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## Statistics and probability

### 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.

### 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 teachers 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, start superscript, start text, t, h, end text, end superscript 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, start superscript, start text, t, h, end text, end superscript student is selected to take a survey.

## 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."(0 votes)
- 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.(43 votes)

- 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?(3 votes)
- Hi, I am a little confused on the difference between a cluster sample and a stratified random sample. Thanks!(3 votes)
- 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!*(3 votes)

- What kind of sampling would this be? "You need a sample of 50 students so you select the first 10 students available for surveying in each of 5 math classes." I am thinking either stratified random sampling or quota (which you don't mention here). Thanks!(1 vote)
- late response, but it sounds like a convenience sample if you're just taking the 10 most available(5 votes)

- Can someone help me?

Dish network sends a survey with their bill this month. They ask customers to return the survey with their payment. What type of sampling method is this?

I couldn't match this with any from the article, because it's not random.(2 votes)- If they send it to every customer, voluntary response because customers choose to be part of the sample. This sample is biased.(2 votes)

- I am looking for a video in terms of calculating the appropriate sample size for an experiment. Do you have a relevant video on this topic?(5 votes)
- Whats it called when u ask everyone?(2 votes)
- census, but it is not a sample since you are asking everyone(2 votes)

- hey, can I make use of convenience sampling and block design at the same time? So, I would randomly ask 150 students from one university to participate and then put half the males in the experimental group and half in the control group (same with the females)?(2 votes)
- An average of many different studies of handedness indicate that in a random sample of adults,14 percent of men are left-handed and 8 percent of women are left-handed. (Assume the rest are right-handed.) Suppose you have a sample of 350 women and 300 men, in which the numbers of left-handed and right-handed people reflect the average percentages. Make a two-way table that shows the distribution you would find.(2 votes)
- The data I'm using is coming from a group of student's "how many times they washed their hands"

3,7,10,10,10,5,2,35,12,7(2 votes)- Washing 35 times! Are you sure?

And what would you like to use this data with?(1 vote)