random assignment vs stratified sampling

Stratified Random Sampling: Definition, Method & Examples

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Julia Simkus is a graduate of Princeton University with a Bachelor of Arts in Psychology. She is currently studying for a Master's Degree in Counseling for Mental Health and Wellness in September 2023. Julia's research has been published in peer reviewed journals.

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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.

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.

Random sampling means choosing a subset of a larger population where each sample has an equal probability of being chosen. Random samples are used in statistical and scientific research to reduce sampling bias and get sample data that is generally representative of a population, which help form unbiased conclusions.

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. 

Why Is Random Sampling Important?

If you’re a data scientist and want to develop models, or a researcher who wants to analyze a population, 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 and create more accurate data models , then you need to know about random sampling and how it works.

More on Data Science Importance Sampling Explained

Types of Random Sampling 

There are four main types of random sampling techniques: simple random sampling, stratified random sampling, cluster random sampling and systematic random sampling. Each is used for different sampling situations.

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.

Frequently Asked Questions

What is random sampling.

Random sampling involves collecting a subset of samples from a population in a way where each sample has an equal chance of being chosen. Random samples are used to ensure a sample adequately represents the larger population and to minimize sampling bias in research results.

What are the 4 types of simple random sampling?

The 4 main types of random sampling are:

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

Which is an example of a random sample?

An example of a random sample would be randomly choosing the names of 10 people from a hat containing the names from a group of 100 people.

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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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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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2.4 - simple random sampling and other sampling methods, sampling methods section  .

Sampling Methods can be classified into one of two categories:

• Probability Sampling : Sample has a known probability of being selected
• Non-probability Sampling : Sample does not have known probability of being selected as an inconvenience or voluntary response surveys

Probability Sampling Section  

In probability sampling, it is possible to both determine which sampling units belong to which sample and the probability that each sample will be selected. The following sampling methods are examples of probability sampling :

• Simple Random Sampling (SRS)
• Stratified Sampling
• Cluster Sampling
• Systematic Sampling
• Multistage Sampling (in which some of the methods above are combined in stages)

Of the five methods listed above, students have the most trouble distinguishing between stratified sampling and cluster sampling .

Stratified Sampling is possible when it makes sense to partition the population into groups based on a factor that may influence the variable that is being measured. These groups are then called strata. An individual group is called a stratum. With stratified sampling one should:

• partition the population into groups (strata)
• obtain a simple random sample from each group (stratum)
• collect data on each sampling unit that was randomly sampled from each group (stratum)

Stratified sampling works best when a heterogeneous population is split into fairly homogeneous groups. Under these conditions, stratification generally produces more precise estimates of the population percents than estimates that would be found from a simple random sample. Table 2.2 shows some examples of ways to obtain a stratified sample.

Cluster Sampling is very different from Stratified Sampling. With cluster sampling , one should

• divide the population into groups (clusters).
• obtain a simple random sample of so many clusters from all possible clusters.
• obtain data on every sampling unit in each of the randomly selected clusters.

It is important to note that, unlike with the strata in stratified sampling, the clusters should be microcosms, rather than subsections, of the population. Each cluster should be heterogeneous. Additionally, the statistical analysis used with cluster sampling is not only different but also more complicated than that used with stratified sampling.

Each of the three examples that are found in Tables 2.2 and 2.3 was used to illustrate how both stratified and cluster sampling could be accomplished. However, there are obviously times when one sampling method is preferred over the other. The following explanations add some clarification about when to use which method.

• With Example 1 : Stratified sampling would be preferred over cluster sampling, particularly if the questions of interest are affected by time zone. For example, the percentage of people watching a live sporting event on television might be highly affected by the time zone they are in. Cluster sampling really works best when there are a reasonable number of clusters relative to the entire population. In this case, selecting 2 clusters from 4 possible clusters really does not provide many advantages over simple random sampling.
• With Example 2 : Either stratified sampling or cluster sampling could be used. It would depend on what questions are being asked. For instance, consider the question "Do you agree or disagree that you receive adequate attention from the team of doctors at the Sports Medicine Clinic when injured?" The answer to this question would probably not be team dependent, so cluster sampling would be fine. In contrast, if the question of interest is "Do you agree or disagree that weather affects your performance during an athletic event?" The answer to this question would probably be influenced by whether or not the sport is played outside or inside. Consequently, stratified sampling would be preferred.
• With Example 3 : Cluster sampling would probably be better than stratified sampling if each individual elementary school appropriately represents the entire population as in a school district where students from throughout the district can attend any school. Stratified sampling could be used if the elementary schools had very different locations and served only their local neighborhood (i.e., one elementary school is located in a rural setting while another elementary school is located in an urban setting.) Again, the questions of interest would affect which sampling method should be used.

The most common method of carrying out a poll today is using Random Digit Dialing in which a machine random dials phone numbers. Some polls go even farther and have a machine conduct the interview itself rather than just dialing the number! Such " robocall polls " can be very biased because they have extremely low response rates (most people don't like speaking to a machine) and because federal law prevents such calls to cell phones. Since the people who have landline phone service tend to be older than people who have cell phone service only, another potential source of bias is introduced. National polling organizations that use random digit dialing in conducting interviewer based polls are very careful to match the number of landline versus cell phones to the population they are trying to survey.

Non-probability Sampling Section  

The following sampling methods that are listed in your text are types of non-probability sampling that should be avoided :

• volunteer samples
• haphazard (convenience) samples

Since such non-probability sampling methods are based on human choice rather than random selection, a statistical theory cannot explain how they might behave and potential sources of bias are rampant. In your textbook, the two types of non-probability samples listed above are called "sampling disasters."

Read the article: " How Polls are Conducted " by the Gallup organization available in Canvas.

The article provides great insight into how major polls are conducted. When you are finished reading this article you may want to go to the Gallup Poll Website  and see the results from recent Gallup polls. Another excellent source of public opinion polls on a wide variety of topics using solid sampling methodology is the Pew Research Center Website . When you read one of the summary reports on the Pew site, there is a link (in the upper right corner) to the complete report giving more detailed results and a full description of their methodology as well as a link to the actual questionnaire used in the survey so you can judge whether there might be bias in the wording of their survey.

