process used to pull samples from the population.

Simple random samples and stratified random samples are both common methods for obtaining a sample. 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. Therefore, a stratified sampling strategy will ensure that members from each subgroup are included in the data analysis.

Key Takeaways

• Simple random and stratified random samples are statistical measurement tools.
• A simple random sample takes a small, basic portion of the entire population to represent the entire data set.
• Stratified random sampling divides a population into different groups based on certain characteristics, and a random sample is taken from each.

Simple random sampling is a statistical tool used to describe a very basic sample taken from a data population. This sample represents the equivalent of the entire population.

The simple random sample is often used when there is very little information available about the data population, when the data population has far too many differences to divide into various subsets, or when there is only one distinct characteristic among the data population.

For instance, a candy company may want to study the buying habits of its customers in order to determine the future of its product line. If there are 10,000 customers, it may use 100 of those customers as a random sample. It can then apply what it finds from those 100 customers to the rest of its base.

Statisticians will devise an exhaustive list of a data population and then select a random sample within that large group. In this sample, every member of the population has an equal chance of being selected to be part of the sample. They can be chosen in two ways:

• Through a manual lottery, in which each member of the population is given a number. Numbers are then drawn at random by someone to include in the sample. This is best used when looking at a small group.
• Computer-generated sampling. This method works best with larger data sets, by using a computer to select the samples rather than a human.

Using simple random sampling allows researchers to make generalizations about a specific population and leave out any bias. This can help determine how to make future decisions. That way, the candy company from the example above can use this tool to develop a new candy flavor to manufacture based on the current tastes of the 100 customers.

However, keep in mind that these are generalizations, so there is room for error. After all, it is a simple sample. Those 100 customers may not have an accurate representation of the tastes of the entire population.

Unlike simple random samples, stratified random samples are used with populations that can be easily broken into different subgroups or subsets. These groups are based on certain criteria, then samples are randomly chosen from each in proportion to the group’s size vs. the population.

This method of sampling means there will be selections from each different group—the size of which is based on its proportion to the entire population. However, the researchers must ensure that the strata do not overlap. Each point in the population must only belong to one stratum so that each point is mutually exclusive . Overlapping strata would increase the likelihood that some data are included, thus skewing the sample.

The candy company may decide to use the random stratified sampling method by dividing its 100 customers into different age groups to help make determinations about the future of its production.

Portfolio managers can use stratified random sampling to create portfolios by replicating an index such as a bond index.

The simple random sample is often used when:

• Very little information is available about the data population.
• The data population has too many differences to divide into various subsets.
• Only one characteristic is distinct among the data population.

Stratified random samples are used with populations that can be easily broken into different subgroups or subsets based on certain criteria. Samples are randomly chosen from each proportional to the group’s size vs. the population.

Stratified random sampling offers some advantages and disadvantages compared to simple random sampling. Because it uses specific characteristics, it can provide a more accurate representation of the population based on what’s used to divide it into different subsets. This often requires a smaller sample size, which can save resources and time. In addition, by including sufficient sample points from each stratum, the researchers can conduct a separate analysis on each individual stratum.

But more work is required to pull a stratified sample than a random sample. Researchers must individually track and verify the data for each stratum for inclusion, which can take a lot more time compared with random sampling.

How Does Simple Random Sampling Work?

Simple random sampling is used to describe a very basic sample taken from a data population. This statistical tool represents the equivalent of the entire population.

How Does Stratified Random Sampling Work?

Stratified random samples are used with populations that can be easily broken into different subgroups or subsets based on certain criteria. Samples are then randomly chosen from each in proportion to the group’s size vs. the population.

How Do Simple Random and Stratified Random Sampling Benefit Researchers?

Simple random sampling lets researchers make generalizations about a specific population and leave out any bias. This can help determine how to make future decisions.

Stratified random sampling lets researchers make selections from each subgroup, the size of which is based on its proportion to the entire population. However, the researchers must make sure that the strata do not overlap.

Simple random samples and stratified random samples are both common methods for obtaining a sample. A simple random sample represents the entire data population and randomly selects individuals from the population without any other consideration. A stratified random sample divides the population into smaller groups, or strata, based on shared characteristics—thus ensuring that members from each subgroup are included in the data analysis.

ScienceDirect. “ Simple Random Sample .”

Qualtrics XM. “ Stratified Random Sampling: Definition & Guide .”

Finance Train. “ Stratified Random Sampling .”

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Statistics By Jim

Making statistics intuitive

Stratified Sampling: Definition, Advantages & Examples

By Jim Frost 4 Comments

What is Stratified Sampling?

Stratified sampling is a method of obtaining a representative sample from a population that researchers have divided into relatively similar subpopulations (strata). Researchers use stratified sampling to ensure specific subgroups are present in their sample. It also helps them obtain precise estimates of each group’s characteristics. Many surveys use this method to understand differences between subpopulations better. This technique is a probability sampling method , and it is also known as stratified random sampling.

