Sample Surveys - Chapter 12

Introduction to Sample Surveys

• Objective: Stretch beyond the data at hand to draw conclusions applicable to a larger population.
• Importance in business decisions, scientific research, investments, and understanding voter behavior.

Three Big Ideas in Surveys

1. Examine a Part of the Whole

• Population: The whole set of individuals we're interested in.
• Sample: A subset of the population used to make inferences about the whole.
• Statistics vs. Parameters:
  • Sample statistics (e.g., X̄ for average, p̂ for proportion).
  • Population parameters (e.g., μ for average, P for proportion).
• Key Measures:
  • Averages (means)
  • Proportions
• Sample Representation: A well-selected sample can accurately reflect the population.

2. Randomization

• Purpose: Protects against biases by ensuring every individual has an equal chance of being selected.
• Importance: Allows for statistical inferences about the population.

3. Sample Size is Key

• Misconception: The fraction of the population sampled is not as important as the actual sample size.
• Ideal Sample Size: Around 1,000 for reliable inferences, regardless of population size.

Avoiding Bias in Samples

Types of Bias

• Selection Bias: Inaccuracies due to poor sample selection.

  • Convenience Bias: Selecting individuals based on ease.
  • Volunteer Bias: Only those with strong opinions volunteer.
  • Non-response Bias: When selected individuals do not respond.

• Response Bias: Bias caused by the method of asking questions.

  • Influences responses by wording or who asks.
  • Social Desirability: Altering answers to appear socially acceptable.

• Measurement Bias: Issues with the tools or methods used to collect data.

Sampling Methods

Census

• Survey of every individual in the population.
• Suitable for small populations.

Simple Random Sample (SRS)

• Every possible sample of size n has an equal chance of being selected.
• Use of random number tables or calculators.

Stratified Random Sample

• Divides population into homogeneous groups before sampling.
• Random selection from each group (e.g., gender, race).

Cluster Sample

• Population divided into heterogeneous groups.
• Entire clusters are randomly selected as the sample.

Systematic Sample

• Selecting every kth individual from a list.
• Caution: Ensure list accurately represents the population.

Additional Topics

Multi-stage Sampling

• Combination of different sampling techniques.

Convenience and Volunteer Samples

• Generally poor methods due to potential biases.

Sampling Error

• Definition: Natural variation between samples.
• Clarification: Not an error, but expected variation in results from different samples.

• Conclusion: Understanding and implementing proper sampling techniques is crucial for accurate data representation.
• Next Steps: Engage in problems and exercises to practice creating effective samples.