It is important to be mindful of margin or error as discussed in this article. We all need to remember that public opinion on a given topic cannot be appropriately measured with one question that is only asked on one poll. Such results only provide a snapshot at that moment under certain conditions. The concept of repeating procedures over different conditions and times leads to more valuable and durable results. Within this section of the Gallup article, there is also an error: "in 95 out of those 100 polls, his rating would be between 46% and 54%." This should instead say that in an expected 95 out of those 100 polls, the true population percent would be within the confidence interval calculated. In 5 of those surveys, the confidence interval would not contain the population percent.

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Stratified random sampling: definition & guide.

12 min read Stratified random sampling helps you pick a sample that reflects the groups in your participant population. Our ultimate guide gives you a clear definition, example, and process for doing it yourself.

When it comes to statistical surveys and getting the data you need, there’s no shortage of sampling techniques you can use.

Simple sampling, systematic sampling, quota sampling, cluster sampling — there are numerous methods for designing a sample to represent your population of interest.

Of course, each varies in accuracy, reliability, and efficiency. No two methods are the same and some are more complicated than others.

In this article, we’re going to focus on one in particular: stratified random sampling. We’re going to highlight what it is, how you can use it to your advantage, and several best-practice tips to help you get going.

Free eBook: How to determine sample size

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 total population is divided into homogenous groups (strata) to complete the sampling process.

Each stratum (the singular for strata) is formed based on shared attributes or characteristics — such as level of education, income and/or gender. Random samples are then selected from each stratum and can be compared against each other to reach specific conclusions.

For example, a researcher might want to know the correlation between income and education — they could use stratified random sampling to divide the population into strata and take a random sample from it.

Stratified random sampling is typically used by researchers when trying to evaluate data from different subgroups or strata. It allows them to quickly obtain a sample population that best represents the entire population being studied.

Stratified random sampling is one of four probability sampling techniques : Simple random sampling, systematic sampling, stratified sampling, and cluster sampling.

Of course, your choice of sampling technique will depend on your goals, budget, and desired level of accuracy. With this in mind, make sure to clearly outline what it is you want to achieve and try out different methods to see which work best for your research.

But for now, where do you start with stratified random sampling?

Process — How do you do stratified random sampling?

1. define the strata needed for your sample..

Strata are usually created based on the differences between participant’s shared characteristics – e.g. their race, gender, nationality, level of education, or age group. Researchers may or may not already have prior knowledge about a population’s shared characteristics.

2. Define your sample size.

It’s important to define the ratio numbers of your sample so it is proportionally representative of the total population (see the FAQ section below for more information).

3. Randomly select from each stratum.

After stratifying each member of the population into relevant subsections, you will apply random sampling techniques to randomly select participants from each stratum. Potential sampling methods for random selection include simple random sampling or systematic random sampling.

4. Review stratum results.

When done correctly, stratified random sampling will provide a final sample that is exhaustive (each participant of the population must belong to one stratum) and mutually exclusive (where participants don’t overlap with another stratum).

5. Combine all stratum samples into one representative sample.

For an accurate, representative sample of the entire population, you must combine all stratum examples into one. This will allow you to carry out a total population analysis.

Why do researchers use stratified random sampling?

Researchers use stratified random sampling when they are already aware of (or have become aware of) subdivisions within a population that need to be accounted for in their research. This leads to several advantages and disadvantages:

Advantages of stratified random sampling

• Stratified random sampling gives you a systematic way of gaining a population sample that takes into account the demographic make-up of the population, which leads to stronger research results.
• The method is fair for participants as the sample from each stratum can be randomly selected, meaning there is no bias in the process.
• As participant grouping must be exhaustive and mutually exclusive, stratified random sampling removes variation and the chances of overlap between each stratum.
• Lastly, it helps with efficient and accurate data collection. Having a smaller, more relevant sample to work with means a more manageable and affordable research project .

Disadvantages of stratified random sampling

• Researchers may hold prior knowledge of the population’s shared characteristics beforehand, which increases the risk for selection bias when strata are defined.
• There is more administration to do to conduct this process, so researchers must include this extra time and order.
• When randomly sampling each stratum, the resulting sample may not be representative of the full population. It is worth reviewing the results to see if the sample is proportional to the whole population.
• Once you have the final sample, data analysis of the information becomes more complicated to take into account the layers of the stratum.

Example — Stratified random sampling in action

Let’s look at an example to bring this method to life:

If we’re investigating wage differences between genders, we can stratify a larger population into different genders (e.g. female and male) or pay grades (e.g. under $50k, $50-100k, $100-250k, over $250k).

If we choose to stratify by gender and randomly select a sample across each of the gender groups, then these samples can be compared using pay grades to explore wage gaps.

So in the example below, the total population is 15. When gender is applied to the population, we can see there are more men (9) than women (6). This gives us a sample ratio of 2:1, or a sample fraction of ⅔ men to ⅓ women.

If we want a sample size of 5 (one-third of the total population), we must randomly select participants in proportion to the size of each stratum. The number of participants selected must reflect the sample ratio.

As a result, the final sample will have 5 randomly selected participants, which will be split by gender (made up of 2 women and 3 men).

Frequently asked questions (FAQs) about stratified random sampling

What is the difference between stratified random sampling and cluster sampling.

Let’s explore cluster sampling vs stratified random sampling.

What is cluster sampling?

There are three forms of cluster sampling: one-stage, two-stage and multi-stage.

One-stage cluster sampling first creates groups, or clusters, from the population of participants that represent the total population. These groups are based on comparable groupings that exist – e.g. zip codes, schools, or cities.

The clusters are randomly selected, and then sampling occurs within these selected clusters. There can be many clusters and these are mutually exclusive, so participants don’t overlap between the groups

Two-stage cluster sampling first randomly selects the cluster, then the participants are randomly selected from within that cluster.

Multi-stage cluster sampling is a more complex process which involves dividing the population into groups before one or more clusters are chosen at random and sampled.

The main difference between stratified sampling and cluster sampling is that with cluster sampling, there are natural groups separating your population. In cluster sampling, the sampling unit is the whole cluster. Instead of sampling individuals from each group, a researcher will study whole clusters.

In stratified random sampling, however, a sample is drawn from each strata (using a random sampling method like simple random sampling or systematic sampling). Elements of each of the samples will be distinct, giving the entire population an equal opportunity to be part of these samples. Typically, natural groups do not exist, so you divide your target population into groups (stratum).