The stratified sampling process starts with researchers dividing a diverse population into relatively homogeneous groups called strata, the plural of stratum. Then, they draw a random sample from each group (stratum) and combine them to form their complete representative sample. Learn more about representative samples . When researchers use non-random selection to choose subjects from the strata, it is known as Quota Sampling .

Strata are subpopulations whose members are relatively similar to each other compared to the broader population. Researchers can create strata based on income, gender, and race, among many other possibilities. For example, if your research question requires you to compare outcomes between income levels, you might base the strata on income. All members of the population should be in only one stratum.

For background information about using samples to draw conclusions about populations, read my posts about Populations, Parameters, and Samples in Inferential Statistics  and Descriptive versus Inferential Statistics .

Learn more about Types of Sampling Methods in Research .

When to Use Stratified Sampling

Stratified sampling is beneficial in cases where the population has diverse subgroups, and researchers want to be sure that the sample includes all of them. Simple random sampling and systematic sampling might not adequately capture all these groups, particularly those that are relatively rare. Use this method when you suspect that the group means are different, and the goal of your study is to understand these differences.

Before using stratified sampling, you must divide the population into mutually exclusive groups that collectively capture all individuals in the population. These strata can be predefined census and demographic variables, such as gender, race, location, etc. And they can include strata that the researchers devise based on the needs of their study. Consequently, stratified samples place more burden on the researchers by requiring them to obtain all this information and assigning individuals into each category. In some cases, the necessary information might not be available.

Stratified sampling requires that you have a sampling frame that contains a complete list of population members, along with their demographic information for the strata and contact information. Learn more about Sampling Frames: Definition, Examples & Uses .

Stratified sampling produces more precise group estimates by placing similar individuals into the groups. Consequently, you must understand the grouping scheme that increases the homogeneity of the groups relative to the entire population. The weighted averages of these groups have less variability than the regular mean from a simple random sample. In other words, this methodology can produce better group estimates in the right circumstances and when you have the necessary information.

Advantages of Stratified Sampling

Many surveys use stratified sampling because it provides vital benefits.

Precise Estimates for subgroups

When members of the subpopulations are relatively homogeneous relative to the entire population, stratified sampling can produce more precise estimates of those subgroups than simple random sampling. In this case, the strata have lower standard deviations than the entire population. The strata are the subpopulations in the study.

This increased precision for the strata can be crucial when a study needs to assess group characteristics. Additionally, the precision gives your analyses greater statistical power for detecting differences between groups. For example, a standardized testing company might want to evaluate how testing scores vary by household income or geographic region, such as urban versus rural.

Related post : Sample Statistics are Always Wrong (to Some Extent)!

Efficiency in Conducting the Survey

Stratified sampling can reduce survey costs and simplify data collection. In many cases, dividing the entire population into strata provides benefits to the survey administrators. Studies can become less expensive and more practical when the researchers divide a large population into smaller groups containing similar members. These benefits occur when specific skills, expertise, or personnel can more efficiently sample a particular stratum. For example, you might use different people to survey rural versus urban areas.

Ensures Representation of all Groups of Interest

By explicitly incorporating the strata into the sampling methodology, you ensure that the sample represents all groups. When you have smaller groups in your study, simple random sampling can miss some of them by chance. Stratified sampling helps retain the complete variety of the population in the sample.

In contrast, convenience sampling does not tend to produce representative samples. These samples are easier to gather but the results are minimally useful.

Disadvantages of Stratified Sampling

Stratified sampling imposes several significant burdens on the researchers.

First, they must devise a scheme for their strata so that every member of the population fits into one, and only one, stratum. These strata must collectively contain all members of the population.

Second, the researchers must then have sufficient information to assign subjects to the correct strata.

Unfortunately, that can involve a lot of planning and information gathering!

Additionally, stratified sampling produces benefits only when the researchers can form subgroups that are relatively homogeneous relative to the entire population. If researchers cannot create appropriate strata or the members of a stratum are not reasonably similar, the stratified sample will be ineffective.

Finally, the feasibility of performing stratified sampling depends on your strata to some degree. Some groups are easy to identify and assign members, such a gender, graduation status, etc. However, other strata can be more complex, such as ethnicity and religion.

Example of Stratified Sampling

Stratified sampling involves multiple steps. First, break down the population into strata. From each stratum, use simple random sampling to draw a sample. This process ensures that you obtain observations for all strata.

For example, imagine we’re assessing standardized testing and our research requires us to compare test scores by income. We can use income levels for our strata. Students from households with similar incomes should be relatively similar compared to the overall state population.

