Statistics Quiz 1.3: Sampling Design

Population Example

All students at La Cueva High School.

Sample Example

100 randomly selected La Cueva students.

Sampling Frame Example

A complete list of all La Cueva students used to select the sample.

Census Example

A school surveys every student instead of selecting a sample.

SRS Example

A school numbers all 2

SRS When to Use

Use when you have a complete list and want every possible sample of the same size to have an equal chance.

SRS Pro

Random selection helps reduce selection bias.

SRS Con

It may be difficult to get a complete list of a large population.

Stratified Example

A school separates students by grade and randomly selects 25 students from each grade.

Stratified When to Use

Use when you want every important subgroup represented.

Stratified Pro

Every subgroup is guaranteed to be represented.

Stratified Con

You need information about the population to create the strata.

Cluster Example

A district randomly selects 4 schools and surveys every student in those schools.

Cluster When to Use

Use when the population is naturally divided into groups and individuals are spread out.

Cluster Pro

It can be cheaper and easier to collect data.

Cluster Con

Selected clusters may not represent the entire population as well as an SRS.

Systematic Example

Randomly choose a starting student and then select every 20th student on the list.

Systematic When to Use

Use when you have an ordered list without a problematic repeating pattern.

Systematic Pro

It is simple and spreads the sample across the population.

Systematic Con

A repeating pattern in the list can create bias.

Multistage Example

Randomly select schools then randomly select classes within those schools then randomly select students within those classes.

Multistage When to Use

Use when the population is very large or spread across a large area.

Multistage Pro

It makes large-scale sampling more practical.

Multistage Con

It is more complicated and can increase sampling variability.

Convenience Example

A student surveys the 30 people sitting closest to them in the cafeteria.

Convenience Bias

The people easiest to reach may be different from the rest of the population.

Convenience Pro

It is quick and easy.

Convenience Con

It can produce a biased sample.

Voluntary Response Example

A school posts an online poll and asks students to choose whether to participate.

Voluntary Response Bias

Students with strong opinions may be more likely to participate.

Voluntary Response Pro

It is easy and inexpensive to collect responses.

Voluntary Response Con

The people who respond may not represent the population.

Undercoverage Example

A school surveys students using a list that does not include transfer students.

Undercoverage Bias

Some members of the population have no chance or a smaller chance of being selected.

How to Recognize Undercoverage

Ask whether an entire group of the population was left out of the sampling frame.

Nonresponse Example

A researcher randomly selects 500 people but 200 do not return the survey.

Nonresponse Bias

People who were selected do not respond and may differ from those who do respond.

How to Recognize Nonresponse

The person was selected but did not provide a response.

Response Bias Example

A survey asks "Don't you agree that our school has terrible lunches?" and students are influenced by the wording.

Response Bias

People give inaccurate answers because of question wording the interviewer or the situation.

How to Recognize Response Bias

The person responds but their answer may not be truthful or accurate.

Sampling Bias Example

A researcher surveys only students in the library to estimate the opinions of all students.

Sampling Bias

The method consistently produces a sample that does not represent the population.

Sampling Frame Bias Example

A survey of all city residents uses a phone list that excludes people without phones.

Sampling Frame Problem

The list used to select the sample does not properly represent the population.

Undercoverage vs Nonresponse Example

If students without school email cannot be selected it is undercoverage; if selected students ignore the survey it is nonresponse.

Voluntary Response vs Convenience Example

If students choose whether to answer an online poll it is voluntary response; if a researcher asks the nearest students it is convenience.

Response vs Nonresponse Example

If someone answers a question dishonestly it is response bias; if they never answer the survey it is nonresponse.