Cal Poly Pomona

Random Samples

  • Selection of students from a class

    • Scenario: 33 students in the classroom.

    • Objective: Choose a random sample of 4 students.

    • Method: Use of random number generator from 1 to 33.

  • Random number generator precautions

    • Issue: Avoiding duplicates (e.g., student 11 appearing twice).

    • Solution: Use "random integer no repeats" function to ensure unique selections.

  • Spreadsheet approach

    • Process: Names assigned random numbers, ranked by size.

    • Example: Identifying top 4 (like Kevin, Rachel, Leonardo, Russell) based on random numbers.

Considerations in Sampling

  • Potential sampling bias

    • Concern: Small samples may not represent larger populations, e.g., all freshmen selected.

    • Implication: Could skew results based on the demographic representation.

Stratified Sampling

  • Definition

    • Concept: Population divided into strata (groups) based on a variable (e.g., grade level).

    • Application: Select members from each stratum randomly.

  • Example scenario

    • Setup: 14 freshmen and 19 non-freshmen in the class.

    • Selection method: Randomly choose 2 from each group to ensure balanced representation.

  • Further stratification potential

    • Greather granularity: Separate by class year (freshmen, sophomores, juniors, seniors) and select from each.

Cluster Sampling

  • Definition

    • Concept: Population is grouped into clusters; random clusters selected.

    • Application: All members from selected clusters comprise the sample.

  • Example scenario

    • Setup: Classes as clusters; select 4 classrooms and sample all students within them.

  • Advantages and disadvantages

    • Efficiency: Easier data collection from fewer clusters.

    • Risk: Potential for bias if clusters share similar demographics.

Systematic Sampling

  • Definition

    • Process: Choose the first individual randomly, then select every kth individual afterward.

    • Example: If k=8, after selecting an individual, every 8th student in line is included.

Convenience Sampling

  • Definition

    • Concept: Sample selected based on ease of access.

    • Examples:

      • First 100 students in the cafeteria.

      • Students in a specific teacher's classes.

  • Disadvantages

    • Bias: Likely unrepresentative of the population.

    • Implication: Results may be skewed due to demographic or situational factors.

Terminology

  • Parameter: A value that describes the entire population.

    • Example: Average enjoyment rating for the entire population.

  • Statistic: A value describing a sample.

    • Example: Average rating for the specific sample chosen.

Conclusion

  • Importance of selecting appropriate sampling methods to reduce bias and ensure representative samples for accurate results.

  • Homework and quizzes related to sampling methods and statistics upcoming.