While we want a random sample for unbiased estimates overall, we also want to obtain precise estimates for each income level in our population. Using simple random sampling, income levels with a small number of students and random chance could conspire to provide small sample sizes for some income levels. These smaller sample sizes produce relatively imprecise estimates for them.

To avoid this problem, we’ll use stratified sampling. Our sampling plan might dictate that we select 100 students from each income level using simple random sampling. Of course, this plan presupposes that we know the household income level for each student, which might be problematic.

The benefit of stratified sampling is that you obtain reasonably precise estimates for all subgroups related to your research question. The drawback is that analyzing these datasets is more complicated. When you use stratified random sampling, you can’t simply take the overall sample average and use it for the general population because you know that the smaller strata are overrepresented. You need to use a weighted average technique.

Proportionate vs. Disproportionate Stratified Sampling

When using stratified sampling, you’ll need to decide whether your strata will be proportionate or disproportionate. Here are the pros and cons of both techniques. Match your research goals to the correct method.

Proportionate sampling

In proportionate stratified sampling, the sample size of each stratum is proportional to its share in the population. For example, if the rural subgroup comprises 40 percent of the population you’re studying, your sampling process will ensure it makes up 40% of the sample.

Use proportionate sampling when you want to ensure that the sample represents all groups of interest and you’re focusing on obtaining a good estimate for the overall population.

Groups with lower representation will also have smaller numbers in a proportionate sample. In turn, these smaller sample sizes will produce less precise sample estimates. Consequently, proportionate stratified sampling yields less precise estimates of smaller groups than disproportionate sampling, but it gives better overall population estimates.

To calculate the sample size for each stratum, take its population share and multiply that by the total sample size for your study. For example, if the rural group is 40% of the overall population and your full sample size will be 200, you need 0.40 X 200 = 80 rural observations.

Disproportionate sampling

Disproportionate stratified sampling does not retain the proportions of the strata in the population. Use this method when you need to obtain precise estimates of each group and the differences between them. However, it sacrifices some precision in the estimate of the whole population.

This process is an excellent choice when you need to study underrepresented groups in a population. In a proportionate sample, you’re likely to have too few observations to draw meaningful conclusions about these smaller groups. A disproportionate sample ensures that you have an adequate number for analyzing even the smallest groups in a population.

Using this method, the researchers can evenly divide the total sample size between the subgroups or use different proportions that make sense for their study.

Alternatively, they can use a disproportionate stratified sampling approach that adjusts the size of the strata by the variability within the strata. The researchers will collect more samples from the strata with greater variability to reduce sampling error. This method requires knowledge during the planning stages about the variability in each stratum.

Example of Proportionate vs. Disproportionate Stratified Sampling

Suppose researchers want to assess opinions and see how they differ by generation. The relative frequency table below shows the population share of each generation. In choosing their stratified sampling method, the critical question they need to consider is whether they are focusing on the estimate for the entire population or the subgroups.

Generation data from Brookings

If their goal is to produce the most precise estimate for the overall population while ensuring that they include all generations in the sample, they should use proportionate stratified sampling. This method ensures that the sample will adequately represent even the Pre-Boomers with a share of only 7.6%. The table displays the sizes of proportionate groups if the researchers have a budget for 3000 surveys (Stratum population share * total sample size = stratum sample size).

However, if their goal is to really understand each group’s mean response and the differences between them with the most precision, they should use a disproportionate stratified sample. However, the estimate for the entire population will be less precise than the proportionate sample. The table displays a disproportionate approach that divides the sample size evenly between the generations.

Cluster sampling is another method that divides a population into subgroups to obtain a representative sample. However, its goals and methods are strikingly different. For more information, read my article about Cluster Sampling .

Sampling in Developmental Science: Situations, Shortcomings, Solutions, and Standards (nih.gov)

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Reader Interactions

May 24, 2023 at 9:13 am

Thank you very much for the post. It’s really interesting and understandable.

I have a question about this sampling method. If I have done a disproportionate stratified sample by 4 variables, can I compare groups splitting only by one variable? For example, I have disproportionate stratified by sex, age, weight and treatment. Can I compare men vs women? Is it correct? And then, with this kind of sample, could I apply a logistic regression? Or now I can only do an ANOVA?

Thank you again for your work.

October 9, 2022 at 9:22 am

Quite understandable. Life made simple

June 7, 2022 at 4:30 am

why disproportionate stratified sample is used to estimate each group’s mean response and the differences between them with the most precision?

June 8, 2022 at 9:17 pm

Hi Sartyaki,

This is true based on how hypothesis tests work. Suppose you are testing the mean difference between two groups. The test is most efficient (has the most power) when the two groups have the same sample size. For example, if you have n = 200, then the test is most powerful when you have 100 in one group and 100 in the other group. They don’t have to be equal, but you’ll get the most precise estimate of the difference when they’re equal. Unequal group sizes are valid, but it reduces the power of the test and lessens the precision of the estimate (wider CI).

