A sample is a small number of individuals representing a larger group.

Sampling

Whether a researcher is drawing a sample or is studying an entire population, the population needs to be defined. This helps focus the research.

Example: If I want to know what type of candy 7th grade students prefer, then my population is defined as the set of all 7th grade students.

Defining the population

• A census is a survey which measures an entire population.

Example: The United States conducts a census of the American population every ten years.

• A census is very tedious and takes a long time to complete. Therefore, we use samples of a population to make inferences about that population.

• Inference: Inferences are made when you use clues from samples to make generalizations about a population.

Census

A sample in a research study is a relatively small number of individuals about whom information is obtained. The larger group to whom the information is then generalized is the population.

Samples and Populations

PopulationSample

Although the best data comes from studying an entire population, samples are used because they are smaller and less clumsy to work with. It can be too time consuming and expensive to study an entire population.

Why use samples?

Random sampling is completely based on chance. Example: one might identify all members of a population, (n=250) write their names on separate pieces of paper, and then draw 25 names out of a hat to determine who is actually to be included in the study.In a nonrandom sample, members are selected on the basis of a particular set of characteristics, rather than a random chance of being included.Example: The first 30 students with red hair are surveyed to determine if students like math.

Random vs. nonrandom sampling

In a simple random sample, each and every member of a population has an equal and independent chance of being selected. Example: Put every student’s name on a piece of paper, then draw one of the names from the group.

Simple random sample

Other Random Sample Selection MethodsStratified random sampling from sub-groups in the population Example: to have a random sample of 100 people evenly divided by gender, you would divide population into male and female groups and randomly select 50 from each group. Proportional sampling to insure maintenance of sub-group proportionsExample: divide the population of DoGood Middle School into male and female groups. If there are 3 girls to every boy, in order to have a random sample of 100 people balanced on gender we need to randomly select 75 girls and 25 boys. Systematic sampling - drawing every kth person.Example: to get a random sample of voters you select every 10th person from the Voter Registration Roles at the courthouse.

When it isn’t possible to draw a random or systematic nonrandom sample, a researcher might choose to study the individuals who are available. This is known as a convenience sample.

Example: If you wanted to know which movie most people want to see, you mi9ht just ask your friends because they are available. However, this is not representative of the entire population of Georgia.

Convenience sample

• It is important to get a representative sample of the population in order to provide the most accurate portrayal of the population being studied.

• Representing sub-groups proportionally is one way to insure a representative sample

• Generally, the larger the sample, the more representative of a population.

Representative samples

Using a ____________ sample increases the chances of collecting a representative sample.

A.) Biased

B.) Convenience

C.) Random

D.) Narrow

Melissa is collecting data to determine the most popular type of car driven by people at her company. Which of the following is an example of a random sample?

A.) Melissa surveys all of the managers at her company.

B.) Melissa uses a computer to randomly choose 20 people from a database that includes every person at her company. She then surveys those 20 people.

C.) Melissa surveys the first 20 people who walk in the door in the morning.

D.) None of these are random.

A sample where the easiest method is used to collect data is known as a ___________ sample.

A.) random

B.) convenience

C.) biased

D.) representative

Your teacher is conducting a survey to determine the average age of students in your class. Which of the following would most likely not result in a representative sample?

A.) Your teacher writes everyone's name down on a piece of paper and draws 10 names from a hat to survey

B.) Your teacher chooses only students wearing a red or blue shirt to survey.

C.) Neither of these would result in a representative sample

D.) Both of these would result in a representative sample