Generally, cluster sampling is much more affordable and “efficient”, whereas stratified random sampling is more precise.

What is the difference between stratified random sampling and simple random sampling?

Let’s explore simple random sampling vs stratified random sampling.

What is simple random sampling?

Simple random sampling selects a smaller group (the sample) from a larger group of the total number of participants (the population). It’s one of the simplest systematic sampling methods used to gain a random sample. Simple random sampling relies on using a selection method that provides each participant with an equal chance of being selected. And, since the selection process is based on probability and a random selection, the smaller sample is more likely to be representative of the total population and free from researcher bias. This method is also called a method of chance.

Simple random sampling involves randomly selecting data from the entire population so each possible sample is likely to occur. There are no constraints with this method and therefore no bias.

Stratified random sampling, on the other hand, divides the population into smaller groups (strata) based on shared characteristics. A random sample is then taken from each (in direct proportion to the size of the stratum compared to the population) and combined to create a random sample.

What should be the size of the sample chosen from each stratum?

The size of the sample you select will vary based on several factors:

• Scale In general, to analyze and draw meaningful conclusions, you need a large sample that can provide you with sufficient data from the total population.
• Practicality From a practical standpoint, if you have a larger population, you want to also have a sample size that does not require a lot of administration to collect and manage.
• Accuracy You want a sample size that is going to accurately represent the total population to make the findings as truthful as possible.

With stratified random sampling, you will end up with a sample that is proportionally representative to the population based on the stratum used.

In most cases, this will work well. However, you may need to vary the proportions manually if you’re aware of additional information that could skew the results.

For instance, using our wage example from above, the sample has 5 randomly selected participants, which will be split by gender (made up of 2 women and 3 men). If you’re aware that the wage gap range is larger across men, then this sample may miss key information as you don’t have enough male data to support the reality.

In this case, you may want to:

Either, adjust the sample ratio to include more men – e.g. from 2:1 (6 men to 3 women) to 3:1 (8 men to 2 women). Or, increase the sample size to include more of the population, to better reflect the wage range in the male proportion of the sample – e.g. increasing the sample size from 5 to 10.

If you’re unsure where to start, try our sample size calculator to get a good indication.

Conclusion: Where to go next to learn more?

And that’s stratified random sampling. Hopefully, you now have a good idea of how to use this probability sampling technique to aid your research and surveys.

But what if you want to simplify the process further by using a research panel?

If you’re thinking of using a research panel instead of conducting research yourself, you may way to read our in-depth eBook: The Panel Management Guide

In it, we discuss how you can:

• Ensure the right panel size
• Create the right profiling questions
• Optimize contact frequency
• Identify the key indicators of a healthy panel
• Find out how rewards and incentives can benefit your surveys

Free eBook: How to determine sample size

Related resources

Simple random sampling 9 min read, sampling methods 15 min read, how to determine sample size 12 min read, selection bias 11 min read, systematic random sampling 15 min read, convenience sampling 18 min read, probability sampling 8 min read, request demo.

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What Are Simple Random Sampling and Stratified Random Sampling Analytical Techniques?

Click to learn more about author Kartik Patel. This article discusses the analytical technique known as sampling and provides a brief explanation of two types of sampling analysis and how each of these methods is applied. What Is Sampling Analysis? Sampling is the technique of selecting a representative part of a population for the purpose of […]

Click to learn more about author  Kartik Patel .

This article discusses the analytical technique known as sampling and provides a brief explanation of two types of sampling analysis and how each of these methods is applied.

Sampling is the technique of selecting a representative part of a population for the purpose of determining the characteristics of the whole population. There are two types of sampling analysis: simple random sampling and stratified random sampling.

Let’s look at both techniques in a bit more detail.

Simple Random Sampling

With this method of sampling, the selection is based on chance , and every item has an equal chance of selection. An example of simple random sampling would be a lottery system.

Example:  If we want to come up with the average value of all cars in the United States, it would be impractical to find every car, assign a value, and then develop an average. Instead, we might randomly select 200 cars, get a value for those cars, and then find an average. The random selection of those 200 cars would be the “sample data of the entire United States” cars’ values (population data).

Pros and Cons of Simple Random Sampling

Pros:  Economical in nature, less time consuming

Cons:  Chance of bias, the difficulty of getting a representative sample

Stratified Random Sampling

Here, the population data is divided into subgroups known as strata. The members in each of the subgroups have similar attributes and characteristics in terms of demographics, income, location, etc. A random sample from each of these subgroups is taken in proportion to the subgroup size relative to the population size. These subsets of subgroups are then added to a final stratified random sample. Improved statistical precision is achieved through this method due to the low variability within each subgroup and the fact that a smaller sample size is required for this method as compared to simple random sampling. This method is used when the researcher wants to examine subgroups within a population.

Example:  One might divide a sample of adults into subgroups by age groups, like 18-29, 30-39, 40-49, 50-59, and 60 and above. To stratify this sample, the researcher would then randomly select proportional amounts of people from each age group. This is an effective sampling technique for studying how a trend or issue might differ across subgroups. Some of the most common strata used in stratified random sampling include age, gender, religion, race, educational attainment, socioeconomic status, and nationality. With stratified sampling, the researcher is guaranteed that the subjects from each subgroup are included in the final sample, whereas simple random sampling does not ensure that subgroups are represented equally or proportionately within the sample.

Pros and Cons of Stratified Random Sampling

Pros:  Economical in nature, less time consuming, less chance of bias as compared to simple random sampling, and higher accuracy than simple random sampling

Cons:  Need to define the categorical variable by which subgroups should be created — for instance, age group, gender, occupation, income, education, religion, region, etc.

Sampling is the technique of selecting a representative part of a population for the purpose of determining the characteristics of the whole population. Sampling is useful in assigning values and predicting outcomes for an entire population based on a smaller subset or sample of the population. The organization will choose either the simple random sampling or the stratified random sampling method, based on the type of data, the need for accuracy and representation of certain subsets and groups, and other analytical requirements of the organization.

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Stratified Random Sampling

A sampling method in which a population group is divided into one or many distinct units – called strata – based on shared behaviors or characteristics

What is Stratified Random Sampling?

Stratified random sampling is a sampling method in which a population group is divided into one or many distinct units – called strata – based on shared behaviors or characteristics.