So, that comes into play when you’re drawing a sample from a population. For simplicity, imagine that we have two strata in our sample. One strata accounts for 90% of the population while the other strata covers the remaining 10%. Now, if we wanted a total n = 200 and we draw a proportionate sample, given the proportions of the strata in the population, we’d end up with 180 for one strata and 20 for the other. We can estimate the difference between the means, but because the sample sizes are fairly unequal, we’ll be fairly far from the most precise estimate possible. The CI will be wider.

However, if we devise a disproportionate stratified sampling design so that we end up with 100 for strata 1 and 100 for strata 2, we now can obtain the most precise estimate possible give our n = 200.

I hope that helps explain it!

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4 Types of Random Sampling Techniques Explained

Collect unbiased data utilizing these four types of random sampling techniques: systematic, stratified, cluster, and simple random sampling.

“Why should I care about random sampling?”

Here’s why: If you’re a data scientist and want to develop models, you need data. And if you need data, someone needs to collect that data. And if someone is collecting data, they need to make sure that it isn’t biased or it will be extremely costly in the long run.

Therefore, if you want to collect unbiased data, then you need to know about random sampling.

4 Types of Random Sampling Techniques

• Simple random sampling.
• Stratified random sampling.
• Cluster random sampling.
• Systematic random sampling.

More From Terence Shin 10 Advanced SQL Concepts You Should Know for Data Science Interviews

What Is Random Sampling?

Random sampling simply describes a state wherein every element in a population has an equal chance of being chosen for the sample.  Sounds simple, right? Well, it’s a lot easier said than done because you must consider a lot of logistics in order to minimize bias. These  four types of random sampling techniques will allow you to do just that.

1. Simple Random Sampling

Simple random sampling requires the use of randomly generated numbers to choose a sample. More specifically, it initially requires a sampling frame, which is a list or database of all members of a population. You can then randomly generate a number for each element, using Excel for example, and take the first n number of samples that you require.

To give an example, imagine the table on the right was your sampling frame. Using software like Excel, you can then generate random numbers for each element in the sampling frame. If you need a sample size of three, then you would take the samples with the random numbers from one to three.

2. Stratified Random Sampling

Stratified random sampling involves dividing a population into groups with similar attributes and randomly sampling each group.

This method ensures that different segments in a population are equally represented. To give an example, imagine a survey is conducted at a school to determine overall satisfaction. Here, stratified random sampling can equally represent the opinions of students in each department.

3. Cluster Random Sampling

Cluster sampling starts by dividing a population into groups or clusters. What makes this different from stratified sampling is that each cluster must be representative of the larger population. Then, you randomly select entire clusters to sample.

For example, if a school had five different eighth grade classes, cluster random sampling means any one class would serve as a sample.

4. Systematic Random Sampling

Systematic random sampling is a common technique in which you sample every k th element. For example, if you were conducting surveys at a mall, you might survey every 100th person that walks in.

If you have a sampling frame, then you would divide the size of the frame, N , by the desired sample size, n , to get the index number, k . You would then choose every k th element in the frame to create your sample.

Using the same charts from the first example, if we wanted a sample size of two this time, then we would take every third row in the sampling frame.

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Random Sampling Explained

You should now have an understanding of what random sampling is and several common techniques for conducting it. Mastering this concept is extremely important to minimize bias and create better models.

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Methodology

• What Is Probability Sampling? | Types & Examples

What Is Probability Sampling? | Types & Examples

Published on July 5, 2022 by Kassiani Nikolopoulou . Revised on June 22, 2023.

Probability sampling is a sampling method that involves randomly selecting a sample, or a part of the population that you want to research. It is also sometimes called random sampling.

To qualify as being random, each research unit (e.g., person, business, or organization in your population) must have an equal chance of being selected. This is usually done through a random selection process, like a drawing.

Table of contents

Types of probability sampling, examples of probability sampling methods, probability vs. non-probability sampling, advantages and disadvantages of probability sampling, other interesting articles, frequently asked questions about probability sampling.

There are four commonly used types of probability sampling designs:

Simple random sampling

• Stratified sampling

Systematic sampling

• Cluster sampling

Simple random sampling gathers a random selection from the entire population, where each unit has an equal chance of selection. This is the most common way to select a random sample.

To compile a list of the units in your research population, consider using a random number generator. There are several free ones available online, such as random.org , calculator.net , and randomnumbergenerator.org .

Writing down the names of all 4,000 inhabitants by hand to randomly draw 100 of them would be impractical and time-consuming, as well as questionable for ethical reasons. Instead, you decide to use a random number generator to draw a simple random sample.

Stratified sampling collects a random selection of a sample from within certain strata, or subgroups within the population. Each subgroup is separated from the others on the basis of a common characteristic, such as gender, race, or religion. This way, you can ensure that all subgroups of a given population are adequately represented within your sample population.

