Bootstrap Resampling Explained: How Sampling With Replacement Estimates Uncertainty

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The article explains how the bootstrap method estimates the variability of a sample mean using only one observed sample, by treating that sample as an empirical distribution. Using the small example dataset 2, 3, 4, 4, 7, it shows how drawing five records with replacement produces resamples whose means differ from the original. It stresses that the resampling unit should match the study design, such as resampling complete pairs for correlations or whole groups for clustered data. The author notes that the spread of repeated statistics can estimate standard error, and that reporting the method, seed, and number of replications is essential. The piece also warns that bootstrapping cannot recover groups missing from the original sample and may be unsuitable for extreme-value targets like maxima.

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