Stratification refers to the process of classifying sampling units of the population into homogeneous units. In stratified random sampling, any feature that explains differences in the characteristics of interest can be the basis of forming strata.

For example, people’s income or education level is a variation that can provide an appropriate backdrop for strata.

• Stratified random sampling refers to a sampling technique in which a population is divided into discrete units called strata based on similar attributes. The selection is done in a manner that represents the whole population.
• The sampling technique is preferred in heterogeneous populations because it minimizes selection bias and ensures that the entire population group is represented.
• It is not suitable for population groups with few characteristics that can be used to divide the population into relevant units.

Understanding Stratified Random Sampling

Sampling a large population is often an underlying challenge in conducting statistical surveys. A more feasible approach to save time and money would be to pick a smaller group or sample size that would be used instead to represent the entire population.

A stratified random sampling approach divides the population into relevant strata to increase a certain population group’s representativeness. However, it is only achievable if relevant strata are known and distinguishable in a population group.

In stratified random sampling, a researcher selects a small sample size with similar characteristics to represent a population group under study. A population being studied in a survey may be too large to be analyzed individually; hence, it is organized into groups with the same features to save costs and time.

The technique offers wide usage, such as estimating the income for varying populations, polling of elections, and life expectancy.

How Random Stratified Sampling Works

A researcher can select a more feasible approach to study an extremely large population. An analysis is forced to divide the population into relevant strata before sampling.

One of the ways researchers use to select a small sample is called stratified random sampling. Estimates generated within strata are more precise than those from random sampling because dividing the population into homogenous groups often reduces sampling error and increases precision.

When seeking a potential stratum, it is always advisable to seek one that best minimizes variation in the characteristics under investigation and maximizes variation among strata. Stratified random sampling is best used with a heterogeneous population that can be divided using ancillary information.

Simple Random Sampling vs. Stratified Random Sampling

1. sampling the population.

Simple random sampling – sometimes known as random selection – and stratified random sampling are both statistical measuring tools. Using random selection will minimize bias, as each member of the population is treated equally with an equal likelihood of being sampled.

In contrast, stratified random sampling breaks the population into distinct subgroups called strata that have similar attributes. A random sample is taken from each stratum, with the sample size proportional to its stratum size compared to the population.  This will ensure that the sample will highlight the differences between stratum groups.

Both simple and stratified random sampling entails sampling without replacement since they do not allow each case’s sample back into the sampling frame.

2. Robustness in sample selection

Overall, simple random sampling is more robust than stratified random sampling, especially when a population has too many differences to be categorized.

Simple random sampling is also effective in situations where a population has little information that will not allow it to be subdivided into distinct units.

For instance, an online retail store may wish to survey its online customers’ purchasing habits to determine the future of its product line. If the store has approximately 50,000 customers, it may select 500 of these customers as the random sample. 500 is the sample frame within which customers are sampled purely at random.

To ensure the number of customers falls within the required range, the repeated selection is replaced. The retail store may then apply the estimated characteristics to the rest of the customers.

It can, therefore, be said that the chosen sample represents the entire customer population of 50,000. In this sense, a simple random sampling analyzes a more evenly dispersed sample throughout the population.

Strengths and Weaknesses of Stratified Random Sampling

Stratified random sampling captures the key attributes of a population group. As a result, it produces characteristics in the sample that are proportional to the entire population. Therefore stratified random sampling provides a higher degree of precision than simple random sampling .

Stratified random sampling is not suitable for every survey. It only works under the condition where a population can be stratified using relevant attributes and that the subgroups are clearly defined and do not overlap. Subjects that fall into multiple groups have a higher likelihood of being chosen and may cause a misrepresented sample.

Additional Resources

Thank you for reading CFI’s guide to Stratified Random Sampling. To keep learning and advancing your career, the following resources will be helpful:

• Simple Random Sample
• Sampling Errors
• Sample Selection Bias
• Statistical Significance
• See all data science resources
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Stratified Random Sampling: Advantages and Disadvantages

Pros and Cons of Stratified Random Sampling

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When researching a group of people, it is often impossible to measure every individual data point. However, statistical methods allow for inferences about a population by analyzing the results of a smaller sample extracted from that population.

Stratified random sampling is one way of doing this. This technique enables researchers to obtain a sample population that best represents the entire population being studied by making sure that each subgroup of interest is represented. However, it is not without its disadvantages.

Key Takeaways

• Stratified random sampling allows researchers to obtain a sample population that best represents the entire population being studied by dividing it into subgroups called strata.
• This method of statistical sampling, however, cannot be used in every study design or with every data set.
• Stratified random sampling differs from simple random sampling, which involves the random selection of data from an entire population so each possible sample is equally likely to occur.

Stratified Random Sampling: An Overview

Stratified random sampling involves dividing a population into subpopulations and then applying random sampling methods to each subpopulation to form a test group.

Stratified random sampling is different from simple random sampling , which involves the random selection of data from the entire population so that each possible sample is equally likely to occur. In contrast, stratified random sampling divides the population into smaller groups, or strata, based on shared characteristics. A random sample is then taken from each stratum in direct proportion to the size of the stratum compared to the population.

Stratified Random Sampling Example

Researchers are performing a study designed to evaluate the political leanings of economics students at a major university. The researchers want to ensure the random sample best approximates the student population, including gender, undergraduates, and graduate students. The total population in the study is 1,000 students and, from there, subgroups are created as shown below.

Total population = 1,000

Researchers would assign every economics student at the university to one of four subpopulations: male undergraduate, female undergraduate, male graduate, and female graduate. Researchers would next count how many students from each subgroup make up the total population of 1,000 students. From there, researchers calculate each subgroup's percentage representation of the total population. 

• Male undergraduates = 450 students or 45% of the population
• Female undergraduates = 200 students or 20%
• Male graduate students = 200 students or 20%
• Female graduate students = 150 students or 15%

Random sampling of each subpopulation is done based on its representation within the population as a whole. Since male undergraduates are 45% of the population, 45 male undergraduates are randomly chosen out of that subgroup. Moreover, because male graduates make up only 20% of the population, 20 are selected for the sample, and so on. 

This method has several conditions, including the need to classify every member of the population into a subgroup, so it can't be used in every study.

Advantages of Stratified Random Sampling

Stratified random sampling has advantages when compared to simple random sampling.

