Paired t-Test Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
hardExplain when to use a paired t-test vs. a two-sample t-test. If shoe comfort is measured on the same subjects wearing Brand A and Brand B, which test is appropriate and why?
Solution
- 1 Shoe comfort: same subjects wear both brands → measurements are paired (matched by person)
- 2 Use paired t-test: removes person-to-person variation in comfort preferences; focuses only on within-person difference between brands
- 3 If paired data treated as two independent samples: inflated variability (person-to-person differences incorrectly included), reduced power
- 4 Decision rule: if data are naturally matched (same subject, same location, twins, siblings) → paired t-test; if groups are independent → two-sample t-test
Answer
Paired t-test: same subjects wear both brands. Pairing removes individual variation and increases power.
Pairing is powerful because it controls for individual differences (some people rate all shoes higher; others lower). The paired test focuses on the within-subject comparison, eliminating this source of noise. Using a two-sample test on paired data loses this efficiency.
About Paired t-Test
A hypothesis test for the mean difference in a paired (matched) data design, where each subject provides two related measurements. The test analyzes the differences as a single sample.
Learn more about Paired t-Test →More Paired t-Test Examples
Example 1 medium
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Example 3 easyFive paired differences are: [formula]. Calculate [formula] and [formula], then set up the t-test st
Example 4 hardA paired t-test for blood pressure before and after medication: [formula] mmHg, [formula] mmHg, [for