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Definition:

Stratified random selectioncreates a sample from a population, reflecting the proportionality of the subgroups to the population in the sample.

## 🤔 Understanding a stratified random sample

Stratified random sampling is a probability sampling technique that creates a sample with subgroups that reflect the proportional makeup of the overall population. Often, a population can be divided into strata (subgroups) according to certain characteristics, eg B. grouping people into different age groups. Individual subjects can then be randomly selected from each stratum to ensure that each stratum is represented in the sample in the same proportion as in the original population. So if 50% of your original population is between 50 and 65 years old, then 50% of your sample will too. Stratified random sampling is used in many fields, including marketing, science, statistics, and investing.

Example

Suppose a researcher wants to track the performance of startups and their founders. One thing to look at might be how these companies perform based on the age, education level, nationality or gender of the founders. To examine this, the researcher analyzed a stratified random sample representing founders based on these characteristics against how many people in each group founded startups during a given time period.

## Go away

The stratified random sample is like a scale model...

A scale model of an airplane is a full-size replica of the airplane because the model maintains the exact physical relationships between its parts. In the model, the relationship between wingspan and fuselage length corresponds to that of a real aircraft. The dimensions are proportional, although it is tiny. A stratified random sample is a sample from a larger population that preserves the proportions of specific subgroups within the population.

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Tell me more…

- What is a stratified random sample?
- How does stratified random sampling work?
- What is the difference between layered random selection and simple random selection?
- What is the difference between stratified random sampling and cluster random sampling?
- What is the difference between proportional and disproportionate stratified random sampling?
- What are the advantages and disadvantages of stratified random sampling?

## What is a stratified random sample?

Sampling is a statistical technique that involves obtaining a representative sample size from a target population to examine the characteristics of the entire population. Observing a smaller sample of a population is more accessible than observing an entire population. There are many different sampling designs.

Stratified random sampling (also known as proportional stratified random sampling) is a type of probability sampling in which an entire population is divided into different subgroups (strata). Then, randomly select individual individuals from each subgroup (strata) to create an accurate mini-sample that is proportional to the overall population.

Stratified random sampling is a sampling technique that portfolio managers often use to create an investment portfolio that tracks an index of stocks or bonds without having to buy every stock or stock.Linkin the index. A portfolio manager can select assets for an index tracking portfolio to replicate the index structure with fewer assets.

Indices can be divided into subgroups based on one or more characteristics, such as market capitalization or industry. A portfolio manager can use the market capitalization of assets in an index to create a stratified sample. Each of the assets selected for thepastawould be relative to the market capitalization of those in the index.

## How does stratified random sampling work?

Stratified random sampling is a sampling method that ensures that the proportion of each subgroup (stratum) to the total population size equals the proportion of the corresponding sampling stratum to the sample size of the population.

First, divide the population into strata based on a specific characteristic. It then randomly selects people from each stratum based on the percentage each group has in the total population.

Suppose we have a huge bag with 1000 gummy bears of different flavors and we want to divide the huge bag into 10 smaller bags of 100 gummy bears each, each containing the exact ratio of flavors that the big bag has. .

- We count the number of orange, lemon, lime and raspberry gummy bears as shown in column 1.
- We calculated the proportion of each flavor to the total population as shown in column 2.
- We chose gummy bears of each flavor for our smaller bag of 100 at the same rate as the jumbo bag of 1000 flavors, as shown in column 3.

In this example, we would randomly select 10 orange gummy bears from the original 100 options to create this sample layer. We would then randomly select 20 lemons, and so on to create our stratified random sample of 100 gummies.

## What is the difference between layered random selection and simple random selection?

Simple random sampling is a sampling method that gives each member of the population an equal chance of being selected. The population is not divided into subpopulations before selecting the random sample.

If you have a population of 100 people and you want a random sample of 10% of the population, you can put 100 names in a hat, draw 10 names and create a simple random sample of 10% of the population. A random sample is easier to create than a stratified random sample, but it may not tell you much about the characteristics of the population.

