# Sampling methods

### Sampling methods

#### Lessons

• Introduction
Importance of knowing the nature of the purpose and the population of your study

Sampling Methods
a) Simple Random:
• Each subject is chosen by chance and all subjects have equal likelihood of being chosen.
• All sub-groups have equal probability of being chosen.
b) Stratified:
• The population is divided into groups (called stratas) based off characteristics, and then random subjects are chosen from each strata.
c) Convenience:
• A non-random sample.
• Formed by subjects who are easy to reach (convenient to reach).
d) Cluster:
• The population is first divided into randomly chosen sub-groups (called clusters), then a random assortment of these clusters are chosen to be the sample.
e) Systematic:
• The population is first formed into an exhaustive list, and then every $k^{th}$ member is chosen to be part of the sample.

• 1.
Observations VS. Experiments
Determine if an observation or experiment should be used for the following situations.
i) A department store wants to know the most common route taken by its customers within the store.
ii) A researcher wants to find out if students will get a better grade if they chew on gums during an exam.
iii) A teacher wants to find out if children behave more aggressively towards each other the day after Halloween.
iv) A company wants to know if a lighter wall colour will improve the performance of its employees.
i) What are they?

• 2.
Two studies were done to find out if the time of a statistics class has an effect on the retention of class material in students. There are two classes: one in the morning and another one in the evening. In study A, 25 students were randomly assigned to the morning class while the other 25 were randomly assigned to the evening class. In study B, 25 students were randomly chosen from the morning class while the other 25 were randomly chosen from the evening class. Then, in both studies, all 50 students from both classes were given a test on the class material at the end of the class.

Which of the following statement(s) is/are true?

i) Both studies were observational studies.
ii) Both studies were experiments.
iii) Study B was an experiment because it had a control group.
iv) Study A was an experiment because it had a control group and a treatment group.

• 3.
Sampling Methods
Define.
i) simple random sampling
ii) stratified sampling
iii) cluster sampling
iv) systematic sampling
v) convenience sampling

• 4.
What kind of sampling technique was in each situation below (simple random, stratified, convenience, cluster, or systematic)?

i) 55 residents living in an apartment building were selected randomly and interviewed about their satisfaction towards the strata company.

ii)A study done by a university student council found that male students who major in Computer Science are 3 times more likely to have an experience staying overnight in the campus than other male students in other majors.

iii) The school board of City A wants to review the current Math curriculum. Therefore, 11 schools in the city were selected randomly and all Math teachers of these schools were asked to fill out a questionnaire on the subject matter.

iv) In a grocery store, every 70th receipt printed out from a cash register will ask the customers to do a survey on their shopping experience in exchange for a coupon.

v) Derek says, "ABC brand is the most popular cellphone brand in my school. I have asked the first 60 students who went to school today."

• 5.
Ivan is a Business student and he is doing a project on where college students usually shop online. He wants to have a simple random sample of 40 college students. Therefore, Ivan randomly interviewed 10 students from each year (first, second, third, and fourth year).

i) Did this sampling method allow Ivan to collect a random sample of 40 college students?