For example, if you are dividing a student population by college majors, Engineering, Linguistics, and Physical Education students are three different strata within that population.

To split your population into different subgroups, first choose which characteristic you would like to divide them by. Then you can select your sample from each subgroup. You can do this in one of two ways:

• By selecting an equal number of units from each subgroup
• By selecting units from each subgroup equal to their proportion in the total population

If you take a simple random sample, children from urban areas will have a far greater chance of being selected, so the best way of getting a representative sample is to take a stratified sample.

First, you divide the population into your strata: one for children from urban areas and one for children from rural areas. Then, you take a simple random sample from each subgroup. You can use one of two options:

• Select 100 urban and 100 rural, i.e., an equal number of units
• Select 80 urban and 20 rural, which gives you a representative sample of 100 people

Systematic sampling draws a random sample from the target population by selecting units at regular intervals starting from a random point. This method is useful in situations where records of your target population already exist, such as records of an agency’s clients, enrollment lists of university students, or a company’s employment records. Any of these can be used as a sampling frame.

To start your systematic sample, you first need to divide your sampling frame into a number of segments, called intervals. You calculate these by dividing your population size by the desired sample size.

Then, from the first interval, you select one unit using simple random sampling. The selection of the next units from other intervals depends upon the position of the unit selected in the first interval.

Let’s refer back to our example about the political views of the municipality of 4,000 inhabitants. You can also draw a sample of 100 people using systematic sampling. To do so, follow these steps:

• Determine your interval: 4,000 / 100 = 40. This means that you must select 1 inhabitant from every 40 in the record.
• Using simple random sampling (e.g., a random number generator), you select 1 inhabitant.
• Let’s say you select the 11th person on the list. In every subsequent interval, you need to select the 11th person in that interval, until you have a sample of 100 people.

Cluster sampling is the process of dividing the target population into groups, called clusters. A randomly selected subsection of these groups then forms your sample. Cluster sampling is an efficient approach when you want to study large, geographically dispersed populations. It usually involves existing groups that are similar to each other in some way (e.g., classes in a school).

There are two types of cluster sampling:

• Single (or one-stage) cluster sampling, when you divide the entire population into clusters
• Multistage cluster sampling, when you divide the cluster further into more clusters, in order to narrow down the sample size

Clusters are pre-existing groups, so each high school is a cluster, and you assign a number to each one of them. Then, you use simple random sampling to further select clusters. How many clusters you select will depend on the sample size that you need.

Multi-stage sampling is a more complex form of cluster sampling, in which smaller groups are successively selected from larger populations to form the sample population used in your study.

First, you take a simple random sample of departments. Then, again using simple random sampling, you select a number of units. Based on the size of the population (i.e., how many employees work at the company) and your desired sample size, you establish that you need to include 3 units in your sample.

In stratified sampling , you divide your population in groups (strata) that share a common characteristic and then select some members from every group for your sample. In cluster sampling , you use pre-existing groups to divide your population into clusters and then include all members from randomly selected clusters for your sample.

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There are a few methods you can use to draw a random sample. Here are a few examples:

• The fishbowl draw
• A random number generator
• The random number function

Fishbowl draw

You are investigating the use of a popular portable e‐reader device among library and information science students and its effects on individual reading practices. You write the names of 25 students on pieces of paper, put them in a jar, and then, without looking, randomly select three students to be interviewed for your research.

All students have equal chances of being selected and no other consideration (such as personal preference) can influence this selection. This method is suitable when your total population is small, so writing the names or numbers of each unit on a piece of paper is feasible.

Random number generator

Suppose you are researching what people think about road safety in a specific residential area. You make a list of all the suburbs and assign a number to each one of them. Then, using an online random number generator, you select four numbers, corresponding to four suburbs, and focus on them.

This works best when you already have a list with the total population and you can easily assign every individual a number.

RAND function in Microsoft Excel

If your data are in a spreadsheet, you can also use the random number function (RAND) in Microsoft Excel to select a random sample.

Suppose you have a list of 4,000 people and you need a sample of 300. By typing in the formula =RAND() and then pressing enter, you can have Excel assign a random number to each name on the list. For this to work, make sure there are no blank rows.

This video explains how to use the RAND function.

Depending on the goals of your research study, there are two sampling methods you can use:

• Probability sampling : Sampling method that ensures that each unit in the study population has an equal chance of being selected
• Non-probability sampling : Sampling method that uses a non-random sample from the population you want to research, based on specific criteria, such as convenience

Probability sampling

In quantitative research , it is important that your sample is representative of your target population. This allows you to make strong statistical inferences based on the collected data. Having a sufficiently large random probability sample is the best guarantee that the sample will be representative and the results are generalizable and free from research biases like selection bias and sampling bias .

