Type I/II Error & Statistical Power
Interactive hypothesis testing visualizer. Adjust Effect Size, Sample Size, and Alpha to instantly see the tradeoff balance between Type I Error, Type II Error, and Statistical Power.
THE RISK OF INFERENCE
In hypothesis testing, we make decisions based on probability. Because we use samples, there is always a chance we reach the wrong conclusion. We categorize these mistakes as Type I and Type II errors.
DEFINING THE ERRORS
1. **Type I Error (\alpha)**: Rejecting the null hypothesis when it is actually true (a "false positive").\n2. **Type II Error (\beta)**: Failing to reject the null hypothesis when it is actually false (a "false negative").
AP EXAM CONNECTION
Unit: Unit 6: Inference for Proportions (Topic 6.5)
Learning Objective: UNC-3.B
COMMON MISCONCEPTIONS
- Thinking you can eliminate both errors simultaneously without increasing sample size.
KEY TAKEAWAYS
- Type I: False Positive.
- Type II: False Negative.
- Power = 1 - Beta.
PRACTICE QUESTIONS
Q1 (CONCEPTUAL): If you decrease the significance level (\alpha), what happens to the probability of a Type II error?
Show Answer & Explanation
Answer: It increases.
Explanation: There is an inverse relationship between and . Making it harder to reject the null (lower ) makes it more likely you will fail to reject it when you should have.
