Sampling: Simple Random, Convenience, systematic, cluster, stratified - Statistics Help

Summary

This script introduces five common sampling methods for population studies: simple random sampling, convenience sampling, systematic sampling, cluster sampling, and stratified sampling. It emphasizes the importance of unbiased and representative samples, acknowledges the inevitability of sampling error, and discusses the practicality and potential biases of each method. The goal is to choose a sampling method that balances accuracy with available resources, and to account for any known bias in analysis.

Takeaways

• 📌 A sample is a subset of a population selected for study, aiming to represent the whole group's characteristics.
• 🔍 The ideal sample should be unbiased, meaning every member of the population has an equal chance of being selected.
• 🍏 In practical scenarios, such as measuring the size of apples in an orchard, it's not feasible to measure every single apple, hence sampling is necessary.
• 💰 The choice of sampling method depends on the nature of the population and the available resources like time and money.
• 🔄 There will always be some sampling error due to the fact that only a part of the population is being studied.
• 🎯 Simple random sampling is the theoretical ideal, providing an unbiased sample, but it can be impractical and costly, especially with human populations.
• 🏢 Convenience sampling is quick and easy but often biased, and may suffer from self-selection bias when participants have a vested interest.
• 🌐 Systematic sampling involves selecting members at regular intervals, which is easier to administer but can be affected by patterns in the population.
• 📚 Cluster sampling involves dividing the population into groups and randomly selecting groups for the sample, which can be practical but may introduce bias if groups differ significantly.
• 📊 Stratified sampling divides the population into subgroups with specific characteristics and takes random samples from each, potentially providing a highly representative sample but requires detailed information about the population.
• 🛠️ Different sampling methods have their advantages and disadvantages, and the choice should be based on the best result achievable with the available resources.
• ⚖️ If a sample is known to have bias, this should be considered during analysis and reporting to ensure accurate representation.

Q & A

What is the primary purpose of taking a sample from a population?

The primary purpose of taking a sample is to gather information about a population of interest when it is impractical or impossible to measure or observe the entire population.

Why is it important for a sample to be unbiased?

An unbiased sample is important because it ensures that every object in the population has an equal chance of being selected, which helps in obtaining a representative sample and reducing sampling error.

What is a sampling frame and why is it necessary for simple random sampling?

A sampling frame is a complete list of all the individuals or objects within the population of interest. It is necessary for simple random sampling to ensure that every member of the population has an equal chance of being selected.

What are the potential issues with convenience sampling?

Convenience sampling can be biased because it selects individuals or objects based on their availability or accessibility rather than randomly, which may not accurately represent the entire population.

How does systematic sampling differ from simple random sampling?

Systematic sampling involves selecting a starting point randomly and then choosing every nth object in a list or sequence, making it easier to administer than simple random sampling but potentially susceptible to bias if there is a pattern in the population.

What is cluster sampling and how does it work?

Cluster sampling involves dividing the population into clusters and then randomly selecting some of these clusters. All members within the chosen clusters are included in the sample, which can be more practical than simple random sampling but may lead to bias if clusters are not representative of the population.

How does stratified sampling aim to improve the representativeness of a sample?

Stratified sampling divides the population into subgroups or strata based on specific characteristics and then takes a random sample from each stratum. This method can produce a very good representative sample by ensuring that each subgroup is proportionally represented.

What is the potential drawback of stratified sampling compared to other methods?

Stratified sampling can be complex to administer and requires a sampling frame with detailed information about the population. It may also be challenging to define the strata in a way that accurately represents the population.

Why is it inevitable to have some sampling error when taking a sample?

Sampling error is inevitable because a sample only includes a part of the population. Even with the best sampling methods, there will always be some variation between the sample and the entire population.

How should known bias in a sample be addressed in the analysis and reporting of results?

Known bias in a sample should be acknowledged and taken into account during the analysis and reporting process. This may involve adjusting the results or interpreting them with caution to reflect the potential impact of the bias.

What should be considered when choosing a sampling method for a study?