Non-probability sampling

Non-probability sampling designs are used in both quantitative and qualitative research when the number of units in the population is either unknown or impossible to individually identify. It is also used when you want to apply the results only to a certain subsection or organization rather than the general public. Non-probability sampling is at higher risk than probability sampling for research biases like sampling bias .

You are unlikely to be able to compile a list of every practicing organizational psychologist in the country, but you could compile a list with all the experts in your area and select a few to interview.

It’s important to be aware of the advantages and disadvantages of probability sampling, as it will help you decide if this is the right sampling method for your research design.

Advantages of probability sampling

There are two main advantages to probability sampling.

• Samples selected with this method are representative of the population at large. Due to this, inferences drawn from such samples can be generalized to the total population you are studying.
• As some statistical tests, such as multiple linear regression , t test , or ANOVA , can only be applied to a sample size large enough to approximate the true distribution of the population, using probability sampling allows you to establish correlation or cause-and-effect relationship between your variables.

Disadvantages of probability sampling

Choosing probability sampling as your sampling method comes with some challenges, too. These include the following:

• It may be difficult to access a list of the entire population, due to ethical or privacy concerns, or a full list may not exist. It can be expensive and time-consuming to compile this yourself.
• Although probability sampling reduces the risk of sampling bias , it can still occur. When your selected sample is not inclusive enough, representation of the full population is skewed .

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If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Student’s  t -distribution
• Normal distribution
• Null and Alternative Hypotheses
• Chi square tests
• Confidence interval
• Quartiles & Quantiles
• Data cleansing
• Reproducibility vs Replicability
• Peer review
• Prospective cohort study

Research bias

• Implicit bias
• Cognitive bias
• Placebo effect
• Hawthorne effect
• Hindsight bias
• Affect heuristic
• Social desirability bias

When your population is large in size, geographically dispersed, or difficult to contact, it’s necessary to use a sampling method .

This allows you to gather information from a smaller part of the population (i.e., the sample) and make accurate statements by using statistical analysis. A few sampling methods include simple random sampling , convenience sampling , and snowball sampling .

Stratified and cluster sampling may look similar, but bear in mind that groups created in cluster sampling are heterogeneous , so the individual characteristics in the cluster vary. In contrast, groups created in stratified sampling are homogeneous , as units share characteristics.

Relatedly, in cluster sampling you randomly select entire groups and include all units of each group in your sample. However, in stratified sampling, you select some units of all groups and include them in your sample. In this way, both methods can ensure that your sample is representative of the target population .

A sampling frame is a list of every member in the entire population . It is important that the sampling frame is as complete as possible, so that your sample accurately reflects your population.

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Stratified Random Sampling: Definition, Method & Examples

Julia Simkus

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Stratified random sampling is a method of selecting a sample in which researchers first divide a population into smaller subgroups, or strata, based on shared characteristics of the members and then randomly select among each stratum to form the final sample.

These shared characteristics can include gender, age, sex, race, education level, or income.

The process of classifying the population into groups before sampling is called stratification. The strata must be mutually exclusive, and all members of the population can only be in one stratum.

When stratifying, researchers tend to use proportionate sampling, where they maintain the correct proportions to represent the population as a whole.

For example, if the larger population contains 40% history majors and 60% English majors, the final sample should reflect these percentages.

Disproportionate sampling is typically only used when studying an underrepresented group.

Applications

• When studying polling of elections, population demographics, or life expectancy.
• When studying the income of varying populations or the income for different jobs across a nation.
• When time is limited, or budgeting is tight as stratified sampling is quicker and cheaper than many other sampling methods.
• When the samples of a population vary drastically as forming strata helps organize a group of people.
• When researchers do not have access to an entire population.
• Define your population of interest and choose the characteristic(s) that you will use to divide your groups.
• Divide your sample into strata depending on the relevant characteristic(s). Each stratum must be mutually exclusive, but together, they must represent the entire population.
• Define the sample size for each stratum and decide whether your sample will be proportionate or disproportionate. The sample size in each stratum should ideally be in proportion to the members of that group within the target population or sampling frame.
• Draw a random sample from each stratum and combine them to form your final sample.

Example Situations

• Public Health Studies: To understand the incidence of disease across different age groups, the population could be stratified into different age brackets (e.g., 0-18, 19-35, 36-50, 51+).
• Investigating the relationship between average travel frequency, trip mode structure, and the characteristics of residential areas (Shi, 2015).
• Examining the prevalence and psychological sequelae of childhood sexual and physical abuse in adults from the general population (Briere & Elliott, 2003).
• Evaluating the usefulness of personality traits in explaining and predicting entrepreneurship (Llewellyn & Wilson, 2003).
• Examining women’s involvement in multiple roles in relation to 3 stress indices: role overload, role conflict, and anxiety (Barnett & Baruch, 1985).
• Studying perceptions of drinking water quality at four locations in Western Australia (Syme & Williams, 1993).

