Type I and Type II Error Visualizer
About This MicroSim
"Acorn for your thoughts on this?" Sylvia asks. "In my acorn quality testing, a Type I error means I reject perfectly good acorns thinking they're bad. A Type II error means I keep bad acorns thinking they're good. Both are problems, but depending on the situation, one might be worse than the other!"
Explore how Type I and Type II errors occur in hypothesis testing through simulation.
How to Use
- Toggle H0 is TRUE or H0 is FALSE to set reality
- When H0 is false, adjust the true proportion slider
- Click Draw Sample to run one hypothesis test
- Click Run 100 Samples to see error rates accumulate
- Adjust sample size (n) and significance level (alpha) to see effects
Key Concepts
| Error Type | What Happened | Probability |
|---|---|---|
| Type I | Rejected H0 when H0 was actually TRUE | alpha |
| Type II | Failed to reject H0 when H0 was actually FALSE | beta |
| Correct | Decision matched reality | varies |
The Four Possible Outcomes
| H0 is True | H0 is False | |
|---|---|---|
| Reject H0 | Type I Error | Correct! |
| Fail to Reject H0 | Correct! | Type II Error |
Lesson Plan
Learning Objective
Students will distinguish between Type I and Type II errors by exploring scenarios where the null hypothesis is either true or false, observing how different sample outcomes lead to correct decisions or errors (Bloom's Taxonomy: Analyze).
Warmup Activity (5 minutes)
Before using the MicroSim, have students describe in their own words: - What is a "false positive" in a medical test context? - What is a "false negative" in a spam filter context?
Guided Exploration (15 minutes)
Part 1: Type I Errors 1. Set H0 to TRUE 2. Run 100 samples and observe the Type I error rate 3. Compare this rate to alpha. What do you notice? 4. Change alpha from 0.05 to 0.10. How does the Type I error rate change?
Part 2: Type II Errors 1. Set H0 to FALSE with true p = 0.55 2. Run 100 samples and observe the Type II error rate 3. Change true p to 0.70. How does the Type II error rate change? 4. Increase sample size. What happens to Type II errors?
Discussion Questions
- Why does the Type I error rate approximately equal alpha when H0 is true?
- Why is there no fixed "beta" value - why does it depend on the true parameter?
- What is the only way to reduce BOTH error types simultaneously?
- In what situations would you prefer a lower alpha (like 0.01)?
Real-World Examples
| Scenario | Type I Error | Type II Error | Which is worse? |
|---|---|---|---|
| Drug trial | Approve useless drug | Reject effective drug | Depends! |
| Fire alarm | Alarm with no fire | No alarm during fire | Type II |
| Court trial | Convict innocent | Acquit guilty | Type I |