p-Values
Probability of results at least as extreme if H₀ is true.
Key idea
Probability of results at least as extreme if H₀ is true.
In depth
The p-value is the probability, assuming H₀ is true, of results at least as extreme as observed. A small p suggests the data are inconsistent with H₀. It is not the probability that H₀ is true.
Worked example
p = 0.03 means that if there were no effect, such a result would arise about 3% of the time.
Real-world uses
- Reading results in medical trials and research papers to judge the evidence against a claim
Common mistake
Reading p as the probability the null hypothesis is true.
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 p-Values?
Probability of results at least as extreme if H₀ is true. It is a topic at the expert level in Probability & Statistics.
Where is p-Values used in real life?
Real-world examples: Reading results in medical trials and research papers to judge the evidence against a claim.
What should I learn before p-Values?
Make sure you are comfortable with Hypothesis Testing Basics, the previous topic in Probability & Statistics.
What is a common mistake with p-Values?
Reading p as the probability the null hypothesis is true.
How can I practise p-Values?
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 p-Values?
Move on to Type I and Type II Errors 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.