Math
Two-sample t-test.
Definition
A two-sample t-test compares the means of two independent groups to determine whether there is a statistically significant difference between them. It is used when the population standard deviations are unknown and the samples are drawn independently.
How it works · 5 phases
Step by step.
- State H₀: μ₁ = μ₂ and the alternative hypothesis.
- Calculate the sample means and standard deviations for both groups.
- Compute the test statistic: t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂).
- Determine degrees of freedom (using the conservative or Welch method).
- Find the p-value and compare to the significance level to draw a conclusion.
Examples
Real-world.
- 1 Comparing the average test scores between students who used a study app and those who did not
- 2 Testing whether two brands of batteries have different average lifetimes
- 3 Determining if there is a difference in average height between basketball and soccer players
Key Fact
t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂)