Matched pairs design

A matched pairs design controls for variation between units by comparing treatments inside pairs that are alike, or on the same unit under both conditions. Because each pair serves as its own comparison, differences between individuals cancel out and the test focuses on the within-pair difference. For example, you measure each runner's time in old shoes and new shoes, then analyze the 20 time differences. The analysis is a one-sample $t$ procedure on the paired differences, using $t = \frac{\bar{x}_d}{s_d / \sqrt{n}}$, where $\bar{x}_d$ is the mean difference, $s_d$ its standard deviation, and $n$ the number of pairs.