If you want a more accurate representation of the total population, you can use a stratified random sample. You can divide the population into subgroups based on a similar attribute such as age, race, gender, income level, etc. This would produce a sample that would more accurately represent the characteristics of the general population.

Let's say we want to study a population by its age. If the original population was 40% under 25 years old, 50% between 25 and 70 years old, and 10% over 70 years old, we could select four people under 25 years old, five people over 25 years old, and one person over 25 years old. 70 years. We would have a population sample of 10 people with age subgroups that accurately represent the proportion of age groups in the target population of 100 people.

## What is the difference between stratified random sampling and cluster random sampling?

Cluster sampling randomly selects some groups from a population. You can omit other groups, and the selected groups may not accurately represent the entire population.

Suppose you want to ask the residents of a neighborhood about their political affiliation, but you don't have much time. You can divide the neighborhood into streets and randomly select some of the streets (clusters) to conduct your search.

Compared to stratified random sampling, cluster sampling is not as accurate and leaves room for error. You can skip some groups and not a specific variety like B. Income levels replicate in the neighborhood.

If you wanted to create a more accurate survey that used income level as an attribute to compare whether survey responses differed in relation to income level in that neighborhood, you would have to choose your samples differently, which would take more time. .

Suppose the neighborhood you want to study has eight different streets, and you can collect data on the income level of each family on each street. You can choose to subdivide each street into subgroups with income levels below $50,000 per year and income levels above $50,000.

They would then quantify how many homes on each street fall into each of these two subgroups (less than $50,000 and more than $50,000). You would then select a random sample from each street that represented the proportion of households with incomes above and below $50,000.

## What is the difference between proportional and disproportionate stratified random sampling?

Proportional stratified random sampling (also known as stratified random sampling) provides a sample from the population that accurately represents the correct proportion of subpopulations. The proportion of the total population that each stratum represents is the same proportion that it represents in the sample population.

In the case of disproportionately stratified random samples, the proportions of subgroups represented in the population are ignored. The population sample contains different strata that do not represent the same proportion of subgroups to the total population. A disproportionately stratified random sample can produce biased results that do not represent the true population.

## What are the advantages and disadvantages of stratified random sampling?

Compared to simple random sampling (picking a name out of a hat) and cluster random sampling (picking a few subgroups), stratified random sampling has some advantages and disadvantages.

Benefits

- More accurate representation of a population.
- More accurate than simple spot checks
- Less time than examining an entire population

Disadvantages

- Requires definition of characteristics to create subgroups
- Mathematically more complex than simple random or cluster sampling
- Longer than simple random or cluster sampling methods

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## FAQs

### What is random stratified random sampling? ›

Stratified random sampling is a type of probability method using which a research organization can branch off the entire population into multiple non-overlapping, homogeneous groups (strata) and randomly choose final members from the various strata for research which reduces cost and improves efficiency.

**What is stratified random sampling with example? ›**

But the most common type is probably proportional stratified random sampling, where **a population divides into strata, and then the random sample is taken from each stratum in proportion to its size**. For example, if the entire population is 60% female and 40% male, then the sample would be 60% female and 40% male.

**What is a stratified random sample quizlet? ›**

Stratified Sampling. **A method of probability sampling (where all members of the population have an equal chance of being included)** Population is divided into 'strata' (sub populations) and random samples are drawn from each. This increases representativeness as a proportion of each population is represented.

**What is an example of a stratified sample? ›**

A stratified sample is one that ensures that subgroups (strata) of a given population are each adequately represented within the whole sample population of a research study. For example, one might **divide a sample of adults into subgroups by age, like 18–29, 30–39, 40–49, 50–59, and 60 and above**.

**Why is stratified random sampling used? ›**

Stratified random sampling is one common method that is used by researchers because **it enables them to obtain a sample population that best represents the entire population being studied, making sure that each subgroup of interest is represented**.

**What are the 2 types of stratified random sampling? ›**

There are two types of stratified sampling – one is **proportionate stratified random sampling and another is disproportionate stratified random sampling**. In the proportionate random sampling, each stratum would have the same sampling fraction.

