STATS Mod6-7

Overview

• Importance of selecting BART riders for research.

• Challenges of sampling from a small group.

• Need for a broad sampling frame to understand all students taking statistics in California.

Sampling Considerations

• The necessity of including high school and middle school students who take statistics.

• Wide Sampling Frame: To obtain comprehensive conclusions about stats students in California.

Sampling Methods

Systematic Sampling

• Definition: Selecting every nth person from a list or out of a building.

• Example: Choosing every fifth person from a list of riders at a BART station.

• Concerns: Possible bias if names repeat (e.g., identical surnames).

Simple Random Sampling

• Ensures everyone has an equal chance of participating.

• Techniques to achieve randomness:

  • Flipping a coin.

  • Using a random number generator.

  • Drawing names from a hat.

Nonresponse Issues

• Definition: Not everyone who is invited to participate will respond.

• Strategies to mitigate nonresponse:

  • Sending follow-up reminders (e.g., promotional messages).

  • Offering incentives like raffles or gift cards to encourage participation.

Well-Posed Research Questions

• Characteristics of a well-defined research question:

  1. Information about the population.

  2. The variable of interest.

  3. A population value to calculate or compare.

• Examples:

  • Categorical Variable: "What percent of CCSF students have blue eyes?"

  • Quantitative Variable: "What is the average height of CCSF students?"

Data Compilation and Calculation

• For quantitative data:

  • Calculate averages through a two-step process: Add all values, then divide by the number of entries.

• Population value informs what to calculate: averages for quantitative data, proportions for categorical data.

Probability Sampling Plans

• Need for randomness in sampling to ensure valid results:

  • Cluster Sampling: Selecting groups and advocating to gather data from all members in those groups.

  • Example: Assessing high school seniors in SF by randomly selecting schools and sampling their seniors.

Multistage Sampling

• Utilized for larger projects with multiple rounds of sampling.

• Example: Assessing all U.S. doctors by randomly choosing states and subsequently choosing doctors from those states.

The Census

• Definition: A comprehensive data collection effort targeting the entire population.

• Frequency: Conducted every ten years in the U.S.

• Challenges: Costly and resource-intensive, often involve follow-ups for nonresponses (e.g., door-to-door inquiries).

Conclusion

• Importance of sampling size and methodology in research.

• Considerations for future researchers on how to design replicable studies.