Efficient and manageable

By organizing a population into groups with similar characteristics, researchers save data collection time and can better manage a sample that would otherwise be too large to analyze.

The research costs for this sampling method are minimized as researchers save money by dividing a large population into smaller groups containing similar members rather than sampling every individual of a larger population.

Stratified sampling can produce more precise estimates than simple random sampling when members of the subpopulations are homogeneous relative to the entire population. This gives a study more statistical power.

Limitations

Too many differences within the population.

A population can’t be organized into subgroups if there are too many differences within the population or if there is not enough information about the population at hand.

Researchers must ensure that every member of the population fits into only one stratum and that all the strata collectively contain every member of the greater population. This involves extra planning and information gathering that simple random sampling does not require.

Sampling errors

Sampling errors can occur when the sample does not accurately represent the population as a whole. If this occurs, the researcher would need to restart the sampling process.

Cluster Sampling vs. Stratified Sampling

Stratified sampling and cluster sampling both involve dividing a large population into smaller groups and then selecting randomly among the subgroups to form a sample.

However, the main difference is that researchers in stratified sampling divide the population into groups based on age, religion, ethnicity, or income level and randomly choose from these strata to form a sample.

Alternatively, researchers in cluster sampling will use naturally divided groups to separate the population (i.e., city blocks or school districts) and then randomly select elements from these clusters to be a part of the sample.

Stratified Sampling vs. Quota Sampling

Quota sampling and stratified sampling both involve dividing a population into mutually exclusive subgroups and sampling a predetermined number of individuals from each.

However, the most significant difference between these two techniques is that quota sampling is a non-probability sampling method, while stratified sampling is a probability sampling method.

In a stratified sample, individuals within each stratum are selected randomly, while in a quota sample, researchers choose the sample instead of randomly selecting it.

Stratified sampling is also known as quota random sampling.

• A sample is the participants you select from a target population (the group you are interested in) to make generalizations about. As an entire population tends to be too large to work with, a smaller group of participants must act as a representative sample.
• Representative means the extent to which a sample mirrors a researcher’s target population and reflects its characteristics (e.g., gender, ethnicity, socioeconomic level). In an attempt to select a representative sample and avoid sampling bias (the over-representation of one category of participant in the sample), psychologists utilize a variety of sampling methods.
• Generalisability means the extent to which their findings can be applied to the larger population of which their sample was a part.

Barnett, R. C., & Baruch, G. K. (1985). Women’s involvement in multiple roles and psychological distress. Journal of Personality and Social Psychology, 49(1), 135–145.

Briere, J., & Elliott, D. M. (2003). Prevalence and psychological sequelae of self-reported childhood physical and sexual abuse in a general population sample of men and women. Child abuse & neglect, 27(10), 1205-1222.

How to use stratified random sampling to your advantage. Qualtrics. (n.d.). Retrieved from https://www.qualtrics.com/experience-management/research/stratified-random-sampling/

Llewellyn, D. J., & Wilson, K. M. (2003). The controversial role of personality traits in entrepreneurial psychology. Education+ Training.

Nickolas, S. (2021, May 19). How stratified random sampling works. Investopedia. Retrieved January 27, 2022, from https://www.investopedia.com/ask/answers/032615/what-are-some-examples-stratified-random-sampling.asp

Shi, F. (2015). Study on a stratified sampling investigation method for resident travel and the sampling rate. Discrete Dynamics in Nature and Society, 2015.

Syme, G. J., & Williams, K. D. (1993). The psychology of drinking water quality: an exploratory study. Water Resources Research, 29(12), 4003-4010.

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Stratified Sampling | A Step-by-Step Guide with Examples

Published on 3 May 2022 by Lauren Thomas .

In a stratified sample , researchers divide a population into homogeneous subpopulations called strata (the plural of stratum) based on specific characteristics (e.g., race, gender identity, location). Every member of the population studied should be in exactly one stratum.

Each stratum is then sampled using another probability sampling method, such as cluster or simple random sampling, allowing researchers to estimate statistical measures for each subpopulation.

Researchers rely on stratified sampling when a population’s characteristics are diverse and they want to ensure that every characteristic is properly represented in the sample.

Table of contents

When to use stratified sampling, step 1: define your population and subgroups, step 2: separate the population into strata, step 3: decide on the sample size for each stratum, step 4: randomly sample from each stratum, frequently asked questions about stratified sampling.

To use stratified sampling, you need to be able to divide your population into mutually exclusive and exhaustive subgroups. That means every member of the population can be clearly classified into exactly one subgroup.