**How do you write a stratified random sample? ›**

To create a stratified random sample, there are seven steps: (a) defining the population; (b) choosing the relevant stratification; (c) listing the population; (d) listing the population according to the chosen stratification; (e) choosing your sample size; (f) calculating a proportionate stratification; and (g) using ...

**How to do a stratified random sample? ›**

**Here are four steps for performing a stratified random sampling:**

- Define the population and subgroups. Start by defining the population where you plan to take your sample. ...
- Split the population into subgroups. ...
- Choose the sample size for subgroups. ...
- Take random samples of the subgroups.

**What is simple random sampling with example? ›**

An example of a simple random sample would be **the names of 25 employees being chosen out of a hat from a company of 250 employees**. In this case, the population is all 250 employees, and the sample is random because each employee has an equal chance of being chosen.

**Is stratified random sampling good? ›**

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.

### What is a stratified random sample AP Stats? ›

A stratified random sample involves **dividing the population into separate strata, based on shared characteristics or attributes**. This ensures that the sample is representative of the overall population in terms of these characteristics.

**What is stratified random sampling in biology? ›**

Stratified sampling

**Divide a habitat into zones which appear different and take samples from each zone**. For example, if vegetation cover in an area of heathland is 60% heather and 40% gorse, for a stratified sample take 60% of the samples from within heather and 40% of the samples from within gorse.

**Is stratified a simple random sample? ›**

**Stratified simple random sampling is a variation of simple random sampling** in which the population is partitioned into relatively homogeneous groups called strata and a simple random sample is selected from each stratum.

**What is simple and stratified sample? ›**

A simple random sample is used to represent the entire data population and randomly selects individuals from the population without any other consideration. A stratified random sample, on the other hand, first divides the population into smaller groups, or strata, based on shared characteristics.

**What is stratified sampling example in healthcare? ›**

**Choose a random sample of 50 nurses from each of the 10 hospitals and interview these 50 * 10 = 500 regarding their job satisfaction**. This is an example of stratified sampling, in which each hospital is a stratum.

**What is the sample size for stratified sampling? ›**

In stratified sampling, **the size of the sample from each stratum is chosen by the sampler**, or to put it another way, given a total sample size n = n_{1} + n_{2} + … + n_{h} + … + n_{k}, a choice can be made on how to allocate the sample among the k strata.

**Why is stratified sampling better than simple? ›**

The advantage of stratified sampling is that **it ensures that each stratum is adequately represented in the sample, and reduces the sampling error and variability within each group**. This can improve the accuracy and precision of your estimates, and allow you to compare the differences between the strata.

**Is stratified sampling non probability? ›**

Stratified sampling is **a probability sampling technique** wherein the researcher divides the entire population into different subgroups or strata, then randomly selects the final subjects proportionally from the different strata.

**Is stratified sampling biased? ›**

When using stratified sampling, you create subgroups based on certain characteristics of your population, such as age, gender, income, or education level. This ensures that each subgroup is a fair representation of the entire population, and that **your sample is not biased towards any particular characteristic**.

**How do you do simple random sampling? ›**

**How to perform simple random sampling**

- Step 1: Define the population. Start by deciding on the population that you want to study. ...
- Step 2: Decide on the sample size. Next, you need to decide how large your sample size will be. ...
- Step 3: Randomly select your sample. ...
- Step 4: Collect data from your sample.

### How do you find the stratified sample in statistics? ›

To implement stratified sampling, first find the total number of members in the population, and then the number of members of each stratum. For each stratum, divide the number of members by the total number in the entire population to get the percentage of the population represented by that stratum.

**How do you select a stratified random sample quizlet? ›**

To select a stratified random sample, **first classify the population into groups of similar individuals, called strata.** **Then choose a separate SRS in each stratum and combine these SRSs to form the full sample**. - We want each stratum to contain similar individuals, and for there to be large differences between strata.