It reflects the population being studied because researchers are stratifying the entire population before applying random sampling methods. In short, it ensures each subgroup within the population receives proper representation within the sample. As a result, stratified random sampling provides better coverage of the population since the researchers have control over the subgroups to ensure all of them are represented in the sampling. 

With simple random sampling , there isn't any guarantee that any particular subgroup or type of person is chosen.

In our earlier example of the university students, using simple random sampling to procure a sample of 100 from the population might result in the selection of only 25 male undergraduates or only 25% of the total population. Also, 35 female graduate students might be selected (35% of the population) resulting in under-representation of male undergraduates and over-representation of female graduate students. Any errors in the representation of the population have the potential to diminish the accuracy of the study.

Disadvantages of Stratified Random Sampling

Stratified random sampling also presents researchers with a disadvantage.

Unfortunately, this method of research cannot be used in every study. The method's disadvantage is that several conditions must be met for it to be used properly. Researchers must identify every member of a population being studied and classify each of them into one, and only one, subpopulation.

As a result, stratified random sampling is disadvantageous when researchers can't confidently classify every member of the population into a subgroup. Also, finding an exhaustive and definitive list of an entire population can be challenging. 

Overlapping can be an issue if there are subjects that fall into multiple subgroups. When simple random sampling is performed, those who are in multiple subgroups are more likely to be chosen. The result could be a misrepresentation or inaccurate reflection of the population. 

In our example, undergraduate, graduate, male, and female are clearly defined groups. In other situations, however, it might be far more difficult. Imagine incorporating characteristics such as race, ethnicity, or religion. The sorting process becomes more difficult, rendering stratified random sampling an ineffective and less-than-ideal method.

What Are the Five Main Types of Sampling?

There are various sampling techniques. The main ones are simple random sampling, systematic sampling, stratified sampling, and cluster sampling. 

Why Is It Called Stratified Random Sampling?

It is called stratified random sampling because the population being analyzed is arranged into subgroups called strata. The data is stratified.

What Is the Difference Between Simple Random Sampling and Stratified Sampling?

Simple random sampling randomly selects data from the population assuming all areas will be covered. Stratified sampling, on the other hand, goes a step further by dividing the population into subpopulations based on shared characteristics to ensure each group within the population is properly represented. In theory, stratified sampling offers a fairer representation of the population. However, this approach is also more time-consuming and not always easy to apply.

When Is it Better to Use Simple Random Sampling Over Stratified Sampling?

Simple random sampling would be used if there is very little information available about the population or if the population is too diverse to divide into subsets or similar and difficult to distinguish. Sometimes grouping people into categories can be helpful. Other times, it is not necessary.

Stratified random sampling, a method of sampling that involves dividing a population into smaller subgroups known as strata, is sometimes preferred over simple random sampling because it ensures each subgroup within the population receives proper representation. However, making this extra effort is not always necessary and guaranteed to make the research more reliable and reflective of the population. Stratified random sampling is not always easy or possible to apply either.

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When should you choose Stratified sampling over random sampling?

Is there a general rule to follow when deciding when it's best to use one over the other?

An example I was looking at was the following:

An example might be to determine the proportions of defective products being assembled in a factory. In this case sampling may be stratified by production lines, factory, etc.

• 1 $\begingroup$ The example might confuse more than it helps, because the "stratification" to which it refers appears not to be stratified sampling at all! It merely describes the (obvious) need to sample different production lines within a factory separately when the objective is to estimate the proportions (plural) of defective products per production line . If, instead, the objective were to estimate the proportion (singular) of defective products in a factory, then separate sampling by production line for the purpose of estimating that single proportion in the factory would be stratified sampling. $\endgroup$ –  whuber ♦ Commented Dec 5, 2015 at 22:35

3 Answers 3

The other answer is wrong, unfortunately. Actually, that should be obvious, otherwise no statistician would ever bother to do SRS and they would happily stratify on utterly useless variables- why not?

It is true that the sum of squared error inside each stratum will drop (i.e. $\sum (x_i - {\overline{x}})^2$ will drop virtually always). This is similar to the fact that adding new variables to a regression will just about always lower the R-squared even if the variable is complete noise. However, the value of $s^2$ also involves dividing by $n_1 - 1$ and not by $n_i$. In other words, if you have $k$ strata, you lose $k-1$ degrees of freedom. So your estimated variances might rise if the stratification variable is sufficiently useless. (The effect is most serious if sample sizes are small in some strata. In the extreme, if they drop to $n_i = 1$, you can't even estimated the standard error.)

Crudely, a fast way to tell if stratification would help is to run an ANOVA on the stratification variable. If it's significant (or, at least, the ADJUSTED R-squared rises), the stratification might help.

In practice, I tell researchers that as long as they have a reasonable sample size available from each strata, and the stratification variable makes sense (they are sure that means of one strata are 'significantly different' from those of other strata), then stratify.

Side note: While lowering variances is the usual reason to stratify, there are others. First, if you want to guarantee sufficient sample size in each stratum so that you can make separate inferences on each one, you should stratify. Second, if costs vary greatly from one stratum to another, you can stratify to optimize costs. Finally, if variability is known to be much higher in some strata than others, you can use stratification (by increasing sample size in the most variable groups) to lower your se. However, if costs and variables don't distinguish your strata, you can definitely get a wider confidence interval if you stratify on an unhelpful variable.

I'll illustrate with an exact computation: I'll start with the population $\lbrace 100, 150, 50, 101, 151, 51\rbrace$. First I'll enumerate the EXACT sampling distribution of the means of all possible Simple Random Samples (SRS) of size n = 4 from the population. Then I'll break this into two strata, each of size three. I'll enumerate all possible means of samples based on an SRS of size 2 from each stratum.

Finally, I'll compute the exact 'population' variance (i.e. sigma squared) of each statistic.

Note that the true variance of the stratification estimator is much larger than the variance of the simple random sample estimator. By the way, if I repeat this for the population $\lbrace 100, 150, 50, 170, 220, 120\rbrace$, where the strata are considerably different, I get the stratification estimator working better:

exact variance of SRS estimator: 289.1667

exact variance of stratification estimator: 208.3333

Actually, it probably would have been easier to just prove this than give an example. But this shows that stratification can fail to give a lower variance estimator. Note that this example is extreme in that the sample sizes are small.

