MathIsimple
Lesson 5.4: Sampling & Bias in Data

Master Sampling & Bias in Data

Learn to collect reliable data! Understand different sampling methods, recognize bias in data collection, and evaluate the quality and reliability of your data sources.

Learning Objectives

Understand different sampling methods
Recognize various types of bias
Evaluate data reliability and validity
Design unbiased data collection methods

Sampling Methods

Random Sampling

• Every member has equal chance of selection

• Most reliable method

• Reduces bias

• Example: Drawing names from a hat

Stratified Sampling

• Population divided into groups (strata)

• Random sample from each group

• Ensures representation of all groups

• Example: Sampling by grade level

Systematic Sampling

• Select every nth member

• Regular interval pattern

• Easy to implement

• Example: Every 10th person in line

Convenience Sampling

• Select easily accessible members

• Quick and inexpensive

• Often biased

• Example: Surveying friends

Types of Bias

Common Types of Bias

Selection Bias: Sample doesn't represent population

Response Bias: People give inaccurate answers

Volunteer Bias: Only certain types of people participate

Question Bias: Questions lead to specific answers

Example 1: Selection Bias

Scenario: A school wants to know students' opinions about homework. They survey only students in the library during lunch.

Problem: Selection Bias

  • • Students in library may be more academically focused
  • • They might have different opinions about homework
  • • Sample doesn't represent all students

Better Method:

Randomly select students from all grade levels and classes to get a representative sample.

Example 2: Response Bias

Scenario: A survey asks: "Don't you think our school needs better sports facilities?" (Yes/No question)

Problem: Question Bias

  • • Question assumes school needs better facilities
  • • "Don't you think" suggests the "correct" answer
  • • Leads respondents toward "Yes"

Better Question:

"How would you rate our school's sports facilities?" (Excellent/Good/Fair/Poor)

Data Reliability & Validity

Reliability

• Consistency of results

• Same results when repeated

• Free from random errors

• Example: Scale gives same weight

Validity

• Measures what it claims to measure

• Accuracy of results

• Free from systematic errors

• Example: Scale measures actual weight

Example 3: Evaluating Data Quality

Scenario: A study claims that 80% of teenagers prefer online learning. The survey was conducted on social media with 100 responses.

Reliability Issues:

  • • Small sample size (100 responses)
  • • Social media users may not represent all teenagers
  • • Results might vary if repeated

Validity Issues:

  • • Convenience sampling (social media users)
  • • Self-selection bias (only interested people respond)
  • • May not measure true preference

Conclusion:

The data has both reliability and validity issues. Results should be interpreted with caution.

Survey Design Best Practices

Good Survey Practices

• Use random sampling

• Ask neutral questions

• Include all response options

• Keep questions simple and clear

• Ensure anonymity

Avoid These Mistakes

• Leading questions

• Double-barreled questions

• Missing response options

• Complex or confusing language

• Small, biased samples

Example 4: Improving a Survey

Original Question: "Don't you agree that our cafeteria food is terrible and needs improvement?"

Problems:

  • • Leading question ("Don't you agree")
  • • Assumes food is "terrible"
  • • Double-barreled (terrible AND needs improvement)
  • • Only Yes/No options

Improved Question:

"How would you rate the quality of our cafeteria food?"

Options: Excellent / Good / Fair / Poor / Very Poor

Real-World Case Study

Case Study: School Uniform Survey

Scenario: A school board wants to know if students support wearing uniforms. They survey 50 students who are waiting in the principal's office.

Survey Results: 70% support uniforms

Bias Analysis:

  • Selection Bias: Students in principal's office may be different from general population
  • Volunteer Bias: Only students willing to wait participated
  • Small Sample: 50 students may not represent entire school
  • Location Bias: Principal's office may influence responses

Better Approach:

  • • Randomly select students from all grade levels
  • • Use anonymous survey method
  • • Increase sample size to at least 200 students
  • • Conduct survey in neutral location

Common Mistakes to Avoid

❌ Mistake 1: Using convenience sampling for important decisions

Convenience sampling is quick but often biased. Use random sampling for reliable results.

❌ Mistake 2: Ignoring non-response bias

People who don't respond may have different opinions than those who do respond.

❌ Mistake 3: Confusing correlation with causation

Just because two things are related doesn't mean one causes the other.

Practice Problems

Problem 1:

A survey asks: "How much do you love our amazing new cafeteria food?" What type of bias is this?

Show Solution

This is question bias. The word "amazing" leads respondents to give positive responses.

Problem 2:

A school surveys only honor roll students about study habits. What type of bias is this?

Show Solution

This is selection bias. Honor roll students may have different study habits than the general student population.

Problem 3:

Which sampling method is most likely to produce unbiased results?

Show Solution

Random sampling is most likely to produce unbiased results because every member has an equal chance of being selected.