Cogito
AP Statistics · Chapter 6 · Lesson 3
Errors and Power
The two ways a test can be wrong.
12 problems · about 21 minutes · UNC-5.A, UNC-5.C
What this lesson teaches
The student identifies Type I and Type II errors and describes what affects power.
- A Type I error is a false alarm; a Type II error is a missed effect.
- Alpha is the Type I error rate, and power is 1 minus the Type II rate.
- Larger samples, larger effects and larger alpha all raise power.
Warm Up
Straightforward practice. Get the method working first.
5 problemsThe Type II error rate is 0.25. What is the power?
Answer 0.75
Why 0.75.
Which change improves both error rates at once?
Answer A larger sample size.
Why Only more data improves both.
Failing to reject a false null. Which error? 1 Type I, 2 Type II.
Answer 2
Why A missed effect.
Alpha is 0.05. What is the Type I error rate?
Answer 0.05
Why They are the same.
Type II rate 0.3. What is the power?
Answer 0.7
Why 1 − 0.3.
Build It Up
The same ideas with more to keep track of.
3 problemsDoes a larger sample raise power? 1 yes, 0 no.
Answer 1
Why Less sampling variability.
Does lowering alpha raise power? 1 yes, 0 no.
Answer 0
Why It makes rejection harder.
Does a larger true effect raise power? 1 yes, 0 no.
Answer 1
Why Easier to detect.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsWhich changes increase power?
Answer A larger sample size; A larger true effect; A larger significance level
Why Variability works against detection.
Power 0.85. What is the Type II error rate?
Answer 0.15
Why 1 − 0.85.
The False Alarm: Rejecting a true null hypothesis. Which error? 1 Type I, 2 Type II.
Answer 1
Why Type I.
The Power: The Type II error rate is 0.2. What is the power?
Answer 0.8
Why 0.8.