Paired vs Independent Data Decision Guide
About This MicroSim
"Don't worry - every statistician drops an acorn sometimes when figuring this out!" Sylvia laughs. "The key question is simple: Is there a natural one-to-one matching between observations? If each observation in Group 1 has a specific partner in Group 2, you've got paired data!"
This MicroSim helps you master the decision between paired and independent samples t-procedures through: - An interactive flowchart with decision questions - A practice quiz with real-world scenarios - Immediate feedback with explanations
How to Use
Flowchart Mode: - Follow the decision diamonds from top to bottom - Answer each yes/no question about your data - Arrive at either "Paired" (green) or "Independent" (orange)
Practice Quiz Mode: - Read each scenario carefully - Click "Paired" or "Independent" to answer - Review the explanation after each question
Decision Criteria
| Question | If Yes... |
|---|---|
| Same individuals measured twice? | Paired |
| Deliberately matched pairs? | Paired |
| Natural one-to-one connection? | Paired |
| None of the above | Independent |
Lesson Plan
Learning Objective
Students will correctly identify whether a given scenario calls for paired or independent samples t-procedures by following a decision flowchart (Bloom's Taxonomy: Analyze L4).
Warm-Up Activity (5 minutes)
Ask students: "Why might we want to measure the SAME people before and after a treatment rather than comparing two different groups?" Lead into discussion of controlling for individual variability.
Guided Practice (10 minutes)
Work through the flowchart together with these examples: 1. Compare blood pressure before and after medication (same patients) 2. Compare blood pressure of patients taking Drug A vs. Drug B (different patients) 3. Compare test scores of twins raised together vs. raised apart
Independent Practice (10 minutes)
Have students complete the Practice Quiz individually, aiming for 8/8 correct.
Discussion Questions
- Why does pairing data often lead to more powerful tests?
- What's the danger of treating independent data as paired, or vice versa?
- Can you think of a scenario where you could design the study either way?
- In a twins study, are the observations within each pair independent?
Common Mistakes to Address
- Assuming any "before/after" comparison is paired (it depends on whether it's the SAME subjects)
- Forgetting that matched pairs based on characteristics count as paired
- Thinking that comparing two time periods automatically means paired
Sylvia's Insight
"Here's my secret: I always ask 'Can I subtract?' If I can naturally take the difference between observation 1 and observation 2 for each pair, that's paired data! Like before minus after for each person. If there's no natural pairing to subtract, it's independent."