When choosing a sampling method, one should consider the nature of the population, the resources available in terms of time and money, the need for representativeness, and the potential for bias. The goal is to select a method that provides the best results given the available resources.

Outlines

00:00

📝 Understanding Sampling Techniques

This paragraph introduces the concept of sampling as a method to gather information about a population. It emphasizes the importance of selecting a sample that is both unbiased and representative. The text explains that while it's impossible to measure every individual in a population, a well-chosen sample can provide a good approximation. It also acknowledges the inherent sampling error and introduces five common sampling methods: simple random sampling, convenience sampling, systematic sampling, cluster sampling, and stratified sampling. Each method is briefly described, highlighting the process, advantages, and potential disadvantages.

Keywords

💡Sample

A 'sample' is a subset of a larger population that is taken to represent the whole for the purpose of study or analysis. In the video's context, it refers to selecting a portion of objects, such as apples in an orchard, to infer characteristics about the entire population. The script discusses the importance of the sample being representative and unbiased to ensure accurate conclusions.

💡Population

The 'population' is the entire group of individuals or items that are the subject of a study. In the script, the population could be all the apples in an orchard at a specific time. The goal is to make inferences about this population based on the sample taken from it.

💡Unbiased Sample

An 'unbiased sample' is one where every member of the population has an equal chance of being selected. The video emphasizes that the ideal sample is unbiased, meaning it is not influenced by any preconceived notions or selection biases, which helps in achieving a representative sample.

💡Representative

A 'representative' sample accurately mirrors the characteristics of the entire population it was drawn from. The script mentions that if the apple population is two-thirds red and one-third green, the sample should reflect this ratio to be considered representative.

💡Sampling Error

'Sampling error' refers to the variation that occurs because a sample is only a part of the whole population. The video script acknowledges that no matter the method, sampling error is inevitable, and it's important to understand this when interpreting results.

💡Simple Random Sampling

This method involves selecting members of the population using random numbers, ensuring each object has an equal chance of being chosen. The script describes it as the ideal method for creating an unbiased and representative sample, but notes its practical challenges, especially with large or dispersed populations.

💡Convenience Sampling

'Convenience sampling' is a non-probability method where subjects are chosen based on their availability or accessibility. The script points out that this method can be biased but is often used for quick and inexpensive surveys, such as asking people nearby or taking items off a production line.

💡Systematic Sampling

In 'systematic sampling', a starting point is chosen randomly, and then every k-th element is selected from the population. The script explains that while this method is easier to administer than simple random sampling, it can be affected by patterns in the data, potentially leading to biased results.

💡Cluster Sampling

'Cluster sampling' involves dividing the population into groups or clusters and then randomly selecting some of these clusters for the sample. The script mentions that within each chosen cluster, all members are included in the sample, making it more convenient than simple random sampling but potentially leading to bias if clusters differ significantly.

💡Stratified Sampling

Stratified sampling involves dividing the population into subgroups, or strata, that share similar characteristics and then taking a random sample from each stratum. The script notes that this method can produce a very good representative sample but requires a complex administration and detailed information about the population.

💡Sampling Frame

A 'sampling frame' is a list or other mechanism that includes all the members of the population from which a sample will be drawn. The script explains that having a good sampling frame is crucial for simple random sampling, especially when dealing with natural or manufacturing populations.

💡Bias

'Bias' in the context of sampling refers to systematic errors introduced by the sampling process that cause the sample to be unrepresentative of the population. The script discusses various types of bias, such as self-selection bias in convenience sampling, and the potential for bias in cluster and stratified sampling if not properly implemented.

Highlights

A sample is a selection of objects and observations taken from a population of interest, like measuring a sample of apples in an orchard to estimate their size.

The ideal sample is unbiased, with each object in the population equally likely to be chosen, and representative of the population characteristics.

Sampling methods depend on the nature of the population and available resources like time and money.

Simple random sampling is theoretically ideal but can be difficult and expensive, especially with human populations.

A sampling frame is a list of all people or objects in the population, useful for implementing simple random sampling.

Convenience sampling is quick and easy but often biased, using nearby people or objects as the sample.

