Topic 3a - Book sec 4.1 Sampling and Surveys

Chapter 4: Designing Studies

4.1 Samples and Surveys

Learning Objectives

• Identify the population and sample in a statistical study.

• Differentiate between sampling methods

  • Voluntary response samples

  • Convenience samples

• Explain bias due to sampling methods.

• Describe methods for obtaining a random sample using:

  • Slips of paper

  • Technology

  • Table of random digits

• Distinguish between types of random sampling:

  • Simple random sample (SRS)

  • Stratified random sample

  • Cluster sample

• Analyze sources of bias in sample surveys, such as:

  • Undercoverage

  • Nonresponse

  • Question wording

Population, Census, and Sample

• Population: The entire group we wish to study.

• Census: Data collection from every individual in the population.

• Sample: A subset of individuals from the population that we collect data from.

  • Use samples to make inferences about the population.

Example: Populations and Samples

1. Furniture Maker:

   • Population: All hardwood pieces in a batch.

   • Sample: Five pieces tested for moisture content.

2. Gallup Poll:

   • Population: All adult U.S. residents.

   • Sample: 1500 adults responding to survey questions.

The Idea of a Sample Survey

• Conclusions are often drawn for the entire population based on a selected sample.

• Key Steps:

  1. Define the population to describe.

  2. Specify what to measure.

  3. Decide how to choose a sample.

How to Sample Badly

• Convenience Sampling: Choosing individuals who are easy to reach, leading to potential bias.

  • Typically generates unrepresentative data due to systematic underrepresentation.

• Voluntary Response Sampling: Individuals self-select to participate through open invitation.

  • Often fails to represent the broader population due to strong opinions from respondents.

Types of Sampling Methods

Convenience Sample

• Definition: Researcher selects readily available participants non-randomly.

• Example: Polling people walking by on the street.

• Bias Explanation: Specific times and locations may lead to non-representative sampling.

Voluntary Response Sample

• Definition: Participants choose to join based on an invitation.

• Example: A TV host soliciting viewers to respond to a poll.

• Bias Explanation: Respondents often share similar strong opinions, skewing results.

Simple Random Sampling (SRS)

• Definition: A sample chosen by chance so each member has an equal chance of inclusion.

• Method: Random number generators or tables of random digits.

Choosing an SRS

1. Label: Assign unique numbers to individuals in the population.

2. Randomize: Use random selection methods to pick samples.

Stratified Random Sample

• Definition: Population divided into strata/groups; an SRS is taken from each stratum.

• Benefit: Ensures representation from all subgroups.

Cluster Sample

• Definition: Classify the population into clusters, then randomly choose entire clusters.

• Benefit: Efficient for large, dispersed populations.

Systematic Random Sample

• Definition: Individuals are ordered, a random starting point is chosen, and every nth member is selected.

• Example: Selecting every 20th student from an alphabetized list.

Inference for Sampling

• Purpose: To provide information about a larger population.

• Relying on random sampling helps avoid bias.

  • Sample results come with a margin of error.

  • Larger samples yield better estimates than smaller ones.

Sample Surveys: What Can Go Wrong?

• Common Errors:

  • Undercoverage: Certain population segments are excluded.

  • Nonresponse: Selected individuals cannot be contacted or choose not to respond.

  • Response Bias: Influences from question wording may skew responses.

Section Summary

• Key Learning Points:

  • Identification of populations and samples in studies.

  • Recognition of sampling methods leading to bias.

  • Methods for obtaining random samples and their types.

  • Understanding factors affecting survey bias.