Abstract
The percentile bootstrap is the Swiss Army knife of statistics: It is a nonparametric method based on data-driven simulations. It can be applied to many statistical problems, as a substitute to standard parametric approaches, or in situations for which parametric methods do not exist. In this Tutorial, we cover R code to implement the percentile bootstrap to make inferences about central tendency (e.g., means and trimmed means) and spread in a one-sample example and in an example comparing two independent groups. For each example, we explain how to derive a bootstrap distribution and how to get a confidence interval and a p value from that distribution. We also demonstrate how to run a simulation to assess the behavior of the bootstrap. For some purposes, such as making inferences about the mean, the bootstrap performs poorly. But for other purposes, it is the only known method that works well over a broad range of situations. More broadly, combining the percentile bootstrap with robust estimators (i.e., estimators that are not overly sensitive to outliers) can help users gain a deeper understanding of their data than they would using conventional methods.
Highlights
The main idea behind the bootstrap is that in some situations, it is better to make inferences about a population parameter using only the data at hand, without making assumptions about underlying distributions
Without going into the details, for the purpose of this Tutorial we focus on bootstrapping as an important statistical concept and use the percentile bootstrap, the simplest form of bootstrap, for illustration
These results confirm the well-known fact that the percentile bootstrap should not be used to make inferences about the mean because it leads to inaccurate confidence intervals when distributions are skewed or outliers are present
Summary
All the figures and analyses presented in this Tutorial can be reproduced using a notebook in the R programming language (R Core Team, 2020) that we have made available on OSF (https://osf.io/dvuze/). We set up our simulation using this code: set.seed(666) # reproducible results nsim
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