Type I and Type II Errors
False positives and false negatives.
Key idea
False positives and false negatives.
In depth
A Type I error rejects a true H₀ (false positive, probability α). A Type II error fails to reject a false H₀ (probability β). Power = 1 − β. Lowering α raises β unless n increases.
Worked example
A smoke detector that sounds with no fire is Type I; one that stays silent in a fire is Type II.
Real-world uses
- Choosing how strict a drug safety test should be, balancing false alarms and missed problems
Common mistake
Mixing up which error is which.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Type I and Type II Errors?
False positives and false negatives. It is a topic at the expert level in Probability & Statistics.
Where is Type I and Type II Errors used in real life?
Real-world examples: Choosing how strict a drug safety test should be, balancing false alarms and missed problems.
What should I learn before Type I and Type II Errors?
Make sure you are comfortable with p-Values, the previous topic in Probability & Statistics.
What is a common mistake with Type I and Type II Errors?
Mixing up which error is which.
How can I practise Type I and Type II Errors?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Type I and Type II Errors?
Move on to z-Test next.
Related expert topics in Probability & Statistics
- Skewness and Kurtosis – Measures of asymmetry and tail heaviness.
- Residuals and R² – Error of a fit and proportion of variance explained.
- Simpson’s Paradox – A trend reverses when groups are combined.
- Law of Total Probability – Split an event over a partition.
- Bayes’ Theorem – Update beliefs with evidence.
- Medical Tests and Base Rates – Why positive results can still be probably false.