• $\begingroup$ Just to clarify, my assertion was that the variance of stratified sampling is strictly smaller than the variance of SRS, not that it was significantly smaller. Under random allocation into strata, the expected value of each group would be the same, and the variance would be the same as SRS. Could you please defend your position that my answer is incorrect? If I am wrong, I would like to know why. $\endgroup$ –  Chris C Commented Dec 6, 2015 at 2:39
• 1 $\begingroup$ @Chris C, your derivations are certainly correct, but there are other considerations besides the size of the true variances. With random allocation, the standard t-based confidence intervals will be wider, because $df = n - L$, whereas in SRS $df = n - 1$. Analysis of small domains (subpopulations) will also be adversely affected, because smaller strata are more likely to have no or only one member of the domain. $\endgroup$ –  Steve Samuels Commented Dec 6, 2015 at 14:20
• $\begingroup$ Thank you @SteveSamuels, I didn't take that into account. $\endgroup$ –  Chris C Commented Dec 6, 2015 at 14:22
• $\begingroup$ @Chris C, I now think that your derivations are confused, because in ordinary stratified sampling formulas, only stratum weights $W_h =\frac{N_h}{N}$ are employed. Your formulas include $w_h =\frac{n_h}{n}$. See Cochran, 1977, I don't know where your $w_h$ come from. You also introduced a constant $h_h$, which is probably a typo. $\endgroup$ –  Steve Samuels Commented Dec 6, 2015 at 16:55
• $\begingroup$ In the disagreement with @ChrisC, you are correct. To quote Cochran, 1977, page 99. "It is not true, however, that any stratified random sample gives a smaller variance than a simple random sample. If the values of the nh are far from optimum, stratified sampling may have a higher variance. In fact, even stratification with optimum allocation for fixed total sample size may give a higher variance, although this result is an academic curiosity rather than something likely to happen in practice." (WG Cochran, 1977, Sampling Techniques, p. 99) $\endgroup$ –  Steve Samuels Commented Dec 6, 2015 at 18:57

I'll make several statements and then prove them mathematically, in case you're interested. If you want a quick summary, I'll provide one at the end.

First of all, both simple random sampling (SRS) and stratified sampling will provide you with an unbiased estimator of population mean $\mu$.

Denote by $\bar{x}_{SRS}$ sample mean for SRS and $\bar{x}_{St}$ sample mean for stratified sampling.

$\bar{x}_{SRS}$ is an unbiased estimator for $\mu$

$$ \begin{aligned} E[\bar{x}_{SRS}] = \frac{1}{N} X_1 + ... + \frac{1}{N} X_N = \bar{X}_{SRS} = \mu \end{aligned} $$

Taking the previous and applying it, given $L$ strata, $\bar{x}_{St}$ is an unbiased estimator for $\mu$

$$ \begin{aligned} E[\bar{x}_{St}] &= E[\sum^L_{i=1} W_i \bar{x}_i] \\ &= \sum^L_{i=1} W_i E(\bar{x}_i) \\ &= \sum^L_{i=1} W_i \bar{X}_i \\ &= \frac{N_1 \bar{X}_1 + ... + N_L \bar{X}_L}{N} \\ &= \frac{\tau_1 + ... \tau_L}{N} \\ &= \bar{X} \\ &= \mu \end{aligned} $$

Since both sampling schemes give you an unbiased estimation, either is fine to use. However, the variances are not equal, and thus we can define conditions under which it is optimal to perform stratified sampling.

Recall that $W$ is the weight per group ie. $\frac{n_h}{N}$. $$ \begin{aligned} V_{prop} &= \sum^L_{h=1} \frac{w^2_h s^2_h}{n W_h} (\frac{N w_h - n W_h}{N W_h }) \\ &= ( \frac{1}{n} \sum^L_{h = 1} w_h s^2_h) \frac{N-n}{N} \\ &= \frac{N-n}{Nn} \sum^L_{h=1} w_h s^2_h \end{aligned} $$

Recall that

$$ \begin{aligned} V_{ran} &= \frac{S^2}{n} (\frac{N-n}{N}) \\ V_{prop} &= \frac{N-n}{Nn} \sum^L_{h=1} W_h S^2_h \\ V_{opt} &= \frac{1}{n} (\sum^L_{h=1} W_h S_h)^2 - \frac{1}{N} \sum^L_{h=1} W_h S^2_h \end{aligned} $$

Recall that $W$ is the weight per group ie. $\frac{n_h}{N}$

$$ \begin{aligned} S^2 &= \frac{1}{N-1} \sum^N_{i=1} (Y_i - \bar{Y})^2 \\ (N-1) S^2 &= \sum^N_{i=1} (Y_i - \bar{Y})^2 \\ &= \sum^L_{h=1} \sum^{N_h}_{i=1} (Y_{hi} - \bar{Y})^2 \\ &= (Y_{hi} - \bar{Y_h} + \bar{Y_h} - \bar{Y})^2 \\ &= \sum^L_{h=1} \sum^{N_h}{i=1} (Y_{hi} - \bar{Y}_h)^2 + \sum^L_{h=1} \sum^{N_h}_{i=1} (\bar{Y}_h - \bar{Y})^2 + 2 \sum^L_{h=1} \sum^{N_h}_{i=1} (Y_{hi} - \bar{Y}_h)(\bar{Y}_h - \bar{Y} \end{aligned} $$

Recall that subtracting the mean from a series of data is always 0. Since $\sum^{N_h}_{i=1} (Y_{hi} - \bar{Y}_h) = 0$, the third term disappears.

$$ \begin{aligned} S^2_h &= \frac{1}{N_h -1} \sum^{N_h}_{i=1} (Y_{hi} - \bar{y}_h)^2 \\ (N-1) S^2 &= \sum^L_{h=1} (N_h -1) S^2_h + \sum^L_{h=1} N_h (\bar{Y}_h - \bar{Y})^2 \end{aligned}$$

