Paired Tests
Compare before/after measurements.
Key idea
Compare before/after measurements.
In depth
When each observation in one group matches one in another (before/after, twins), compute differences and run a one-sample t-test on them. It removes between-subject variation, increasing power.
Worked example
Weights before and after a diet: differences average −2 kg with SE 0.8 → t = −2.5.
Real-world uses
- Measuring whether a fitness programme improved each person’s results before and after
Common mistake
Running a two-sample test on paired data, which wastes information.
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 Paired Tests?
Compare before/after measurements. It is a topic at the expert level in Probability & Statistics.
Where is Paired Tests used in real life?
Real-world examples: Measuring whether a fitness programme improved each person’s results before and after.
What should I learn before Paired Tests?
Make sure you are comfortable with Two-Sample Tests, the previous topic in Probability & Statistics.
What is a common mistake with Paired Tests?
Running a two-sample test on paired data, which wastes information.
How can I practise Paired Tests?
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 Paired Tests?
Move on to Chi-Square 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.