The bootstrap, the jackknife, and the randomization test: A sampling taxonomy

A simple sampling taxonomy is defined that shows the differences between an d relationships among the bootstrap, the jackknife, and the randomization t est. Each method has as its goal the creation of an empirical sampling dist ribution that can be used to test statistical hypotheses, estimate standard errors, and/or create confidence intervals. Distinctions between the metho ds can be made based on the sampling approach (with replacement versus with out replacement) and the sample size (replacing the whole original sample v ersus replacing a subset of the original sample). The taxonomy is useful fo r teaching the goals and purposes of resampling schemes. An extension of th e taxonomy implies other possible resampling approaches that have not previ ously been considered. Univariate and multivariate examples are presented.