Bootstrap

Abstract

This article provides an introduction to the bootstrap. The bootstrap provides statistical inferences—standard error and bias estimates, confidence intervals, and hypothesis tests—without assumptions such as normal distributions or equal variances. As such, bootstrap methods can be remarkably more accurate than classic inferences based on normal or t distributions. The bootstrap uses the same basic procedure regardless of the statistic being calculated, without requiring the use of application-specific formulae.

This article may provide two big surprises for many readers. The first is that the bootstrap shows that common t confidence intervals are woefully inaccurate when populations are skewed, with one-sided coverage levels off by factors of two or more, even for very large samples. The second is that the number of bootstrap samples required is much larger than generally realized.