Stratified sampling is the best choice among the probability sampling methods when you believe that subgroups will have different mean values for the variable(s) you’re studying. It has several potential advantages:

Ensuring the diversity of your sample

A stratified sample includes subjects from every subgroup, ensuring that it reflects the diversity of your population. It is theoretically possible (albeit unlikely) that this would not happen when using other sampling methods such as simple random sampling .

Ensuring similar variance

If you want the data collected from each subgroup to have a similar level of variance , you need a similar sample size for each subgroup.

With other methods of sampling, you might end up with a low sample size for certain subgroups because they’re less common in the overall population.

Lowering the overall variance in the population

Although your overall population can be quite heterogeneous, it may be more homogenous within certain subgroups.

For example, if you are studying how a new schooling program affects the test scores of children, both their original scores and any change in scores will most likely be highly correlated with family income. The scores are likely to be grouped by family income category.

In this case, stratified sampling allows for more precise measures of the variables you wish to study, with lower variance within each subgroup and therefore for the population as a whole.

Allowing for a variety of data collection methods

Sometimes you may need to use different methods to collect data from different subgroups.

For example, in order to lower the cost and difficulty of your study, you may want to sample urban subjects by going door to door, but rural subjects by post.

Because only a small proportion of this university’s graduates have obtained a doctoral degree, using a simple random sample would likely give you a sample size too small to properly compare the differences between men, women, and those who do not identify as men or women with a doctoral degree vs those without one.

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As with other methods of probability sampling , you should begin by clearly defining the population from which your sample will be taken.

Choosing characteristics for stratification

You must also choose the characteristic that you will use to divide your groups. This choice is very important: since each member of the population can only be placed in only one subgroup, the classification of each subject to each subgroup should be clear and obvious.

Stratifying by multiple characteristics

You can choose to stratify by multiple different characteristics at once, so long as you can clearly match every subject to exactly one subgroup. In this case, to get the total number of subgroups, you multiply the numbers of strata for each characteristic.

For instance, if you were stratifying by both race and gender identity, using four groups for the former and three for the latter, you would have 4 × 3 = 12 groups in total.

Next, collect a list of every member of the population, and assign each member to a stratum.

You must ensure that each stratum is mutually exclusive (there is no overlap between them), but that together, they contain the entire population.

Combining these characteristics, you have nine groups in total. Each graduate must be assigned to exactly one group.

First, you need to decide whether you want your sample to be proportionate or disproportionate.

Proportionate vs disproportionate sampling

In proportionate sampling, the sample size of each stratum is equal to the subgroup’s proportion in the population as a whole.

Subgroups that are less represented in the greater population (for example, rural populations, which make up a lower portion of the population in most countries) will also be less represented in the sample.

In disproportionate sampling, the sample sizes of each strata are disproportionate to their representation in the population as a whole.

You might choose this method if you wish to study a particularly underrepresented subgroup whose sample size would otherwise be too low to allow you to draw any statistical conclusions.

Sample size

Next, you can decide on your total sample size. This should be large enough to ensure you can draw statistical conclusions about each subgroup.

If you know your desired margin of error and confidence level as well as estimated size and standard deviation of the population you are working with, you can use a sample size calculator to estimate the necessary numbers.

Finally, you should use another probability sampling method , such as simple random or systematic sampling , to sample from within each stratum.

If properly done, the randomisation inherent in such methods will allow you to obtain a sample that is representative of that particular subgroup.

In stratified sampling , researchers divide subjects into subgroups called strata based on characteristics that they share (e.g., race, gender, educational attainment).

Once divided, each subgroup is randomly sampled using another probability sampling method .

You should use stratified sampling when your sample can be divided into mutually exclusive and exhaustive subgroups that you believe will take on different mean values for the variable that you’re studying.

Using stratified sampling will allow you to obtain more precise (with lower variance ) statistical estimates of whatever you are trying to measure.

For example, say you want to investigate how income differs based on educational attainment, but you know that this relationship can vary based on race. Using stratified sampling, you can ensure you obtain a large enough sample from each racial group, allowing you to draw more precise conclusions.

Yes, you can create a stratified sample using multiple characteristics, but you must ensure that every participant in your study belongs to one and only one subgroup. In this case, you multiply the numbers of subgroups for each characteristic to get the total number of groups.

For example, if you were stratifying by location with three subgroups (urban, rural, or suburban) and marital status with five subgroups (single, divorced, widowed, married, or partnered), you would have 3 × 5 = 15 subgroups.

Probability sampling means that every member of the target population has a known chance of being included in the sample.

Probability sampling methods include simple random sampling , systematic sampling , stratified sampling , and cluster sampling .

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Thomas, L. (2022, May 03). Stratified Sampling | A Step-by-Step Guide with Examples. Scribbr. Retrieved 5 August 2024, from https://www.scribbr.co.uk/research-methods/stratified-sampling-method/

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