Two-Sample Tests
Compare two group means.
Key idea
Compare two group means.
In depth
Compare means of two independent groups: t = (x̄₁ − x̄₂)/√(s₁²/n₁ + s₂²/n₂). Check each group’s data are roughly normal or samples are large, and that groups are independent.
Worked example
Group A mean 75, group B mean 70, SEs combined 2: t = 2.5.
Real-world uses
- Comparing average delivery times of two courier companies or two training methods
Common mistake
Using it when the observations are paired.
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 Two-Sample Tests?
Compare two group means. It is a topic at the expert level in Probability & Statistics.
Where is Two-Sample Tests used in real life?
Real-world examples: Comparing average delivery times of two courier companies or two training methods.
What should I learn before Two-Sample Tests?
Make sure you are comfortable with t-Test, the previous topic in Probability & Statistics.
What is a common mistake with Two-Sample Tests?
Using it when the observations are paired.
How can I practise Two-Sample 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 Two-Sample Tests?
Move on to Paired Tests 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.