Day 9: Populations vs Sample

From Theory to Practice: Making Sense of Survey Data

January 12, 2025

Population vs Sample: The Fundamentals

What is a Population?

Complete set of all subjects/items of interest
Example: All students in a university (50,000 students)
Often too large or impractical to study entirely
Contains all possible observations of interest

What is a Sample?

Subset selected from the population
Example: 500 randomly selected university students
Must be representative of the population
Used to make inferences about the population

Aspect	Population	Sample
Size	Complete set (N)	Subset (n)
Time to Study	Longer	Shorter
Cost	Higher	Lower
Accuracy	Perfect	Has margin of error

2. Understanding Sample Size

Mathematical Foundation

Margin of Error = 1/√n × 100

Why Sample Size Matters:

Affects confidence level in results
Determines margin of error
Impacts study cost and duration
Influences statistical power

Real-World Applications

1. Movie Theater Case Study

Detailed Population vs Sample Breakdown:

Population: All moviegoers (100,000 viewers)
- Multiple theaters
- Different show times
- Various demographics
Sample: Selected viewers (500 people)
- Random selection
- Different days/times
- Representative demographics

2. Sample Size Impact

Sample Size	Margin of Error	Confidence Level
100 people	10%	Lower confidence
400 people	5%	Moderate confidence
1,000 people	3%	Higher confidence

3. Movie Rating Example in Detail

Initial Rating: 4/5 stars
- Based on 500 reviews
- Margin of Error: ±4.5%
- True Rating Range: 3.5 to 4.5 stars
- 95% confidence level

Practical Guidelines for Sampling

Essential Considerations:

Population Characteristics
- Size of total population
- Demographic distribution
- Geographic spread
Sample Selection Method
- Random sampling
- Stratified sampling
- Cluster sampling
Quality Control
- Bias prevention
- Representative sample
- Proper documentation

Common Sampling Mistakes to Avoid

Selection Bias: Only sampling convenient or easily accessible subjects
Undercoverage: Missing important segments of the population
Voluntary Response Bias: Only including self-selected participants
Non-response Bias: Not accounting for those who decline to participate

Final Key Takeaways

Balance sample size with practical constraints
Focus on sample quality and representativeness
Consider both margin of error and confidence level
Document sampling methodology thoroughly
Account for potential biases in your analysis