**What is unique about a stratified sample? ›**

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.

**What are the 4 types of random sampling? ›**

There are four primary, random (probability) sampling methods – **simple random sampling, systematic sampling, stratified sampling, and cluster sampling**.

**What is the sample size for simple random sampling? ›**

**The minimum sample size is 100**

Most statisticians agree that the minimum sample size to get any kind of meaningful result is 100. If your population is less than 100 then you really need to survey all of them.

**What are the benefits of stratified randomization? ›**

Stratified randomization **makes a smaller error than other sampling methods** such as cluster sampling, simple random sampling, and systematic sampling or non-probability methods since measurements within strata could be made to have a lower standard deviation.

**How is sampling used in real life? ›**

Sampling is very often used in our daily life. For example, **while purchasing fruits from a shop, we usually examine a few to assess the quality**. A doctor examines a few drops of blood as a sample and draws a conclusion about the blood constitution of the whole body.

**How can you tell the difference between simple and stratified? ›**

The fundamental difference between simple and stratified epithelial tissue is that **simple epithelial tissue has only one cell layer.** **In contrast, stratified epithelial tissue has two or more cell layers piled upon each other**.

**What is the difference between random systematic and stratified sampling? ›**

It is possible to combine stratified sampling with random and systematic sampling. **Stratified random sampling - random samples are taken from within certain categories.** **Stratified systematic sampling - regular samples are taken from within certain categories**.

**What is the simple definition of random 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.

### What is the difference between systematic sampling and stratified random sampling? ›

In systematic sampling, the list of elements is "counted off". That is, every kth element is taken. Stratified sampling also divides the population into groups called strata. However, this time it is by some characteristic, not geographically.

**What is the difference between cluster sampling and stratified random sampling? ›**

Cluster sampling and stratified sampling share the following differences: Cluster sampling divides a population into groups, then includes all members of some randomly chosen groups. Stratified sampling divides a population into groups, then includes some members of all of the groups.

**Why is stratified better than simple random? ›**

The advantage of stratified sampling is that **it ensures that each stratum is adequately represented in the sample, and reduces the sampling error and variability within each group**. This can improve the accuracy and precision of your estimates, and allow you to compare the differences between the strata.

**How to do stratified sampling? ›**

- STEP ONE: Define the population.
- STEP TWO: Choose the relevant stratification.
- STEP THREE: List the population.
- STEP FOUR: List the population according to the chosen stratification.
- STEP FIVE: Choose your sample size.
- STEP SIX: Calculate a proportionate stratification.

**What makes a good random sample? ›**

What makes a good sample? A good sample should be **a representative subset of the population we are interested in studying**, therefore, with each participant having equal chance of being randomly selected into the study.

**Why is simple random sampling the best? ›**

**Lack of Bias**

The use of simple random sampling removes all hints of bias—or at least it should. Because individuals who make up the subset of the larger group are chosen at random, each individual in the large population set has the same probability of being selected.

**What is systematic sampling and stratified sampling? ›**

Stratified sampling

**Based on the overall proportions of the population, you calculate how many people should be sampled from each subgroup.** Then you use random or systematic sampling to select a sample from each subgroup. Example: Stratified sampling The company has 800 female employees and 200 male employees.

**What is stratified or systematic sample? ›**

Stratified systematic sampling techniques are **generally used when the population is heterogeneous, or dissimilar, or where certain homogeneous, or similar, sub-populations can be isolated** (strata).

**What is the difference between stratified random and simple random? ›**

A simple random sample is used to represent the entire data population and randomly selects individuals from the population without any other consideration. A stratified random sample, on the other hand, first divides the population into smaller groups, or strata, based on shared characteristics.

**What are the three major differences between cluster sampling and stratified sampling? ›**

Factors for Comparison | Cluster Sampling | Stratified Sampling |
---|---|---|

Division type | Naturally formed | Depends on the researcher |

Heterogeneity | Internally, with the clusters | Externally, between various strata |

Homogeneity | Externally, between various clusters | Internally, with the strata |