Correct decision
You kept the null hypothesis because the evidence was not strong enough to say otherwise.
AP Statistics: Type I & Type II Errors
A visual guide to false positives, false negatives, significance level, and power.
The big idea
In hypothesis testing, we make a decision using sample data even though we do not know the truth with certainty. That means there are two ways to be wrong: we can reject a null hypothesis that is actually true, or we can fail to reject a null hypothesis that is actually false.
AP Statistics expects you to connect those errors to context, use the words null hypothesis and alternative hypothesis correctly, and explain the tradeoff created by changing the significance level α.
Type I
False alarm
Type II
Missed signal
Power
1 - β
Decision table
Type I error
You found “significance” even though the null hypothesis was actually correct.
Type II error
You missed a real effect because the data were not strong enough to push you past the cutoff.
Correct decision
You detected evidence for the alternative hypothesis when a real difference was present.
Type I error
Definition: Rejecting H0 when H0 is actually true.
AP Stats wording: A false positive. You claim there is evidence of an effect, difference, or change when there really is not one.
- Probability: The probability of a Type I error is the significance level, α.
- Memory tip: Type I = “I cried wolf.”
- Example: A medical test says a healthy patient has a disease.
Type II error
Definition: Failing to reject H0 when H0 is actually false.
AP Stats wording: A false negative. A real effect exists, but your test does not detect it.
- Probability: The probability of a Type II error is called β.
- Memory tip: Type II = “I ignored a real warning.”
- Example: A medical test says a sick patient is healthy.
What happens when you change α?
Move the slider to see an illustrative tradeoff. The exact numbers depend on the test, sample size, effect size, and variability, but the overall direction is the key AP Statistics idea.
Selected significance level: 0.05
More conservative test
Easier to reject H0
Type I error rate (α)
5%
Type II error rate (β)
30%
Power (1 - β)
70%
Interpret the tradeoff
At α = 0.05, the test allows a 5% chance of a Type I error. In many fixed testing situations, that gives a moderate balance between protecting against false positives and still being able to detect real effects.
Important AP exam idea: If everything else stays the same, increasing α makes Type I errors more likely but Type II errors less likely. Decreasing α does the opposite.
Why? A larger significance level makes the rejection region bigger, so it becomes easier to reject H0. That catches more real effects, but it also creates more false alarms.
How to reduce both kinds of mistakes
You usually cannot lower both α and β just by changing the cutoff. But you can often improve the situation by increasing the sample size, reducing variability, or using a more sensitive design.
How p-values connect
The p-value is the probability, assuming H0 is true, of getting a result at least as extreme as the one observed. You reject H0 when p-value ≤ α.
When a small α makes sense
If a false positive would be especially harmful, researchers often choose a smaller significance level. For example, they may want strong evidence before claiming a new treatment works.
AP Statistics-style examples
Practice putting the errors into context using complete sentences.
- Spam filter: A Type I error happens if the filter marks a real email as spam. A Type II error happens if the filter lets actual spam into the inbox.
- School intervention: If H0 says a tutoring program does not increase scores, then a Type I error means concluding the program helps when it really does not. A Type II error means missing a program that truly helps.
- Factory quality test: If H0 says parts meet specifications, then a Type I error means wrongly flagging a good batch, while a Type II error means passing a defective batch.
Exam writing tip: Always describe the error in the context of the problem. Avoid saying only “false positive” or “false negative” without mentioning what was falsely concluded.