The bootstrap, introduced in Efron (1979. Bootstrap methods: another look at the jackknife. The Annals of Statistics7, 1–26), is a landmark method for quantifying variability. It uses sampling with replacement with a sample size equal to that of the original data. We propose the upstrap, which samples with replacement either more or fewer samples than the original sample size. We illustrate the upstrap by solving a hard, but common, sample size calculation problem. The data and code used for the analysis in this article are available on GitHub (2018.

This work is written by US Government employees and is in the public domain in the US.