Type I Error, Type II Error, and Power
A free Statistics and Data Analysis lesson from the “Inference and Conclusions” unit, with a worked example and practice problems including step-by-step solutions.
Hypothesis tests can make two kinds of errors. Type I error rejects a true null hypothesis. Type II error fails to reject a false null hypothesis. Power is the chance of detecting a real effect. This lesson builds the habit of reading the context first, choosing the right statistical tool, calculating carefully, and then writing what the result means. By the end, students should be able to do the computation and explain why that computation answers the question.
What you'll learn
- Identify Type I and Type II errors
- Connect significance level to Type I error risk
- Explain power as the chance of detecting a real effect
Worked example
Problem. A test rejects a medicine's 'no effect' null hypothesis even though the medicine truly has no effect. What kind of error is this?
- Worked Example: First identify exactly what the question is asking: A test rejects a medicine's 'no effect' null hypothesis even though the medicine truly has no effect. What kind of error is this?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Type I error rejects a true null hypothesis.
- This is a false alarm.
Answer: Type I error
Practice problems
1. Practice case A: A false alarm in a hypothesis test is:
Choices: Type I error · Type II error · power · confidence level
Show solution
- Warm-up: First identify exactly what the question is asking: A false alarm in a hypothesis test is:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Type I error is a false alarm.
- It rejects a null that is actually true.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Type I error
2. Practice case B: Saying there is not enough evidence when a real effect exists is:
Choices: Type I error · alpha · placebo effect · Type II error
Show solution
- Warm-up: First identify exactly what the question is asking: Saying there is not enough evidence when a real effect exists is:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Type II error misses a real effect.
- It fails to reject a null that is false.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Type II error
3. Practice case C: Power is the probability of:
Choices: choosing a sample conveniently · proving the null true · detecting a real effect · making a Type I error
Show solution
- Warm-up: First identify exactly what the question is asking: Power is the probability of:
- For probability, count favorable outcomes and total outcomes carefully before writing the ratio.
- Power is the chance of rejecting a false null.
- That means detecting a real effect.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: detecting a real effect
4. Practice case D: Using a smaller significance level mainly lowers the chance of:
Choices: the population parameter · Type I error risk · sample size · all uncertainty
Show solution
- Warm-up: First identify exactly what the question is asking: Using a smaller significance level mainly lowers the chance of:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Alpha controls the false-alarm rate.
- Lower alpha makes rejecting harder.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Type I error risk
5. Practice case E: More data often improves a test by increasing:
Choices: power · undercoverage · response bias · the null hypothesis
Show solution
- Warm-up: First identify exactly what the question is asking: More data often improves a test by increasing:
- For data questions, identify what each statistic measures before calculating so the result matches the question.
- Larger samples can make real effects easier to detect.
- That raises power.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: power
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