An introduction to the bootstrap: a versatile method to make inferences by using data-driven simulations.




robust statistics, median, trimmed mean, quantiles, correlation, Monte-Carlo simulations, confidence intervals, p values, percentile bootstrap, bootstrap-t, hierarchical bootstrap


The bootstrap is a versatile technique that relies on data-driven simulations to make statistical inferences. When combined with robust estimators, the bootstrap can afford much more powerful and flexible inferences than is possible with standard approaches such as T-tests on means. In this tutorial, we use detailed illustrations of bootstrap simulations to give readers an intuition of what the bootstrap does and how it can be applied to solve many practical problems, such as building confidence intervals for many aspects of the data. In particular, we illustrate how to build confidence intervals for measures of location, including measures of central tendency, in the one-sample case, for two independent and two dependent groups. We also demonstrate how to compare correlation coefficients using the bootstrap and to perform simulations to determine if the bootstrap is fit for purpose for a particular application. Our approach is to suggest and motivate what could be done in a situation, with an understanding that various options are valid, though they may help answer different questions about a dataset. The tutorial also addresses two widespread misconceptions about the bootstrap: that it makes no assumptions about the data, and that it leads to robust inferences on its own. The tutorial focuses on detailed graphical descriptions, with data and code available online to reproduce the figures and analyses in the article (OSF:; GitHub:


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