The paired bootstrap is a hypothesis-testing and confidence-interval procedure for comparing two procedures (or systems) $A$ and $B$ evaluated on the same $n$ items. Let $d_i = m(A,i) - m(B,i)$ be the per-item paired difference of a performance metric $m$, with observed mean $\bar d$. For $b = 1,\dots,B$ replicates (with $B$ typically in the thousands), draw a bootstrap index set $I^{*(b)} \subset \{1,\dots,n\}$ of size $n$ with replacement and recompute the paired statistic on the same resampled items for both systems, e.g. $\bar d^{*(b)} = \tfrac{1}{n}\sum_{i\in I^{*(b)}} d_i.$ The empirical distribution $\{\bar d^{*(b)}\}_{b=1}^{B}$ approximates the sampling distribution of the paired difference, from which a percentile confidence interval $[\bar d^{*(\alpha/2)},\bar d^{*(1-\alpha/2)}]$ is read off and a two-sided p-value can be derived (e.g., as the bootstrap probability that the difference reverses sign). Resampling item indices rather than the two systems independently preserves the pairing structure, which removes between-item variance and gives more power than an unpaired test.