Note that $f = \frac{n}{N}$ aka finite population correction.**

$$ \begin{aligned} V_{ran} ( \bar{y}) &= \frac{1 - f}{n} S^2 \\ &\approx \frac{1-f}{n} \sum^L_{h=1} W_h S^2_h + \frac{1-f}{n} \sum^L_{h=1} W_h (\bar{Y}_h \bar{Y})^2 \\ V_{SRS} - V_{St} &= \frac{1-f}{n} \sum^L_{h=1} W_h S^2_h + \frac{1-f}{n} \sum W_h (\bar{Y}_h - \bar{y})^2 - \frac{1}{n} (\sum^L_{h=1} W-h_h S_h)^2 + \frac{1}{N} \sum^L_{h=1} W_h S^2_h \\ &= \frac{1}{n} \sum^L_{h=1} W_h S^2_h - \frac{1}{N} \sum^L_{h=1} W_h S^2_h + \frac{1-f}{n} \sum W_h (\bar{Y}_h - \bar{Y})^2 + \frac{1}{N} \sum^L_{h=1} W_h S^2_h - \frac{1}{n} (\sum^L_{h=1} W_h S_h)^2 \\ &= \frac{1}{n} \sum^L_{h=1} W_h S^2_h - (\sum^L_{h=1} W_h S_h)^2) + \sum^L_{h=1} W_h (\bar{Y}_h - \bar{Y})^2 \\ &= \frac{1}{n} \sum^L_{h=1} W_h (S_h \bar{S})^2 + \sum^L_{h=1} W_h (\bar{Y}_h - \bar{Y})^2 \\ V_{ran} - V_{prop} &= \frac{1-f}{n} \sum^L_{h=1} W_h S^2_h + \frac{1-f}{n} \sum^L_{h=1} W_h (\bar{Y}_h - \bar{Y})^2 - \frac{1}{n} W_h S^2_h + \frac{1}{N} W_h S^2_h \\ &= \frac{1-f}{n} \sum^L_{h=1} W_h (\bar{Y}_h - \bar{Y})^2 \end{aligned} $$

Interpretation:

We look at two kinds of stratified sampling schemes, proportion and optimum (Neymar Allocation) and show that both are better than simple random sampling. The proportional allocation method performs better than SRS when the following is maximized:

$$ \frac{1-f}{n} \sum^L_{h=1} W_h (\bar{Y}_h - \bar{Y})^2 $$

The only control we have over this expression is the difference between $\bar{Y}_h$ and $\bar{Y}$. This means that if you have strata that have means far from the grand mean, then proportional allocation will give you a smaller variance, and thus an optimal, better, sample.

The second kind, Neymar or optimal allocation, wants us to maximize the following in order to have the biggest difference, and thus the smallest variance:

$$ \frac{1}{n} \sum^L_{h=1} W_h (S_h - \bar{S})^2 + \sum^L_{h=1} W_h (\bar{Y}_h - \bar{Y})^2 $$

This gives us an additional term to the proportional allocation above. Thus, optimal allocation is better than proportional allocation because if the standard deviations of the groups are different than the grand standard deviation, then this term is bigger than the one above. There is no way that it is smaller. Thus, as a summary:

$$ V_{opt} (\bar{y}_{st}) \leq V_{prop} (\bar{y}_{st}) \leq V_{SRS} (\bar{y}_{SRS}) $$

Note that the above formulations hold when we assume $\frac{1}{N} \approx \frac{1}{N_i} \overset{.}{=} 0$ and assume that $\frac{N_h - 1}{N-1} \approx \frac{N_h}{N}$. When this assumption is not made, the above is slightly more complex, but still follows.

I've probably made some mistakes and some typos; I'll fix them when I have a little more time, but hopefully the general idea comes across.

Stratification is always better, assuming equal costs of sampling each strata. It's best when the mean and standard deviation of your strata are really different than your grand mean and standard deviation.

References:

Elementary Survey Sampling 7th Edition, Richard L. Scheaffer (Author), III William Mendenhall (Author), R. Lyman Ott (Author), Kenneth G. Gerow (Author), ISBN-13: 978-0840053619

• $\begingroup$ I seem to have switched from $X$ to $Y$ in the middle there, I'll fix that as soon as I have a chance. $\endgroup$ –  Chris C Commented Dec 6, 2015 at 0:58
• $\begingroup$ Nice answer. But what if you don't know the distribution of Y? $\endgroup$ –  tomka Commented Dec 8, 2015 at 17:30

I've taken many samples, large and small, simple and complex, over the years. My conclusion: Simple random sampling (SRS) alone is almost never the choice for a real-world problem.

On the other hand the theory of SRS is important, because it underlies the theory of other techniques.

The alternatives to SRS: stratified sampling, systematic sampling, in some instances, unequal probability sampling, or a combination of these. It is okay to take an SRS within strata.

In my comments, I quoted Cochran as saying stratified sampling isn't always more precise than SRS. However increased precision is not the only, or even the main, reason for choosing a stratifed design.

Reasons to stratify

Look for stratifying factors for at five reasons (Lohr (2009) p. 74; Valliant, Dever, & Kreuter, 2013, p. 44):

To avoid selecting a sample that badly misrepresents the population. I've seen many instances of such SRSs. In some, reweighting was a partial fix. In others, no recovery was possible. One such was the object of a question to Statalist. A senior public health official wanted to estimate characteristics of an epidemic by studying tf patients who attended medical clinics during that time. There were 40 clinics in the city, and 10 were drawn by SRS. Unfortunately, the 10 did not include the two very large hospital clinics in the city, which between them saw over 30% of all outpatients, usually the sickest. This bias made the sample useless for the satisfying its original purpose. At a minimum, the two large hospital clinics should have been selected with certainty before taking the simple random sample.

Closely related: stratify to "cover" the entire population. (This is also a reason to do systematic sampling.)

To guarantee a minimum sample size for group that are going receive separate analyses. For a study of occupational health and safety in California farms, for example, farms were stratified by size and major crop.

To control costs. Example: charts were to be abstracted in a sample of California hospitals. Rural hospitals were placed in a separate stratum and sampled at a lower rate than urban hospitals. Why? Experienced abstractors lived in urban areas and could study 1-2 hospitals per day, then go home at night. To study a rural hospital took one abstractor two days, including travel, and incurred the cost of an overnight stay.

To improve sample efficiency (i.e. get smaller standard errors) by grouping together observations with similar means and variances. Some national surveys stratify as finely as possible and draw a SRS with $n= 1$ unit from each stratum. Because a minimum of $n = 2$ observations per stratum is needed to compute standard errors, such designs are analyzed by combining neighboring strata. The "true" standard errors for the design are then likely to be smaller than the estimated standard errors, clearly a good thing.