Systematic sampling involves choosing a random starting point and taking objects at regular intervals, which is easier to administer than simple random sampling.

Systematic sampling can be affected by patterns in the population, leading to biased selection if not carefully designed.

Cluster sampling divides the population into clusters, which are then randomly selected, with all objects in each cluster included in the sample.

Cluster sampling can be more convenient and practical than simple random sampling but may lead to bias if clusters differ significantly.

Stratified sampling involves dividing the population into strata representing different characteristics, taking random samples from each to ensure representation.

Stratified sampling can produce a very good representative sample but requires a complex administration and detailed sampling frame.

Sampling error or variation is always present since only a part of the population is examined, not the whole.

The video on variation covers sampling concepts more thoroughly, providing a deeper understanding of sampling errors.

Five sampling methods are presented in the video, each with its own process, advantages, and disadvantages.

When choosing a sampling method, consider the best result achievable with the available resources, including time, money, and information about the population.

If a sample has known bias, it should be accounted for in analysis and reporting to ensure accurate results.

Transcripts

To find things out about a population of interest,

it is common practice to take a sample. A sample is a selection of objects and observations

taken from the population of interest. For example,

a population might be all apples in an orchard at a given time.

We wish to know how big the apples are. We can't measure all of them,

so we take a sample of some of them and measure them.

The method chosen for taking the sample depends on the nature of the population,

and the resources available in terms of time and money.

The ideal is for each object in a population to be equally likely to be

chosen as part of the sample.

This is called an unbiased sample. It is also desirable for the sample to be

representative of the population.

if the population of apples were two thirds red and one-third green,

the sample should be similarly split. Note that no matter what we do, there will

always be sampling error

or variation due to sampling, as we are looking at a part of the population,

not the whole population. The video on variation covers these concepts more thoroughly.

This video presents five methods of sampling:

For each method we will outline the process

and the advantages and disadvantages.

Simple random sampling is theoretically the ideal method of Sampling.

You list each member the population and use random numbers to decide which

objects are in the sample. Each object is equally likely to be selected.

This produces an unbiased sample which we hope is representative.

However it can be difficult and expensive

to take a simple random sample when dealing with people. Simple random

sampling is more practical when the population is geographically concentrated

and when a good sampling frame exists. A sampling frame is a list of all the people or objects

in the population interest. Simple random sampling can be more easily implemented

for natural and manufacturing populations.

Convenience sampling is just that: Convenient!

You ask people nearby, or people who walk past at a shopping mall,

or you take the next 20 objects off the production line.

You do what is easy or convenient. Convenience samples are often biased in some way.

But, for a quick and cheap poll it may not really matter.

Convenience samples can also have self-selection bias when people choose

to participate, because they have an interest in the issue in question.

With systematic sampling you choose a starting point at random,

and then systematically take objects at a certain number apart.

For example, if there are a thousand in the population

and you want a sample of fifty, you would take every twentieth object.

Systematic samples are easier to administer than simple random samples

and are usually a good approximation of a random sample.

However, if there's a pattern in the population,

certain types of objects could be chosen more or less often than others.

Cluster sampling the population is divided into clusters

which are then chosen at random.

For example, departments of a business can be clusters,

or suburbs within a city. Within each cluster,

all of the objects are included in the sample. Cluster sampling can be more

convenient and practical

than simple random sampling. However, if the clusters are different from each other

with regard to the elements we are measuring,

it can lead to bias or non-representativeness.

Stratified sampling seems like cluster sampling,

but the strata, or groups, are chosen specifically to represent different

characteristics within the population,

such as ethnicity, location, age

or occupation. Within each group,

a random sample is taken, sometimes in proportion to the size of the group.

Stratified sampling can lead to a very good random representative sample.

However it can be complex to administer, and a sampling frame with considerable

information about the population is required.

There are other sampling methods. The five explained here give an idea of the advantages

and disadvantages of various methods.

You should attempt to use a sampling method that produces the best result

for the resources you have available.

If your sample has known bias, this should be taken into account

in analysis and reporting.