Paired t-test

Math

Definition

A hypothesis test that compares two related measurements from the same subjects to determine if there is a significant mean difference. It analyzes the differences between paired observations rather than the raw values.

How It Works

  1. Calculate the difference d for each pair of observations
  2. State hypotheses about the mean difference μ_d
  3. Check conditions: random sample, approximately normal differences
  4. Calculate t = d̄ / (s_d/√n) where d̄ is the mean of differences
  5. Find the p-value and make a conclusion

Examples

  • Comparing students' test scores before and after a tutoring program
  • Measuring blood pressure of patients before and after taking medication
  • Comparing reaction times of the same people under two different conditions
Key Fact

t = d̄ / (s_d/√n), df = n - 1, where d = difference for each pair

Related Terms

One-sample t-test Two-sample t-test T-intervals

Study This Concept

Practice paired t-test with free review games in these units:

AP Statistics Unit 7: Inference for Means