To sample with probability approximately proportional to size.

Systematic sampling

Many frames have a natural ordering, for example date of event. Systematic samples capture the natural stratification contained in this ordering.

Lohr, Sharon L. 2009. Sampling: Design and Analysis. Boston, MA: Cengage Brooks/Cole.

Valliant, Richard, Jill A. Dever, and Frauke Kreuter. 2013. Practical Tools for Designing and Weighting Survey Samples. Statistics for Social and Behavioral Sciences. Springer.

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Random Sampling vs. Random Assignment

Random sampling and random assignment are fundamental concepts in the realm of research methods and statistics. However, many students struggle to differentiate between these two concepts, and very often use these terms interchangeably. Here we will explain the distinction between random sampling and random assignment.

Random sampling refers to the method you use to select individuals from the population to participate in your study. In other words, random sampling means that you are randomly selecting individuals from the population to participate in your study. This type of sampling is typically done to help ensure the representativeness of the sample (i.e., external validity). It is worth noting that a sample is only truly random if all individuals in the population have an equal probability of being selected to participate in the study. In practice, very few research studies use “true” random sampling because it is usually not feasible to ensure that all individuals in the population have an equal chance of being selected. For this reason, it is especially important to avoid using the term “random sample” if your study uses a nonprobability sampling method (such as convenience sampling).

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Random assignment refers to the method you use to place participants into groups in an experimental study. For example, say you are conducting a study comparing the blood pressure of patients after taking aspirin or a placebo. You have two groups of patients to compare: patients who will take aspirin (the experimental group) and patients who will take the placebo (the control group). Ideally, you would want to randomly assign the participants to be in the experimental group or the control group, meaning that each participant has an equal probability of being placed in the experimental or control group. This helps ensure that there are no systematic differences between the groups before the treatment (e.g., the aspirin or placebo) is given to the participants. Random assignment is a fundamental part of a “true” experiment because it helps ensure that any differences found between the groups are attributable to the treatment, rather than a confounding variable.

So, to summarize, random sampling refers to how you select individuals from the population to participate in your study. Random assignment refers to how you place those participants into groups (such as experimental vs. control). Knowing this distinction will help you clearly and accurately describe the methods you use to collect your data and conduct your study.

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Methodology

• Simple Random Sampling | Definition, Steps & Examples

Simple Random Sampling | Definition, Steps & Examples

Published on August 28, 2020 by Lauren Thomas . Revised on December 18, 2023.

A simple random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected.

This method is the most straightforward of all the probability sampling methods , since it only involves a single random selection and requires little advance knowledge about the population. Because it uses randomization, any research performed on this sample should have high internal and external validity, and be at a lower risk for research biases like sampling bias and selection bias .

Table of contents

When to use simple random sampling, how to perform simple random sampling, other interesting articles, frequently asked questions about simple random sampling.

Simple random sampling is used to make statistical inferences about a population. It helps ensure high internal validity : randomization is the best method to reduce the impact of potential confounding variables .

In addition, with a large enough sample size, a simple random sample has high external validity : it represents the characteristics of the larger population.

However, simple random sampling can be challenging to implement in practice. To use this method, there are some prerequisites:

• You have a complete list of every member of the population .
• You can contact or access each member of the population if they are selected.
• You have the time and resources to collect data from the necessary sample size.

Simple random sampling works best if you have a lot of time and resources to conduct your study, or if you are studying a limited population that can easily be sampled.

In some cases, it might be more appropriate to use a different type of probability sampling:

• Systematic sampling involves choosing your sample based on a regular interval, rather than a fully random selection. It can also be used when you don’t have a complete list of the population.
• Stratified sampling is appropriate when you want to ensure that specific characteristics are proportionally represented in the sample. You split your population into strata (for example, divided by gender or race), and then randomly select from each of these subgroups.
• Cluster sampling is appropriate when you are unable to sample from the entire population. You divide the sample into clusters that approximately reflect the whole population, and then choose your sample from a random selection of these clusters.

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There are 4 key steps to select a simple random sample.

Step 1: Define the population

Start by deciding on the population that you want to study.

It’s important to ensure that you have access to every individual member of the population, so that you can collect data from all those who are selected for the sample.

Step 2: Decide on the sample size

Next, you need to decide how large your sample size will be. Although larger samples provide more statistical certainty, they also cost more and require far more work.

There are several potential ways to decide upon the size of your sample, but one of the simplest involves using a formula with your desired confidence interval and confidence level , estimated size of the population you are working with, and the standard deviation of whatever you want to measure in your population.

The most common confidence interval and levels used are 0.05 and 0.95, respectively. Since you may not know the standard deviation of the population you are studying, you should choose a number high enough to account for a variety of possibilities (such as 0.5).

You can then use a sample size calculator to estimate the necessary sample size.

Step 3: Randomly select your sample

This can be done in one of two ways: the lottery or random number method.

In the lottery method , you choose the sample at random by “drawing from a hat” or by using a computer program that will simulate the same action.

In the random number method , you assign every individual a number. By using a random number generator or random number tables, you then randomly pick a subset of the population. You can also use the random number function (RAND) in Microsoft Excel to generate random numbers.

Step 4: Collect data from your sample

Finally, you should collect data from your sample.

To ensure the validity of your findings, you need to make sure every individual selected actually participates in your study. If some drop out or do not participate for reasons associated with the question that you’re studying, this could bias your findings.

For example, if young participants are systematically less likely to participate in your study, your findings might not be valid due to the underrepresentation of this group.

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
• Cluster sampling
• Stratified sampling
• 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

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 .

Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population . Each member of the population has an equal chance of being selected. Data is then collected from as large a percentage as possible of this random subset.

The American Community Survey  is an example of simple random sampling . In order to collect detailed data on the population of the US, the Census Bureau officials randomly select 3.5 million households per year and use a variety of methods to convince them to fill out the survey.

If properly implemented, simple random sampling is usually the best sampling method for ensuring both internal and external validity . However, it can sometimes be impractical and expensive to implement, depending on the size of the population to be studied,

If you have a list of every member of the population and the ability to reach whichever members are selected, you can use simple random sampling.

Samples are used to make inferences about populations . Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

Sampling bias occurs when some members of a population are systematically more likely to be selected in a sample than others.

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