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### Course: Statistics and probability>Unit 6

Lesson 3: Sampling methods

# Sampling methods review

## What are sampling methods?

In a statistical study, sampling methods refer to how we select members from the population to be in the study.
If a sample isn't randomly selected, it will probably be biased in some way and the data may not be representative of the population.
There are many ways to select a sample—some good and some bad.

### Bad ways to sample

Convenience sample: The researcher chooses a sample that is readily available in some non-random way.
Example—A researcher polls people as they walk by on the street.
Why it's probably biased: The location and time of day and other factors may produce a biased sample of people.
Voluntary response sample: The researcher puts out a request for members of a population to join the sample, and people decide whether or not to be in the sample.
Example—A TV show host asks his viewers to visit his website and respond to an online poll.
Why it's probably biased: People who take the time to respond tend to have similarly strong opinions compared to the rest of the population.
Practice problem 1
A restaurant leaves comment cards on all of its tables and encourages customers to participate in a brief survey to learn about their overall experience.
What type of sampling is this?

### Good ways to sample

Simple random sample: Every member and set of members has an equal chance of being included in the sample. Technology, random number generators, or some other sort of chance process is needed to get a simple random sample.
Example—A teacher puts students' names in a hat and chooses without looking to get a sample of students.
Why it's good: Random samples are usually fairly representative since they don't favor certain members.
Stratified random sample: The population is first split into groups. The overall sample consists of some members from every group. The members from each group are chosen randomly.
Example—A student council surveys $100$ students by getting random samples of $25$ freshmen, $25$ sophomores, $25$ juniors, and $25$ seniors.
Why it's good: A stratified sample guarantees that members from each group will be represented in the sample, so this sampling method is good when we want some members from every group.
Cluster random sample: The population is first split into groups. The overall sample consists of every member from some of the groups. The groups are selected at random.
Example—An airline company wants to survey its customers one day, so they randomly select $5$ flights that day and survey every passenger on those flights.
Why it's good: A cluster sample gets every member from some of the groups, so it's good when each group reflects the population as a whole.
Systematic random sample: Members of the population are put in some order. A starting point is selected at random, and every ${n}^{\text{th}}$ member is selected to be in the sample.
Example—A principal takes an alphabetized list of student names and picks a random starting point. Every ${20}^{\text{th}}$ student is selected to take a survey.
practice problem 1
Each student at a school has a student identification number. Counselors have a computer generate $50$ random identification numbers and those students are asked to take a survey.
What type of sampling is this?

## Want to join the conversation?

• hey, i was wondering, what type of sampling method does this sentence use? "a biologist surveys all students from each of 15 randomly selected classes."
• I'm pretty sure it's a cluster. Because it's all the students from the randomly selected classes, not x people from each class.
• Hi, I am a little confused on the difference between a cluster sample and a stratified random sample. Thanks!
• Hi Ishaq,
Cluster samples put the population into groups, and then selects the groups at random and asks EVERYONE in the selected groups.
A stratified random sample puts the population into groups (eg categories, like freshman, sophomore, junior, senior) and then only a few (people for example) are selected from each sample.
An example to clarify
Mia has a population of 50 pupils in her class. She wants to know whether most people like homework or not.
1. Cluster sampling- she puts 50 into random groups of 5 so we get 10 groups then randomly selects 5 of them and interviews everyone in those groups --> 25 people are asked
2. Stratified sampling- she puts 50 into categories: high achieving smart kids, decently achieving kids, mediumly achieving kids, lower poorer achieving kids and clueless class-skippers. She then asks 5 of each group at random and sends up asking 25.

In this case stratified sampling would be a good method to use in my point of view because it is representative of both studious pupils and poorer achieving ones. However, cluster sampling would also be good seeing that it is very random and could also be representative, but it may be more biased to one category of students (eg the smarter ones) than another.

Hopefully this helped!
• I have to design a study and I devide population into 3 age groups. I randomly ask people to answer the survey but only one of three groups are my target and I only take the data of the targeted group. So which sampling method is this case belong to?
• Whats it called when u ask everyone?
• census, but it is not a sample since you are asking everyone
• When taking a stratified random sample, do the strata need to be proportionate to that group's representation in the population?

For example if a school wants to do a stratified random sample of 100 students and it has 1000 students and 200 are freshmen, 400 are sophomores, 300 are juniors and 100 are seniors should the number selected for the study be 20-40-30-10 or should it be 25-25-25-25 for each of the grades?